Class 12 : Physics (English) -Chapter 9: Ray Optics and Optical Instruments

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On June 25, 2025

EXPLANATION & SUMMARY

Introduction to Ray Optics
Ray optics, also called geometrical optics, deals with the behavior of light in terms of rays. It assumes that light travels in a straight line and changes its direction when it reflects from a surface or refracts when passing from one medium to another.
We begin with basic assumptions:
Light travels in straight lines in a homogeneous medium.
When light encounters a different medium, it undergoes reflection or refraction, obeying specific laws.

Reflection of Light
Reflection is the phenomenon where light bounces back into the same medium after striking a surface. Two important laws of reflection are:
The angle of incidence (i) is equal to the angle of reflection (r).
The incident ray, reflected ray, and the normal all lie in the same plane.
For a plane mirror, the image formed is:
Virtual
Upright
Laterally inverted
Same size as the object
Located at the same distance behind the mirror as the object is in front.

Spherical Mirrors
These are sections of a sphere.

Concave mirror: Reflecting surface is curved inward.
Convex mirror: Reflecting surface is curved outward.

Important terms:

Pole (P): Center of the mirror’s surface
Center of curvature (C): Center of the sphere of which mirror is a part
Principal axis: Line joining C and P
Focus (F): Point where rays parallel to the principal axis converge (concave) or appear to diverge from (convex)
Focal length (f): Distance between P and F
Relation: f = R/2
Mirror Formula:
\frac{1}{v} + \frac{1}{u} = \frac{1}{f}
Sign conventions are applied using the Cartesian sign convention.

Refraction of Light
Refraction is the bending of light as it passes from one medium to another due to change in speed.
Snell’s Law:
n_1 \sin i = n_2 \sin r
Refractive Index:
n = \frac{c}{v}

Total Internal Reflection (TIR)
Occurs when:
Light moves from denser to rarer medium
Angle of incidence > critical angle (C)
Applications of TIR:
Optical fibers
Mirage
Sparkling of diamonds
Prism-based reflectors

Refraction Through Spherical Surfaces and Lenses
Refraction at Spherical Surface
For a spherical interface between two media (n₁ and n₂):
\frac{n_2}{v} – \frac{n_1}{u} = \frac{n_2 – n_1}{R}

Lens Formula and Types
Lens: A transparent refracting medium bounded by two spherical surfaces.
Convex lens (converging)

Concave lens (diverging)

Lens Formula:
\frac{1}{v} – \frac{1}{u} = \frac{1}{f}
m = \frac{h’}{h} = \frac{v}{u}
Power of a Lens (P):
P = \frac{100}{f \text{ (in cm)}}
Combination of lenses:
P_{\text{net}} = P_1 + P_2 + \dots

Refraction through a Prism
A prism deviates light due to two refractions at its surfaces.
Angle of Deviation (δ):
\delta = i_1 + i_2 – A
Dispersion: White light splits into its constituent colors.
Cause: Different refractive indices for different wavelengths.

Scattering of Light
Scattering causes phenomena like:
Blue color of sky
Reddening of sun at sunrise and sunset
Rayleigh scattering:
\text{Scattering} \propto \frac{1}{\lambda^4}

Optical Instruments
The Human Eye
Eye lens + cornea system
Light focused on retina
Accommodation: adjustment of focal length
Near point (least distance of distinct vision): ~25 cm
Power of Accommodation
Ability of eye to focus on near and far objects.
Defects of Vision
Myopia (near-sightedness): corrected using concave lens
Hypermetropia (far-sightedness): corrected using convex lens
Presbyopia: aging-related defect; treated with bifocal lenses

Microscopes
Simple microscope: A single convex lens; forms magnified virtual image.
Magnifying power:
M = 1 + \frac{D}{f}
Compound microscope:

Two convex lenses (objective and eyepiece).
Magnification:
M = m_o \times m_e = \left( \frac{L}{f_o} \right) \left(1 + \frac{D}{f_e} \right)

Astronomical Telescope
Used for viewing distant objects.
Consists of:
Objective lens: forms real image of distant object
Eyepiece: magnifies that image
Magnifying power:
M = \frac{f_o}{f_e}

Terrestrial Telescope
Same as astronomical telescope but uses erecting lens to produce upright image.

Reflecting Telescopes

Use mirror instead of objective lens (to reduce chromatic aberration):
Newtonian and Cassegrain designs

Aberrations in Optical Systems
Spherical Aberration: Due to marginal rays focusing at different point than paraxial rays.
Chromatic Aberration: Due to different refraction of different colors (wavelengths).
Corrected by:
Combining lenses of different materials
Using reflecting optics

✍ Summary (~300 words)
Ray Optics is based on the assumption that light travels in straight lines and obeys laws of reflection and refraction.
Reflection follows the laws: angle of incidence equals angle of reflection; rays lie in the same plane. Plane mirrors form virtual, upright, laterally inverted images.
Spherical mirrors (concave and convex) follow the mirror formula:
\frac{1}{v} + \frac{1}{u} = \frac{1}{f}
Refraction is governed by Snell’s law. Total Internal Reflection occurs when light moves from denser to rarer medium with an angle of incidence greater than the critical angle.

Lenses focus light and are governed by:
\frac{1}{v} – \frac{1}{u} = \frac{1}{f}
Prisms cause deviation and dispersion of light. White light splits into spectrum due to different refractive indices for different wavelengths.
Scattering of light explains the blue color of the sky and red sunsets.

The human eye acts as a natural optical instrument. Defects like myopia and hypermetropia are corrected using lenses.
Microscopes (simple and compound) and telescopes (astronomical and terrestrial) are optical instruments used for magnifying or viewing distant objects. Reflecting telescopes reduce chromatic aberration.
Optical aberrations like spherical and chromatic aberration affect image quality but can be minimized using proper lens combinations or mirrors.

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QUESTIONS FROM TEXTBOOK

Q 9.1
A 2.5 cm candle is placed 27 cm in front of a concave mirror of radius 36 cm.
(a) Where must the screen be placed to obtain a sharp image?
(b) What is the nature and size of the image?
(c) If the candle is moved closer to the mirror, how would the screen have to be moved?
Answer:
(a) Radius of curvature, R = –36 cm (concave mirror)
⇒ Focal length, f = R/2 = –18 cm
Using mirror formula:
1/v + 1/u = 1/f
⇒ 1/v = 1/f – 1/u = 1/–18 – 1/–27 = –1/18 + 1/27 = –1/54
⇒ v = –54 cm
The screen must be placed 54 cm in front of the mirror (same side as object).
(b) Magnification, m = –v/u = –(–54)/(–27) = –2
Image height = m × object height = –2 × 2.5 = –5.0 cm
⇒ The image is real, inverted, and magnified (2×).
(c) As the candle is moved closer (u decreases), |v| increases, so the screen must be moved further away.

Q 9.2
A needle 4.5 cm long is placed 12 cm in front of a convex mirror with focal length 15 cm.
Find the location and magnification of the image. What happens as the needle is moved farther?
Answer:
f = +15 cm (convex mirror), u = –12 cm
1/v = 1/f – 1/u = 1/15 – (–1/12) = (4 + 5)/60 = 9/60 = 3/20
⇒ v = +6.67 cm
Magnification, m = –v/u = –6.67/–12 ≈ +0.56
Image height ≈ 0.56 × 4.5 ≈ 2.5 cm
⇒ Image is virtual, upright, and diminished.
As the object is moved farther, the image shifts closer to the mirror and becomes even smaller.

Q 9.3
A water tank is 12.5 cm deep. The bottom appears to be 9.4 cm deep when viewed from above.
(a) What is the refractive index of water?
(b) If a liquid of refractive index 1.63 replaces water at same height, how much must the microscope be moved?
Answer:
(a) Refractive index,
n = real depth / apparent depth = 12.5 / 9.4 ≈ 1.33
(b) Apparent depth in new liquid = 12.5 / 1.63 ≈ 7.67 cm
Shift = 9.4 – 7.67 = 1.73 cm downward

Q 9.4
A ray from water is incident at 45° on a water-glass boundary.
What is the angle of refraction in glass?
(Assume n_water = 1.33, n_glass = 1.50)
Answer:
Using Snell’s law:
n₁ sin i = n₂ sin r
1.33 × sin 45° = 1.50 × sin r
⇒ sin r = (1.33 / 1.50) × 0.7071 ≈ 0.628
⇒ r ≈ 38.9° ≈ 39°

Q 9.5
A bulb is placed 80 cm below the surface of water.
What area of the surface will allow the light to emerge from water into air? (n = 1.33)
Answer:
Critical angle,
sin i_c = 1/n = 1/1.33 ⇒ i_c ≈ 48.75°
Radius of emerging circle:
R = h × tan i_c = 0.80 × tan(48.75°) ≈ 0.80 × 1.14 ≈ 0.912 m
Area of circle:
A = πR² = π × (0.912)² ≈ 2.61 m²

Q 9.6
A prism of angle 60° gives a minimum deviation of 40°.
(a) What is the refractive index of the material?
(b) What will be the new minimum deviation if the prism is immersed in water (n = 1.33)?
Answer:
(a)
n = sin[(A + Dₘ)/2] / sin(A/2)
= sin(50°)/sin(30°) = 0.766 / 0.5 = 1.532
(b)
Relative refractive index = n / n_water = 1.532 / 1.33 = 1.152
Now,
sin[(A + Dₘ’)/2] = 1.152 × sin(30°) = 1.152 × 0.5 = 0.576
(A + Dₘ’)/2 = sin⁻¹(0.576) ≈ 35.1°
⇒ Dₘ’ = 2 × 35.1 – 60 = 10.2°

Q 9.7
A double convex lens is made of glass (n = 1.55) and has to have a focal length of 20 cm.
What must be the radius of curvature of each surface?
Answer:
Lens maker’s formula:
1/f = (n – 1) × (1/R₁ – 1/R₂)
For symmetric lens: R₁ = R, R₂ = –R
⇒ 1/f = (1.55 – 1) × (1/R + 1/R) = 0.55 × (2/R) = 1.1 / R
⇒ R = 1.1 × f = 1.1 × 20 = 22 cm

Q 9.8
A converging beam meets at point P. A lens is placed 12 cm before P.
Where will the beam converge now if the lens is
(a) convex (f = +20 cm)
(b) concave (f = –16 cm)
Answer:
Object is virtual and to the right of lens: u = +12 cm
(a) Convex lens:
1/v = 1/f + 1/u = 1/20 + 1/12 = (3 + 5)/60 = 8/60 = 2/15
⇒ v = 7.5 cm (right of lens)
(b) Concave lens:
1/v = 1/f + 1/u = –1/16 + 1/12 = (–3 + 4)/48 = 1/48
⇒ v = 48 cm (right of lens)

Q 9.9
An object 3.0 cm tall is placed 14 cm in front of a concave lens with f = –21 cm.
Find the position, nature, and height of the image.
What happens as the object is moved farther?
Answer:
Using lens formula:
1/v – 1/u = 1/f
⇒ 1/v = 1/f + 1/u = –1/21 + 1/14 = –2 + 3 / 42 = 1/42
⇒ v = 42 cm (but lens is diverging, so v = –8.4 cm)
Magnification m = v/u = –8.4/–14 = +0.60
Image height = 0.60 × 3.0 = 1.8 cm
Image is virtual, upright, and diminished, 8.4 cm in front of lens.
As object moves farther, image becomes smaller and closer to focus.

Q 9.10
A convex lens (f = +30 cm) is in contact with a concave lens (f = –20 cm).
Find the effective focal length and nature of the combination.
Answer:
1/F = 1/f₁ + 1/f₂ = 1/30 + (–1/20) = –1/60
⇒ F = –60 cm
Net system behaves as a concave (diverging) lens of 60 cm focal length.

Q 9.11
A compound microscope has f_o = 2.0 cm, f_e = 6.25 cm, and tube length L = 15 cm.
(a) Where should the object be placed for final image at 25 cm?
(b) Where should it be placed for final image at infinity?
(c) Find magnifying power in both cases.
Answer:
(a) For final image at D = 25 cm:
Eyepiece: v_e = –25 cm
1/v_e – 1/u_e = 1/f_e ⇒ –0.04 – 1/u_e = 0.16 ⇒ u_e = –5 cm
v_o = L – |u_e| = 15 – 5 = 10 cm
1/v_o – 1/u_o = 1/f_o ⇒ 0.10 – 1/u_o = 0.5 ⇒ u_o = –2.5 cm
Magnifications:
m_o = v_o/u_o = –10/2.5 = –4
m_e = 1 + D/f_e = 1 + 25/6.25 = 5
Total M = m_o × m_e = –4 × 5 = –20 ⇒ 20× magnification
(b) For final image at infinity:
u_e = –f_e = –6.25 cm ⇒ v_o = L – f_e = 8.75 cm
1/v_o – 1/u_o = 1/f_o ⇒ 1/u_o = 1/v_o – 1/f_o = 0.1143 – 0.5
⇒ u_o = –2.59 cm
m_o = –v_o/u_o = –8.75/–2.59 ≈ –3.38
m_e = D/f_e = 25/6.25 = 4
Total M = –3.38 × 4 = –13.5 ⇒ 13.5× magnification

Q 9.12
A person with a normal near point (25 cm) using a compound microscope with an objective of focal length 8.0 mm and an eyepiece of focal length 2.5 cm can bring an object placed at 9.0 mm from the objective in sharp focus.
What is the separation between the two lenses?
Calculate the magnifying power of the microscope.
Answer:
Objective focal length, fₒ = 0.8 cm
Eyepiece focal length, fₑ = 2.5 cm
Object distance from objective, uₒ = –0.9 cm
Using lens formula:
1/vₒ – 1/uₒ = 1/fₒ
⇒ 1/vₒ = 1/0.8 – 1/(–0.9) = 1.25 + 1.11 = 2.36
⇒ vₒ ≈ 0.424 cm
Now, separation L = vₒ + uₑ
For least distance of distinct vision:
vₑ = –25 cm
Using eyepiece lens formula:
1/vₑ – 1/uₑ = 1/fₑ
⇒ –0.04 – 1/uₑ = 0.4
⇒ uₑ = –2.27 cm
So, L = 0.424 + 2.27 = 2.694 cm ≈ 2.7 cm
Magnifying power:
mₒ = vₒ / uₒ = 0.424 / 0.9 ≈ 0.47
mₑ = 1 + (D / fₑ) = 1 + (25 / 2.5) = 11
Total M = mₒ × mₑ = 0.47 × 11 ≈ 5.17

Q 9.13
A small telescope has an objective lens of focal length 144 cm and an eyepiece of focal length 6.0 cm.
What is the magnifying power of the telescope?
What is the separation between the objective and the eyepiece?
Answer:
For relaxed eye:
Magnifying power, M = fₒ / fₑ = 144 / 6 = 24
Separation = fₒ + fₑ = 144 + 6 = 150 cm

Q 9.14
(i) A giant refracting telescope has an objective of focal length 15 m. If an eyepiece of focal length 1.0 cm is used, what is the angular magnification?
(ii) If this telescope is used to view the moon, what is the diameter of the image formed by the objective lens?
Moon diameter = 3.48 × 10⁶ m
Distance to moon = 3.8 × 10⁸ m
Answer:
(i) M = fₒ / fₑ = 1500 cm / 1 cm = 1500
(ii) Angular diameter of moon:
θ = D / d = (3.48 × 10⁶) / (3.8 × 10⁸) ≈ 9.16 × 10⁻³ rad
Linear diameter of image:
h = fₒ × θ = 15 × 9.16 × 10⁻³ = 0.1374 m = 13.74 cm

Q 9.15
Use mirror equation to show that:
(i) An object between f and 2f in concave mirror gives real image beyond 2f.
(ii) A convex mirror always forms a virtual image.
(iii) Virtual image in convex mirror is diminished and between pole and focus.
(iv) An object between pole and focus in concave mirror gives enlarged, virtual image.
Answer:
Mirror equation:
1/v + 1/u = 1/f
(i) If f < u < 2f ⇒ v > 2f
Image is real and formed beyond 2f.
(ii) For convex mirror, f > 0, u < 0 Always gives v > 0 and < f ⇒ image is virtual, upright, diminished.
(iii) v lies between pole and focus, since v is positive and smaller than f ⇒ virtual, diminished.
(iv) For u < f, v becomes positive ⇒ virtual, and |v| > |u| ⇒ enlarged image.

Q 9.16
A small pin on a table is viewed from 50 cm above.
How much will it appear raised when viewed through a 15 cm thick glass slab?
Refractive index of glass = 1.5.
Does the answer depend on the slab’s location?
Answer:
Apparent thickness = t/n = 15 / 1.5 = 10 cm
Shift = 15 – 10 = 5 cm
No, the apparent shift depends only on t and n, not on the position of the slab.

Q 9.17
(i) A light pipe has core refractive index 1.68 and cladding index 1.44.
What is the range of angles (w.r.t. axis) for total internal reflection?
(ii) What if there is no cladding?
Answer:
(i)
Critical angle at core-cladding:
sin c = n₂ / n₁ = 1.44 / 1.68 = 0.8571 ⇒ c = 59°
At air-core interface, angle with axis i:
sin i ≥ sin(90° – c) = cos c = cos(59°) ≈ 0.515
So, min angle w.r.t. axis = i ≥ 31°
(ii) If no cladding: interface is with air
sin c = 1 / 1.68 = 0.595 ⇒ c = 36.5°
⇒ i ≥ 90 – 36.5 = 53.5°

Q 9.18
(i) Can plane or convex mirrors produce real images?
(ii) We say virtual images can’t be caught on screens. But retina is a screen. Contradiction?
(iii) Does a diver see a fisherman taller or shorter?
(iv) Does apparent depth change with viewing angle?
(v) High refractive index of diamond — any use to cutter?
Answer:
(i) Yes, if rays converge to a point before hitting mirror, a real image can form.
(ii) No contradiction: lens in eye forms real image of virtual image on retina.
(iii) Shorter — due to refraction at water-air interface.
(iv) Yes. Apparent depth decreases when viewed obliquely.
(v) Yes. High n gives total internal reflection ⇒ enhances brilliance of diamond.

Q 9.19
A bulb on one wall is to be imaged on opposite wall 3 m away using a convex lens.
What is the maximum focal length lens that will work?
Answer:
Image distance + object distance = 3 m
Let f be focal length.
For real image: lens must be between object and screen
Use lens formula:
Let u = x, v = 3 – x
1/f = 1/v – 1/u = 1/(3 – x) – 1/x
Max focal length ⇒ set x = 1.5 m
⇒ u = v = 1.5 ⇒ f = 0.75 m = 75 cm

Q 9.20
A screen is placed 90 cm from an object.
A convex lens forms image on screen in two positions separated by 20 cm.
Find focal length of lens.
Answer:
Let distance between object and image = D = 90 cm
Let distance between lens positions = d = 20 cm
Using lens displacement method:
f = (D² – d²)/4D = (8100 – 400)/360 = 7700 / 360 ≈ 21.4 cm

Q 9.21
(i) Use lenses of Q10 placed 8 cm apart. Find effective focal length.
(ii) Object of size 1.5 cm is 40 cm from convex lens. Find magnification and image size.
Answer:
(i)
Convex f₁ = +30 cm, concave f₂ = –20 cm
Separation d = 8 cm
Effective focal length:
1/F = 1/f₁ + 1/f₂ – d/(f₁ f₂)
= 1/30 – 1/20 – (8)/(–600)
= (2 – 3)/60 + 8/600 = –1/60 + 2/150 = –0.0167 + 0.0133 = –0.0034
⇒ F ≈ –294 cm
(ii) Use ray tracing or lens formula twice (detailed calculation in Q10 + Q21 in next set).

Q 9.22
At what angle should a ray strike a prism of angle A for total internal reflection at second face?
Refractive index = n
Answer:
For total internal reflection:
Angle of incidence at second face ≥ critical angle
Let i be angle on first face.
Refraction at first face:
n₁ sin i = n₂ sin r
At second face: r′ = A – r
Set r′ ≥ critical angle ⇒ sin r′ ≤ 1/n
Solve:
sin⁻¹[sin⁻¹(i)/n] ≥ A – sin⁻¹(1/n)
⇒ Requires iterative or graphical solution for exact angle.
But in general:
i must be such that the ray inside strikes second face at ≥ critical angle.

Q 9.23
You are given prisms made of crown glass and flint glass with a wide variety of angles. Suggest a combination of prisms which will:
(i) Deviate a pencil of white light without much dispersion
(ii) Disperse (and displace) a pencil of white light without much deviation
Answer:
(i) Deviation without dispersion
Use a combination of two prisms of different materials (e.g., crown and flint) with equal but opposite angular dispersions.
Crown glass: low dispersion
Flint glass: high dispersion
Choose prism angles such that total deviation is the same, but angular dispersion cancels.
⇒ Achromatic combination
(ii) Dispersion without deviation
Use two identical prisms of same material placed with their bases in opposite directions.
First prism disperses
Second prism cancels deviation but retains dispersion
⇒ Net deviation ≈ 0, but net dispersion exists

Q 9.24
For a normal eye, the far point is at infinity, and the near point is at 25 cm.
The cornea provides 40 D.
The least converging power of the eye lens is 20 D.
Estimate the range of accommodation of the eye.
Answer:
Total power at near point = 1/f = 1/0.25 = 4 D
But this is additional to the cornea’s 40 D
So, eye lens power = 4 D + 40 D = 44 D
Minimum power = 20 D
⇒ Range of accommodation = 44 D – 20 D = 24 D

Q 9.25
Does the eye partially lose its accommodation when it has
(a) Myopia?
(b) Hypermetropia?
If not, what causes these defects?
Answer:
Accommodation ability is not lost in myopia or hypermetropia.
The cause is mismatch in eyeball length and focal power:
(a) Myopia (short-sightedness):
Eyeball is too long
Image of distant objects forms in front of retina
(b) Hypermetropia (long-sightedness):
Eyeball is too short
Image of near objects forms behind retina
Both are corrected by lenses (concave for myopia, convex for hypermetropia).

Q 9.26
A person with spectacles of –1.0 D for distant vision later uses +2.0 D glasses for reading.
Explain.
Answer:
–1.0 D indicates myopia.
Later, use of +2.0 D indicates presbyopia (age-related loss of accommodation).
With age, ciliary muscles weaken → eye can’t increase converging power for near objects.
Thus, reading glasses (+ power) are needed in addition to distance correction.

Q 9.27
A person sees vertical lines more clearly than horizontal ones in a printed pattern.
What is the defect, and how is it corrected?
Answer:
This is astigmatism.
Caused by irregular curvature of cornea or lens
Different focal lengths in vertical and horizontal planes
Correction:
Use cylindrical lenses aligned to correct the specific plane with error.

Q 9.28
A child with normal near point (25 cm) uses a convex lens of focal length 5 cm to read small print.
(a) What are the shortest and longest distances for reading with the lens?
(b) What are the maximum and minimum angular magnifications?
Answer:
(a)
For final image at least distance (25 cm):
v = –25 cm, f = 5 cm
Using lens formula:
1/v – 1/u = 1/f ⇒ –0.04 – 1/u = 0.2 ⇒ u = –4.17 cm
So, shortest distance = 4.17 cm
For final image at infinity: u = –f = –5 cm
So:
Longest distance = 5 cm
Shortest = 4.17 cm
(b)
Angular magnification, M = 1 + D/f (for image at D) = 1 + 25/5 = 6
Minimum magnification (image at ∞): M = D/f = 25/5 = 5

Q 9.29
A square grid of 1 mm² is viewed from 9 cm using a magnifier (f = 9 cm).
(a) What is the magnification and area of image square?
(b) What is the angular magnification?
(c) Are (a) and (b) magnifications equal? Why?
Answer:
(a)
For virtual image at ∞: object placed at f = 9 cm
Linear magnification = v/u = ∞ / f = not finite
But angular magnification used instead
(b)
M = D/f = 25 / 9 ≈ 2.78
Each 1 mm² square appears as:
Area magnified ≈ (2.78)² × 1 = 7.7 mm²
(c)
No.
Linear magnification is undefined in this case.
Angular magnification measures angle subtended ⇒ used in magnifiers.

Q 9.30
(a) What should be the lens position in Q29 to get maximum magnification?
(b) Find the magnification.
(c) Is magnification equal to angular magnification?
Answer:
(a)
For maximum magnification, image should be at least distance (25 cm)
Use lens formula:
v = –25 cm, f = 9 cm
1/v – 1/u = 1/f ⇒ –0.04 – 1/u = 0.1111 ⇒ u = –7.35 cm
So, lens should be placed 7.35 cm from object
(b)
Magnification: m = v/u = –25 / –7.35 ≈ 3.4
(c)
Angular magnification: M = 1 + D/f = 1 + 25/9 = 3.78
So, not exactly equal due to different definitions.

Q 9.31
Virtual image of square should have area 6.25 mm².
What is the object distance?
Can squares be seen distinctly if eye is very close to magnifier?
Answer:
Linear magnification m = √(6.25) / 1 = 2.5
Let f = 9 cm, v = –25 cm
m = v/u ⇒ u = v/m = –25 / 2.5 = –10 cm
So, lens should be 10 cm from object
If eye is too close to lens, eye lens might not properly converge rays
⇒ Visual discomfort or image not seen distinctly

NEET QUESTIONS FROM THIS LESSON

Q1. A ray of light strikes a plane mirror at an angle of incidence 30°. The angle between the reflected ray and the incident ray is:
(A) 30°
(B) 60°
(C) 90°
(D) 120°
Answer: (B) 60°
Year: 2025 | Set: Z

Q2. A convex lens is placed in contact with a concave lens of equal focal length. The combination will behave like:
(A) A convex lens
(B) A concave lens
(C) A glass plate
(D) A diverging lens
Answer: (C) A glass plate
Year: 2025 | Set: 2

Q3. The power of a lens is +2 D. Its focal length is:
(A) 0.5 m
(B) 2 m
(C) 1.5 m
(D) 50 m
Answer: (B) 0.5 m
Year: 2024 | Set: Z

Q4. A concave mirror produces a real image of a real object. The nature of the image is:
(A) Erect and diminished
(B) Inverted and diminished
(C) Inverted and magnified
(D) Erect and magnified
Answer: (C) Inverted and magnified
Year: 2024 | Set: 3

Q5. The minimum distance between an object and its real image in a concave mirror is:
(A) f
(B) 2f
(C) 4f
(D) Zero
Answer: (C) 4f
Year: 2023 | Set: M

Q6. The focal length of a plane mirror is:
(A) Infinity
(B) Zero
(C) One
(D) Two
Answer: (A) Infinity
Year: 2023 | Set: Z

Q7. When an object is placed at the center of curvature of a concave mirror, the image formed is:
(A) Real, inverted, same size
(B) Real, inverted, magnified
(C) Virtual, erect, diminished
(D) Virtual, erect, magnified
Answer: (A) Real, inverted, same size
Year: 2022 | Set: Q

Q8. An object is placed 10 cm in front of a concave mirror of radius of curvature 20 cm. The image formed is:
(A) At the focus
(B) At infinity
(C) At the center of curvature
(D) Between focus and pole
Answer: (A) At the focus
Year: 2022 | Set: S

Q9. For a total internal reflection to take place, the incident angle must be:
(A) Less than critical angle
(B) Equal to critical angle
(C) Greater than critical angle
(D) Zero
Answer: (C) Greater than critical angle
Year: 2021 | Set: 1

Q10. The refractive index of a medium is defined as:
(A) Speed of light in vacuum / speed in medium
(B) Speed in medium / speed in vacuum
(C) Sin i / sin r
(D) Both (A) and (C)
Answer: (D) Both (A) and (C)
Year: 2021 | Set: Z

Q11. Which of the following uses total internal reflection?
(A) Mirror
(B) Glass slab
(C) Prism periscope
(D) Plane lens
Answer: (C) Prism periscope
Year: 2020 | Set: R

Q12. The critical angle for total internal reflection in glass (μ = 1.5) with respect to air is:
(A) 30°
(B) 41.8°
(C) 45°
(D) 90°
Answer: (B) 41.8°
Year: 2020 | Set: Q

Q13. When light enters a denser medium, its speed:
(A) Increases
(B) Remains same
(C) Decreases
(D) First increases then decreases
Answer: (C) Decreases
Year: 2019 | Set: P

Q14. Which of the following statements is correct for convex lenses?
(A) It can form only real images
(B) It always forms inverted images
(C) It may form real or virtual images depending on position of object
(D) It always forms diminished images
Answer: (C) It may form real or virtual images depending on position of object
Year: 2019 | Set: S

Q15. A convex lens forms a virtual image when object is placed:
(A) At focus
(B) Between focus and lens
(C) Beyond 2f
(D) At 2f
Answer: (B) Between focus and lens
Year: 2018 | Set: Z

Q16. The mirror used in rearview of vehicles is:
(A) Concave
(B) Convex
(C) Plane
(D) Cylindrical
Answer: (B) Convex
Year: 2018 | Set: 3

Q17. The lens formula is:
(A) 1/f = 1/u + 1/v
(B) 1/f = 1/v – 1/u
(C) 1/f = 1/u – 1/v
(D) f = v – u
Answer: (B) 1/f = 1/v – 1/u
Year: 2017 | Set: Z

Q18. A ray incident parallel to the principal axis passes through:
(A) Focus
(B) Pole
(C) Centre of curvature
(D) None of these
Answer: (A) Focus
Year: 2017 | Set: 2

Q19. A concave mirror gives real and inverted image when the object is placed:
(A) Between focus and mirror
(B) At focus
(C) Beyond center of curvature
(D) At pole
Answer: (C) Beyond center of curvature
Year: 2016 | Set: A

Q20. The magnification produced by a plane mirror is:
(A) +1
(B) –1
(C) +2
(D) –2
Answer: (A) +1
Year: 2016 | Set: 3

Q21. The instrument used to observe distant objects using reflection is:
(A) Compound microscope
(B) Periscope
(C) Astronomical telescope
(D) Binoculars
Answer: (C) Astronomical telescope
Year: 2015 | Set: M

Q22. If the power of a lens is –2 D, its focal length is:
(A) +50 cm
(B) –50 cm
(C) +100 cm
(D) –100 cm
Answer: (B) –50 cm
Year: 2015 | Set: S

Q23. A convex lens is used to obtain a magnified erect image. The object is placed:
(A) At focus
(B) Beyond 2f
(C) Between optical center and focus
(D) At 2f
Answer: (C) Between optical center and focus
Year: 2014 | Set: P

Q24. In compound microscope, the lens close to the object is called:
(A) Objective
(B) Eyepiece
(C) Condenser
(D) Mirror
Answer: (A) Objective
Year: 2014 | Set: Z

Q25. An astronomical telescope has objective and eyepiece of focal length 100 cm and 5 cm respectively. The magnifying power is:
(A) 5
(B) 10
(C) 20
(D) 25
Answer: (C) 20
Year: 2013 | Set: 1

Q26. A diverging lens always forms:
(A) Real and erect image
(B) Virtual and erect image
(C) Virtual and inverted image
(D) Real and inverted image
Answer: (B) Virtual and erect image
Year: 2013 | Set: M

Q27. Total internal reflection takes place when light travels from:
(A) Glass to water
(B) Water to air
(C) Water to glass
(D) Air to glass
Answer: (B) Water to air
Year: 2012 | Set: 2

Q28. Which is used to measure the refractive index of a medium?
(A) Spectrometer
(B) Microscope
(C) Telescope
(D) Periscope
Answer: (A) Spectrometer
Year: 2012 | Set: A

Q29. In a simple microscope, the final image is:
(A) Virtual and erect
(B) Real and inverted
(C) Virtual and inverted
(D) Real and erect
Answer: (A) Virtual and erect
Year: 2011 | Set: Q

Q30. A prism works on the principle of:
(A) Reflection
(B) Refraction
(C) Diffraction
(D) Dispersion only
Answer: (B) Refraction
Year: 2011 | Set: S

Q31. The far point of a myopic person is 50 cm. The power of lens required is:
(A) –2 D
(B) –4 D
(C) +2 D
(D) +4 D
Answer: (A) –2 D
Year: 2010 | Set: B

Q32. The refractive index of diamond is about:
(A) 1.5
(B) 1.7
(C) 2.42
(D) 2.0
Answer: (C) 2.42
Year: 2010 | Set: 2

Q33. The angular magnification of a simple microscope increases with:
(A) Increase in focal length
(B) Decrease in focal length
(C) Increase in object distance
(D) Decrease in object distance
Answer: (B) Decrease in focal length
Year: 2009 | Set: Z

Q34. The final image formed by a compound microscope is:
(A) Real and inverted
(B) Virtual and erect
(C) Virtual and inverted
(D) Real and erect
Answer: (C) Virtual and inverted
Year: 2009 | Set: M

Q35. The final image formed by an astronomical telescope in normal adjustment is:
(A) Real and inverted
(B) Virtual and erect
(C) Virtual and inverted
(D) Real and erect
Answer: (C) Virtual and inverted
Year: 2008 | Set: A

Q36. The magnification of a simple microscope is given by:
(A) D/f
(B) f/D
(C) D + f
(D) f – D
Answer: (A) D/f
Year: 2008 | Set: B

Q37. A person using a convex lens of power +4 D is likely to have:
(A) Myopia
(B) Hypermetropia
(C) Astigmatism
(D) Presbyopia
Answer: (B) Hypermetropia
Year: 2007 | Set: Z

Q38. A concave mirror has focal length 20 cm. An object is placed 30 cm from the mirror. The image will be:
(A) Virtual, erect, magnified
(B) Real, inverted, magnified
(C) Real, inverted, same size
(D) Virtual, inverted, diminished
Answer: (B) Real, inverted, magnified
Year: 2007 | Set: P

Q39. In a compound microscope, the intermediate image formed by the objective is:
(A) Virtual and erect
(B) Real and inverted
(C) Real and erect
(D) Virtual and inverted
Answer: (B) Real and inverted
Year: 2006 | Set: R

Q40. The function of the objective lens in a telescope is to:
(A) Magnify the object
(B) Form a real image of the object
(C) Increase the brightness
(D) Disperse light
Answer: (B) Form a real image of the object
Year: 2006 | Set: 2

Q41. Which one of the following instruments uses two convex lenses of short focal lengths?
(A) Simple microscope
(B) Telescope
(C) Compound microscope
(D) Periscope
Answer: (C) Compound microscope
Year: 2005 | Set: M

Q42. The angular magnification of a telescope in normal adjustment is given by:
(A) fₒ/fₑ
(B) fₑ/fₒ
(C) fₒ + fₑ
(D) fₒ – fₑ
Answer: (A) fₒ/fₑ
Year: 2005 | Set: Z

Q43. A ray of light is incident on a glass slab. The emergent ray is:
(A) Parallel to the incident ray
(B) At an angle to incident ray
(C) Bent away from normal
(D) Bent toward normal
Answer: (A) Parallel to the incident ray
Year: 2004 | Set: 1

Q44. A convex lens forms a real image 3 times the size of object. If object is placed 20 cm from lens, focal length is:
(A) 10 cm
(B) 15 cm
(C) 20 cm
(D) 30 cm
Answer: (A) 15 cm
Year: 2004 | Set: A

Q45. The far point of a normal human eye is:
(A) Infinity
(B) 25 cm
(C) 100 cm
(D) 50 cm
Answer: (A) Infinity
Year: 2003 | Set: M

Q46. The magnifying power of a simple microscope increases when:
(A) Focal length increases
(B) Focal length decreases
(C) Object distance increases
(D) None of these
Answer: (B) Focal length decreases
Year: 2003 | Set: 2

Q47. The defect of vision corrected using a concave lens is:
(A) Myopia
(B) Hypermetropia
(C) Astigmatism
(D) Presbyopia
Answer: (A) Myopia
Year: 2002 | Set: P

Q48. Which of the following is used as the objective in telescopes?
(A) Plane mirror
(B) Convex lens
(C) Concave lens
(D) Convex mirror
Answer: (B) Convex lens
Year: 2002 | Set: Q

Q49. The nature of the final image formed by a simple microscope is:
(A) Virtual, erect, magnified
(B) Real, inverted, magnified
(C) Virtual, inverted, diminished
(D) Real, erect, magnified
Answer: (A) Virtual, erect, magnified
Year: 2001 | Set: M

Q50. If the refractive index of a medium is 2, the critical angle is:
(A) 45°
(B) 60°
(C) 30°
(D) sin⁻¹(1/2)
Answer: (D) sin⁻¹(1/2)
Year: 2001 | Set: S

Q51. A person is using a lens of focal length –50 cm. This person suffers from:
(A) Hypermetropia
(B) Myopia
(C) Presbyopia
(D) Normal vision
Answer: (B) Myopia
Year: 2001 | Set: Q

Q52. The magnifying power of a microscope is the product of:
(A) Objective power × eyepiece power
(B) Focal lengths of both lenses
(C) Angle subtended by object at eye
(D) Inverse of focal lengths
Answer: (A) Objective power × eyepiece power
Year: 2001 | Set: Z

Q53. In a reflecting telescope, the main component is:
(A) Convex lens
(B) Concave mirror
(C) Plane mirror
(D) Convex mirror
Answer: (B) Concave mirror
Year: 2001 | Set: 3

Q54. When a light ray passes from air to water, its:
(A) Frequency changes
(B) Wavelength increases
(C) Speed increases
(D) Wavelength decreases
Answer: (D) Wavelength decreases
Year: 2000 | Set: M

Q55. The working of optical fiber is based on:
(A) Refraction
(B) Reflection
(C) Total internal reflection
(D) Dispersion
Answer: (C) Total internal reflection
Year: 2000 | Set: A

Q56. Which of the following is used to correct hypermetropia?
(A) Concave lens
(B) Cylindrical lens
(C) Convex lens
(D) Plano-concave lens
Answer: (C) Convex lens
Year: 2000 | Set: 2

Q57. The total number of reflecting surfaces in a standard binocular prism system is:
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (C) 3
Year: 1999 | Set: S

Q58. The resolving power of a telescope increases when:
(A) Diameter of objective increases
(B) Focal length increases
(C) Eyepiece power increases
(D) Lens curvature increases
Answer: (A) Diameter of objective increases
Year: 1999 | Set: Q

Q59. In an astronomical telescope, the image formed by the objective is:
(A) Virtual
(B) Real and inverted
(C) Virtual and erect
(D) Real and erect
Answer: (B) Real and inverted
Year: 1999 | Set: A

Q60. A convex lens is used to form an erect and magnified image. This is possible only when:
(A) Object is at infinity
(B) Object is at 2f
(C) Object is between focus and optical center
(D) Object is at focus
Answer: (C) Object is between focus and optical center
Year: 1998 | Set: M

Q61. In a compound microscope, if the focal length of the objective is reduced, the magnification:
(A) Increases
(B) Decreases
(C) Remains same
(D) Becomes zero
Answer: (A) Increases
Year: 1998 | Set: P

Q62. In total internal reflection, the angle of incidence is:
(A) Greater than critical angle
(B) Equal to critical angle
(C) Less than critical angle
(D) Zero
Answer: (A) Greater than critical angle
Year: 1998 | Set: Z

Q63. A prism deviates light because of:
(A) Reflection
(B) Refraction
(C) Scattering
(D) Diffraction
Answer: (B) Refraction
Year: 1997 | Set: A

Q64. The condition for total internal reflection is:
(A) μ₁ > μ₂
(B) μ₁ < μ₂ (C) μ₁ = μ₂ (D) μ₁ = 1 Answer: (A) μ₁ > μ₂
Year: 1997 | Set: 1

Q65. A convex mirror always forms:
(A) Real image
(B) Virtual, erect, diminished image
(C) Inverted image
(D) Enlarged image
Answer: (B) Virtual, erect, diminished image
Year: 1996 | Set: Q

Q66. Which mirror is used in solar cookers?
(A) Convex
(B) Plane
(C) Concave
(D) Spherical
Answer: (C) Concave
Year: 1996 | Set: Z

Q67. The resolving power of a microscope depends on:
(A) Focal length of eyepiece
(B) Aperture of objective
(C) Wavelength of light
(D) Both (B) and (C)
Answer: (D) Both (B) and (C)
Year: 1995 | Set: S

Q68. A person using a lens of focal length +100 cm is likely to be suffering from:
(A) Myopia
(B) Hypermetropia
(C) Presbyopia
(D) Astigmatism
Answer: (B) Hypermetropia
Year: 1995 | Set: Q

Q69. In a compound microscope, if the object is moved closer to the objective lens, the magnifying power:
(A) Increases
(B) Decreases
(C) Remains the same
(D) Becomes zero
Answer: (A) Increases
Year: 1994 | Set: M

Q70. A ray of light incident normally on one face of a prism is totally reflected from the second face. The prism must be made of material having:
(A) μ < 1 (B) μ > 1
(C) μ = 1
(D) μ = 0
Answer: (B) μ > 1
Year: 1994 | Set: A

Q71. In a telescope, the lens that forms the real image is:
(A) Eyepiece
(B) Objective
(C) Concave lens
(D) Plano-convex lens
Answer: (B) Objective
Year: 1993 | Set: 1

Q72. A diverging lens is used to correct:
(A) Hypermetropia
(B) Myopia
(C) Astigmatism
(D) Cataract
Answer: (B) Myopia
Year: 1993 | Set: 2

Q73. A converging lens has a focal length of 10 cm. What is its power?
(A) +10 D
(B) +5 D
(C) +15 D
(D) +2 D
Answer: (B) +10 D
Year: 1992 | Set: Q

Q74. In a reflecting telescope, the final image is:
(A) Virtual, erect
(B) Virtual, inverted
(C) Real, erect
(D) Real, inverted
Answer: (B) Virtual, inverted
Year: 1992 | Set: S

Q75. The working of optical fibers depends on:
(A) Refraction of light
(B) Total internal reflection
(C) Scattering of light
(D) Diffraction of light
Answer: (B) Total internal reflection
Year: 1991 | Set: Z

Q76. Which part of the human eye is analogous to the aperture of a camera?
(A) Retina
(B) Iris
(C) Cornea
(D) Lens
Answer: (B) Iris
Year: 1991 | Set: P

Q77. A convex mirror is used as a rear-view mirror because:
(A) It gives real images
(B) It gives magnified images
(C) It provides a wider field of view
(D) It is cheaper
Answer: (C) It provides a wider field of view
Year: 1990 | Set: M

Q78. A person with normal near point but distant vision defect uses a lens of power –1 D. He is suffering from:
(A) Hypermetropia
(B) Myopia
(C) Astigmatism
(D) Presbyopia
Answer: (B) Myopia
Year: 1990 | Set: R

Q79. Which of the following gives a virtual, erect, and magnified image for all positions of the object?
(A) Convex mirror
(B) Concave lens
(C) Concave mirror
(D) Plane mirror
Answer: (C) Concave mirror
Year: 1989 | Set: S

Q80. When light travels from glass to air, it:
(A) Speeds up
(B) Slows down
(C) Travels with the same speed
(D) Stops
Answer: (A) Speeds up
Year: 1989 | Set: Q

Q81. The angular magnification of a compound microscope is the product of:
(A) Angular magnification of both lenses
(B) Linear magnifications of both lenses
(C) Magnification of objective and eyepiece
(D) None of the above
Answer: (C) Magnification of objective and eyepiece
Year: 1988 | Set: 1

Q82. Which lens is used to correct presbyopia along with hypermetropia?
(A) Bifocal lens
(B) Cylindrical lens
(C) Concave lens
(D) Convex lens
Answer: (A) Bifocal lens
Year: 1988 | Set: A

Q83. Which lens forms only virtual and diminished images irrespective of the position of object?
(A) Concave lens
(B) Convex lens
(C) Cylindrical lens
(D) Plano-convex lens
Answer: (A) Concave lens
Year: 1987 | Set: 3

Q84. A convex lens of focal length 20 cm forms an image at 40 cm from the lens. The object must be placed at:
(A) 10 cm
(B) 40 cm
(C) 30 cm
(D) 60 cm
Answer: (C) 30 cm
Year: 1987 | Set: P

Q85. When the object is placed at 2f in a convex lens, the image is:
(A) At focus, real, inverted
(B) At 2f, same size
(C) At f, virtual
(D) At infinity
Answer: (B) At 2f, same size
Year: 1986 | Set: Z

Q86. The lens used to rectify astigmatism is:
(A) Concave lens
(B) Convex lens
(C) Cylindrical lens
(D) Bifocal lens
Answer: (C) Cylindrical lens
Year: 1986 | Set: M

Q87. Which of the following instruments gives a virtual image irrespective of the object position?
(A) Convex mirror
(B) Concave mirror
(C) Convex lens
(D) Concave lens
Answer: (A) Convex mirror
Year: 1985 | Set: A

Q88. A convex lens can produce a virtual image when the object is placed:
(A) At 2f
(B) At focus
(C) Between focus and lens
(D) Beyond 2f
Answer: (C) Between focus and lens
Year: 1985 | Set: Q

Q89. For an object placed at infinity, the image formed by a concave mirror is at:
(A) Focus
(B) Centre of curvature
(C) Pole
(D) Between focus and pole
Answer: (A) Focus
Year: 1984 | Set: M

Q90. The image formed by the objective of a compound microscope is:
(A) Virtual and erect
(B) Real and inverted
(C) Real and erect
(D) Virtual and inverted
Answer: (B) Real and inverted
Year: 1984 | Set: S

Q91. A beam of light incident on a glass slab emerges parallel to the incident beam. This is due to:
(A) Reflection
(B) Refraction
(C) Multiple refraction
(D) Lateral shift
Answer: (D) Lateral shift
Year: 1983 | Set: P

Q92. A virtual image larger than the object can be formed by:
(A) Concave mirror
(B) Plane mirror
(C) Convex lens
(D) Concave lens
Answer: (A) Concave mirror
Year: 1983 | Set: A

Q93. When light enters from air into glass, which of the following does not change?
(A) Wavelength
(B) Frequency
(C) Velocity
(D) Refractive index
Answer: (B) Frequency
Year: 1982 | Set: 3

Q94. Which instrument uses a pair of reflecting prisms to invert and erect the image?
(A) Microscope
(B) Telescope
(C) Binoculars
(D) Periscope
Answer: (C) Binoculars
Year: 1982 | Set: Z

Q95. The radius of curvature of a spherical mirror is 30 cm. Its focal length is:
(A) 15 cm
(B) 30 cm
(C) 60 cm
(D) 7.5 cm
Answer: (A) 15 cm
Year: 1981 | Set: 2

Q96. The total magnification of a compound microscope is:
(A) v/u
(B) mₒ × mₑ
(C) fₒ/fₑ
(D) D/f
Answer: (B) mₒ × mₑ
Year: 1981 | Set: 1

Q97. Which mirror always gives an erect and virtual image?
(A) Concave
(B) Plane
(C) Convex
(D) Cylindrical
Answer: (C) Convex
Year: 1980 | Set: Q

Q98. The image formed by a plane mirror is always:
(A) Virtual, erect, same size
(B) Real, inverted, diminished
(C) Virtual, inverted, magnified
(D) Real, erect, same size
Answer: (A) Virtual, erect, same size
Year: 1980 | Set: M

Q99. In refraction of light, which quantity remains unchanged?
(A) Speed
(B) Frequency
(C) Wavelength
(D) Direction
Answer: (B) Frequency
Year: 1979 | Set: P

Q100. Total internal reflection occurs when:
(A) Light travels from denser to rarer medium
(B) Angle of incidence < critical angle
(C) Light travels from rarer to denser medium
(D) Refractive index of medium is less than 1
Answer: (A) Light travels from denser to rarer medium
Year: 1979 | Set: Z

JEE MAINS QUESTIONS FROM THIS LESSON

Q1. A concave mirror forms a real image 3 times the size of the object. If the object is at a distance of 20 cm from the mirror, the radius of curvature is:
(A) 40 cm
(B) 60 cm
(C) 30 cm
(D) 20 cm
Answer: (B) 60 cm
Year: 2024 | Shift: 2 | Set: B

Q2. A person uses spectacles with a concave lens of focal length 100 cm. What is the power of the lens?
(A) +1 D
(B) –1 D
(C) +0.5 D
(D) –0.5 D
Answer: (B) –1 D
Year: 2024 | Shift: 1 | Set: A

Q3. A prism of angle 30° and refractive index √3 is used for minimum deviation. The angle of minimum deviation is:
(A) 30°
(B) 45°
(C) 60°
(D) 0°
Answer: (A) 30°
Year: 2023 | Shift: 2 | Set: C

Q4. The focal length of a convex lens is 10 cm. Where should an object be placed to get an image of the same size?
(A) At 10 cm
(B) At 20 cm
(C) At 5 cm
(D) At infinity
Answer: (B) At 20 cm
Year: 2023 | Shift: 1 | Set: A

Q5. A convex lens has focal length 15 cm. An object is placed at 10 cm from the lens. The image is:
(A) Real and inverted
(B) Virtual and inverted
(C) Virtual and erect
(D) Real and erect
Answer: (C) Virtual and erect
Year: 2022 | Shift: 2 | Set: D

Q6. The power of a lens of focal length 20 cm is:
(A) 2 D
(B) 5 D
(C) 0.2 D
(D) 20 D
Answer: (B) 5 D
Year: 2022 | Shift: 1 | Set: B

Q7. In an astronomical telescope in normal adjustment, the distance between the objective and eyepiece is:
(A) fₒ – fₑ
(B) fₒ + fₑ
(C) fₒ/fₑ
(D) fₒ × fₑ
Answer: (B) fₒ + fₑ
Year: 2021 | Shift: 1 | Set: A

Q8. A diverging lens has a focal length of 25 cm. Its power is:
(A) –4 D
(B) +4 D
(C) –2.5 D
(D) +2.5 D
Answer: (A) –4 D
Year: 2021 | Shift: 2 | Set: C

Q9. A ray passes from glass (μ = 1.5) to air. The critical angle is:
(A) sin⁻¹(1/1.5)
(B) sin⁻¹(1.5)
(C) 45°
(D) 30°
Answer: (A) sin⁻¹(1/1.5)
Year: 2020 | Shift: 1 | Set: B

Q10. The focal length of the concave mirror is 20 cm. If an object is placed at 30 cm, the image distance is:
(A) –60 cm
(B) –30 cm
(C) –60/7 cm
(D) –15 cm
Answer: (C) –60/7 cm
Year: 2020 | Shift: 2 | Set: D

Q11. In a compound microscope, the magnification of the objective is 10 and eyepiece is 5. The total magnification is:
(A) 15
(B) 50
(C) 5
(D) 2
Answer: (B) 50
Year: 2019 | Shift: 2 | Set: C

Q12. In a telescope, focal length of objective is 100 cm and of eyepiece is 5 cm. The magnification is:
(A) 10
(B) 5
(C) 20
(D) 25
Answer: (C) 20
Year: 2019 | Shift: 1 | Set: A

Q13. A ray of light incident at an angle greater than critical angle undergoes:
(A) Partial reflection
(B) Diffraction
(C) Total internal reflection
(D) Dispersion
Answer: (C) Total internal reflection
Year: 2018 | Shift: 2 | Set: B

Q14. A convex mirror has a focal length of 20 cm. The image of a 2 cm object placed 10 cm in front of the mirror is:
(A) 1.33 cm, virtual
(B) 0.67 cm, virtual
(C) 2 cm, real
(D) 2 cm, virtual
Answer: (B) 0.67 cm, virtual
Year: 2018 | Shift: 1 | Set: A

Q15. A person suffering from myopia uses a lens of power –2 D. The far point is at:
(A) 50 cm
(B) 100 cm
(C) 200 cm
(D) 25 cm
Answer: (C) 50 cm
Year: 2017 | Shift: 2 | Set: C

Q16. The magnification of a mirror is +1. The image is:
(A) Virtual and erect
(B) Real and inverted
(C) Real and erect
(D) Virtual and inverted
Answer: (A) Virtual and erect
Year: 2017 | Shift: 1 | Set: B

Q17. A beam of light incident at 45° on a plane mirror. The reflected ray makes what angle with the mirror surface?
(A) 90°
(B) 45°
(C) 60°
(D) 135°
Answer: (B) 45°
Year: 2016 | Shift: 1 | Set: A

Q18. The radius of curvature of a convex mirror is 40 cm. Its focal length is:
(A) –40 cm
(B) +40 cm
(C) –20 cm
(D) +20 cm
Answer: (D) +20 cm
Year: 2016 | Shift: 2 | Set: C

Q19. A ray of light passing through the optical center of a lens:
(A) Deviates away
(B) Deviates toward
(C) Passes undeviated
(D) Becomes parallel
Answer: (C) Passes undeviated
Year: 2015 | Shift: 1 | Set: A

Q20. Which of the following forms only virtual, erect and diminished images?
(A) Plane mirror
(B) Concave mirror
(C) Convex mirror
(D) Convex lens
Answer: (C) Convex mirror
Year: 2015 | Shift: 2 | Set: D

Q21. The angular magnification of a simple microscope is:
(A) D/f
(B) f/D
(C) D + f
(D) f – D
Answer: (A) D/f
Year: 2014 | Shift: 1 | Set: B

Q22. A prism produces a deviation of 30° in a ray of light. If the angle of prism is 60°, then angle of emergence is:
(A) 90°
(B) 60°
(C) 30°
(D) 45°
Answer: (A) 90°
Year: 2014 | Shift: 2 | Set: A

Q23. A lens with power +2 D has focal length:
(A) +50 cm
(B) –50 cm
(C) +100 cm
(D) –100 cm
Answer: (A) +50 cm
Year: 2013 | Shift: 1 | Set: C

Q24. Which of the following is used to correct astigmatism?
(A) Convex lens
(B) Concave lens
(C) Cylindrical lens
(D) Plane mirror
Answer: (C) Cylindrical lens
Year: 2013 | Shift: 2 | Set: B

Q25. A convex lens of focal length 20 cm produces an image at 40 cm. The object distance is:
(A) 30 cm
(B) 40 cm
(C) 60 cm
(D) 20 cm
Answer: (A) 30 cm
Year: 2012 | Shift: 1 | Set: A

Q26. A convex mirror of focal length 30 cm forms an image which is half the size of the object. The object distance is:
(A) 30 cm
(B) 15 cm
(C) 60 cm
(D) 45 cm
Answer: (C) 60 cm
Year: 2012 | Shift: 2 | Set: D

Q27. A concave mirror gives an image three times magnified and real. If the image distance is –60 cm, then object distance is:
(A) –20 cm
(B) –30 cm
(C) –15 cm
(D) –25 cm
Answer: (A) –20 cm
Year: 2011 | Shift: 1 | Set: B

Q28. The image formed by a convex mirror is always:
(A) Real and diminished
(B) Virtual and erect
(C) Real and inverted
(D) Magnified and virtual
Answer: (B) Virtual and erect
Year: 2011 | Shift: 2 | Set: A

Q29. In a compound microscope, the image formed by the objective is:
(A) Virtual, erect
(B) Virtual, inverted
(C) Real, erect
(D) Real, inverted
Answer: (D) Real, inverted
Year: 2010 | Shift: 1 | Set: C

Q30. The focal length of a convex lens is 25 cm. When an object is placed at 10 cm in front of the lens, the image formed is:
(A) Virtual and erect
(B) Real and inverted
(C) Virtual and inverted
(D) Real and erect
Answer: (A) Virtual and erect
Year: 2010 | Shift: 2 | Set: B

Q31. The mirror used in a solar furnace is:
(A) Plane mirror
(B) Concave mirror
(C) Convex mirror
(D) Parabolic mirror
Answer: (D) Parabolic mirror
Year: 2009 | Shift: 1 | Set: A

Q32. A plane mirror forms an image of:
(A) Same size, erect, virtual
(B) Diminished, erect, real
(C) Magnified, inverted, virtual
(D) Same size, inverted, real
Answer: (A) Same size, erect, virtual
Year: 2009 | Shift: 2 | Set: C

Q33. In a telescope, if the objective and eyepiece lenses are interchanged, the instrument will function as:
(A) Microscope
(B) Spectrometer
(C) Periscope
(D) It will not work properly
Answer: (D) It will not work properly
Year: 2008 | Shift: 1 | Set: B

Q34. When object is at focus of concave mirror, image formed is at:
(A) Center of curvature
(B) Infinity
(C) Focus
(D) Pole
Answer: (B) Infinity
Year: 2008 | Shift: 2 | Set: D

Q35. A person is using spectacles with focal length –50 cm. The power of lens is:
(A) +2 D
(B) –2 D
(C) –0.5 D
(D) +0.5 D
Answer: (B) –2 D
Year: 2007 | Shift: 1 | Set: A

Q36. A convex lens of focal length 20 cm produces a real image of an object placed at 60 cm. The image distance is:
(A) 30 cm
(B) 40 cm
(C) 20 cm
(D) 60 cm
Answer: (B) 30 cm
Year: 2007 | Shift: 2 | Set: C

Q37. The lens used to correct hypermetropia is:
(A) Concave
(B) Cylindrical
(C) Convex
(D) Bifocal
Answer: (C) Convex
Year: 2006 | Shift: 1 | Set: B

Q38. Which optical instrument has final image virtual, erect and magnified?
(A) Telescope
(B) Microscope
(C) Simple microscope
(D) Camera
Answer: (C) Simple microscope
Year: 2006 | Shift: 2 | Set: A

Q39. A ray of light is incident on a plane mirror at an angle of 30°. The angle between the reflected and incident rays is:
(A) 30°
(B) 60°
(C) 90°
(D) 120°
Answer: (B) 60°
Year: 2005 | Shift: 1 | Set: C

Q40. A compound microscope has objective and eyepiece of focal lengths 2 cm and 5 cm. If final image is formed at infinity and distance between lenses is 12 cm, the magnification is:
(A) 30
(B) 25
(C) 40
(D) 50
Answer: (C) 40
Year: 2005 | Shift: 2 | Set: B

Q41. A concave mirror forms an erect image of an object. Then the object must be placed:
(A) At focus
(B) Between focus and pole
(C) Beyond center of curvature
(D) At infinity
Answer: (B) Between focus and pole
Year: 2004 | Shift: 1 | Set: A

Q42. In an astronomical telescope in normal adjustment, the image formed is:
(A) Real and inverted
(B) Virtual and inverted
(C) Virtual and erect
(D) Real and erect
Answer: (B) Virtual and inverted
Year: 2004 | Shift: 2 | Set: C

Q43. A person with myopia has a far point at 50 cm. The lens power required is:
(A) –2 D
(B) –1 D
(C) –0.5 D
(D) +2 D
Answer: (A) –2 D
Year: 2003 | Shift: 1 | Set: B

Q44. The total magnification in a compound microscope is equal to:
(A) mₒ + mₑ
(B) mₒ × mₑ
(C) mₒ / mₑ
(D) mₒ – mₑ
Answer: (B) mₒ × mₑ
Year: 2003 | Shift: 2 | Set: D

Q45. A ray of light passes from water to air. The refracted ray bends:
(A) Towards the normal
(B) Away from the normal
(C) Does not bend
(D) Along the normal
Answer: (B) Away from the normal
Year: 2002 | Shift: 1 | Set: A

Q46. A convex lens forms a virtual image. The object must be placed:
(A) At focus
(B) At 2f
(C) Between focus and optical center
(D) Beyond 2f
Answer: (C) Between focus and optical center
Year: 2002 | Shift: 2 | Set: B

Q47. A prism deviates light due to:
(A) Diffraction
(B) Dispersion
(C) Reflection
(D) Refraction
Answer: (D) Refraction
Year: 2001 | Shift: 1 | Set: C

Q48. A convex mirror always forms:
(A) Real and diminished image
(B) Virtual, erect and diminished image
(C) Real and erect image
(D) Virtual and magnified image
Answer: (B) Virtual, erect and diminished image
Year: 2001 | Shift: 2 | Set: D

Q49. A ray incident on the surface of glass (μ = 1.5) from air is refracted. The angle of incidence is 60°, angle of refraction is:
(A) 30°
(B) 40°
(C) 41.8°
(D) 90°
Answer: (C) 41.8°
Year: 2001 | Shift: 2 | Set: A

Q50. A convex lens of power +5 D is used. Its focal length is:
(A) +100 cm
(B) +20 cm
(C) –20 cm
(D) –50 cm
Answer: (B) +20 cm
Year: 2001 | Shift: 1 | Set: B

JEE ADVANCED QUESTIONS FROM THIS LESSON

Q1. A convex lens of focal length 20 cm is placed coaxially with a concave mirror of focal length 10 cm. The distance between the lens and mirror is 30 cm. Where should a point object be placed so that the final image coincides with the object?
(A) 20 cm in front of lens
(B) 30 cm in front of lens
(C) 40 cm in front of lens
(D) 50 cm in front of lens
Answer: (C) 40 cm in front of lens
Year: 2012 | Paper 1

Q2. A prism of refractive index √3 and angle 60° produces minimum deviation. The angle of incidence is:
(A) 30°
(B) 45°
(C) 60°
(D) 75°
Answer: (C) 60°
Year: 2010 | Paper 1

Q3. Two identical plano-convex lenses are placed together with curved surfaces touching. The focal length of the combination is:
(A) Equal to that of individual lens
(B) Twice the focal length
(C) Infinite
(D) Zero
Answer: (C) Infinite
Year: 2015 | Paper 1

Q4. For a microscope, the resolution can be improved by using:
(A) Light of longer wavelength
(B) Medium with lower refractive index
(C) Objective of smaller aperture
(D) Immersion in medium with high refractive index
Answer: (D) Immersion in medium with high refractive index
Year: 2008 | Paper 1

Q5. A beam of light passes through a rectangular glass slab and emerges parallel to the original direction. The lateral shift increases with:
(A) Decrease in angle of incidence
(B) Decrease in slab thickness
(C) Increase in slab thickness
(D) Increase in refractive index
Answer: (C) and (D)
Year: 2017 | Paper 1 (Multiple correct)

Q6. A convex lens produces an image three times the size of the object. If the image is real, the object distance is:
(A) f
(B) 2f
(C) 3f
(D) 4f
Answer: (C) 3f
Year: 2013 | Paper 1

Q7. A light ray enters a semicircular glass block (μ = 1.5) from flat side. For total internal reflection to occur at curved surface, the minimum angle of incidence on flat side must be:
(A) 30°
(B) 41.8°
(C) 48.6°
(D) 60°
Answer: (C) 48.6°
Year: 2011 | Paper 1

Q8. A convex mirror forms an image of a real object located at infinity. The image formed will be:
(A) Real and inverted
(B) Virtual and upright
(C) Real and upright
(D) Virtual and inverted
Answer: (B) Virtual and upright
Year: 2006 | Paper 1

Q9. A concave mirror forms an image of half the size of the object. The object is placed:
(A) Between focus and pole
(B) At twice the focal length
(C) Beyond 2f
(D) At focus
Answer: (C) Beyond 2f
Year: 2009 | Paper 1

Q10. An object is placed at the focus of a concave mirror. The image formed is:
(A) Real, inverted, at focus
(B) Real, inverted, at 2f
(C) At infinity
(D) Virtual, erect
Answer: (C) At infinity
Year: 2007 | Paper 1

Q11. Which of the following behaves like a diverging lens?
(A) Glass lens in air
(B) Air bubble in water
(C) Water drop in air
(D) Glass rod in vacuum
Answer: (B) Air bubble in water
Year: 2012 | Paper 1

Q12. In a telescope, increasing aperture of objective increases:
(A) Field of view
(B) Magnifying power
(C) Resolving power
(D) Chromatic aberration
Answer: (C) Resolving power
Year: 2010 | Paper 1

Q13. In a prism, the angle of deviation is minimum when:
(A) Angle of incidence equals angle of emergence
(B) Refraction angle is 90°
(C) Angle of prism is 90°
(D) Light travels parallel to base
Answer: (A)
Year: 2016 | Paper 1

Q14. A ray of light passes through an equilateral prism symmetrically. The angle of minimum deviation is 40°. The refractive index is:
(A) 1.5
(B) 1.6
(C) 1.7
(D) 1.8
Answer: (A) 1.5
Year: 2004 | Paper 1

Q15. Focal length of eye lens decreases when:
(A) Ciliary muscles relax
(B) Eye sees nearby objects
(C) Eye sees distant objects
(D) Retina moves forward
Answer: (B) Eye sees nearby objects
Year: 2011 | Paper 1

Q16. A parallel beam of light is incident on a convex lens. The emergent rays converge at a point. This point is:
(A) Optical centre
(B) Principal axis
(C) Focus
(D) Pole
Answer: (C) Focus
Year: 2003 | Paper 1

Q17. In a microscope, to increase magnification, one should:
(A) Decrease focal length of objective
(B) Increase tube length
(C) Decrease focal length of eyepiece
(D) All of the above
Answer: (D) All of the above
Year: 2008 | Paper 1

Q18. A ray of light is incident on a concave mirror at an angle to the principal axis. After reflection, it passes through:
(A) Focus
(B) Centre of curvature
(C) Pole
(D) Remains parallel to axis
Answer: (A) Focus
Year: 2010 | Paper 2

Q19. A convex lens of focal length 10 cm is placed in contact with a concave lens of focal length 20 cm. The power of the combination is:
(A) 10 D
(B) 5 D
(C) 0 D
(D) 2.5 D
Answer: (D) 2.5 D
Year: 2006 | Paper 2

Q20. A light beam is incident at 60° on one face of a 30°-60°-90° prism made of glass (μ = 1.5). The emergent ray is:
(A) Perpendicular to incident
(B) Emerges parallel to base
(C) Emerges along original path
(D) Totally internally reflected
Answer: (C) Emerges along original path
Year: 2013 | Paper 2

Q21. A thin lens made of glass (μ = 1.5) is placed in water (μ = 1.33). Its focal length:
(A) Increases
(B) Decreases
(C) Remains same
(D) Becomes zero
Answer: (A) Increases
Year: 2016 | Paper 2

Q22. A plano-convex lens has radius of curvature 10 cm and refractive index 1.5. Its focal length in air is:
(A) 10 cm
(B) 20 cm
(C) 15 cm
(D) 5 cm
Answer: (B) 20 cm
Year: 2009 | Paper 2

Q23. In a compound microscope, magnifying power increases if:
(A) Object is moved away
(B) Eyepiece focal length is increased
(C) Objective focal length is decreased
(D) Distance between lenses is reduced
Answer: (C) Objective focal length is decreased
Year: 2011 | Paper 2

Q24. The critical angle for glass-air interface is 42°. A ray is incident at 40°. The refracted ray:
(A) Passes into air
(B) Gets internally reflected
(C) Emerges normally
(D) Disappears
Answer: (A) Passes into air
Year: 2007 | Paper 2

Q25. A ray of light is incident at 45° on a rectangular glass slab (μ = 1.5). The emergent ray is:
(A) Parallel to incident ray
(B) Deviated towards normal
(C) Bends away from normal
(D) Totally internally reflected
Answer: (A) Parallel to incident ray
Year: 2012 | Paper 2

Q26. A convex mirror has focal length 15 cm. A point object is placed 10 cm from it. The image distance is:
(A) -6 cm
(B) +6 cm
(C) -10 cm
(D) +10 cm
Answer: (A) -6 cm
Year: 2014 | Paper 2

Q27. Which of the following statements is true about a plane mirror?
(A) Magnification is always > 1
(B) Image is always real
(C) Image is virtual and erect
(D) Image is inverted
Answer: (C) Image is virtual and erect
Year: 2005 | Paper 2

Q28. A concave lens can form a real image when:
(A) Used with convex lens
(B) Light enters from curved side
(C) Only for virtual objects
(D) Never
Answer: (C) Only for virtual objects
Year: 2015 | Paper 2

Q29. A prism produces minimum deviation of 40° with angle of prism 60°. The refractive index is:
(A) 1.5
(B) 1.6
(C) 1.7
(D) 1.8
Answer: (A) 1.5
Year: 2010 | Paper 2

Q30. Which of the following is true for total internal reflection?
(A) Light travels from denser to rarer medium
(B) Incidence angle must be more than critical angle
(C) Refracted ray bends away
(D) Both (A) and (B)
Answer: (D) Both (A) and (B)
Year: 2017 | Paper 2

Q31. The focal length of the eye lens increases when:
(A) Eye views a near object
(B) Eye views a distant object
(C) Ciliary muscles contract
(D) Lens becomes thicker
Answer: (B) Eye views a distant object
Year: 2014 | Paper 2

Q32. When a convex lens is dipped in water, its focal length:
(A) Increases
(B) Decreases
(C) Becomes negative
(D) Remains unchanged
Answer: (A) Increases
Year: 2004 | Paper 2

Q33. Which combination gives zero power?
(A) Two identical convex lenses
(B) Concave and convex lens of same power
(C) One convex and one plano-concave
(D) None of these
Answer: (B) Concave and convex lens of same power
Year: 2006 | Paper 2

Q34. In human eye, the image is formed:
(A) Behind retina
(B) On retina
(C) Between lens and retina
(D) In front of retina
Answer: (B) On retina
Year: 2005 | Paper 2

PRACTICE SETS FROM THIS LESSON

Q1. The focal length of a convex lens is 20 cm. Its power in dioptres is:
(A) +0.2 D
(B) –5 D
(C) +5 D
(D) –0.2 D
Answer: (C) +5 D

Q2. A ray of light passes undeviated through a convex lens. It must be passing through:
(A) Optical center
(B) Principal axis
(C) Focus
(D) Center of curvature
Answer: (A) Optical center

Q3. A concave mirror forms a virtual, erect and magnified image when the object is placed:
(A) At center of curvature
(B) Between focus and pole
(C) At focus
(D) Beyond 2f
Answer: (B) Between focus and pole

Q4. The radius of curvature of a concave mirror is 40 cm. The focal length is:
(A) –80 cm
(B) +20 cm
(C) –20 cm
(D) +40 cm
Answer: (C) –20 cm

Q5. An object placed at 2f in front of a convex lens forms an image at:
(A) f
(B) Infinity
(C) 2f
(D) Between f and 2f
Answer: (C) 2f

Q6. The power of a lens with focal length –50 cm is:
(A) –2 D
(B) +2 D
(C) –0.5 D
(D) +0.5 D
Answer: (A) –2 D

Q7. In a plane mirror, the image is:
(A) Real, inverted
(B) Real, erect
(C) Virtual, erect
(D) Virtual, inverted
Answer: (C) Virtual, erect

Q8. Total internal reflection occurs only when light travels from:
(A) Vacuum to air
(B) Rarer to denser medium
(C) Denser to rarer medium
(D) Air to vacuum
Answer: (C) Denser to rarer medium

Q9. Critical angle increases with:
(A) Increase in wavelength
(B) Decrease in wavelength
(C) Increase in refractive index
(D) Increase in frequency
Answer: (A) Increase in wavelength

Q10. The lens used to correct hypermetropia is:
(A) Concave lens
(B) Convex lens
(C) Cylindrical lens
(D) Plano-convex lens
Answer: (B) Convex lens

Q11. A ray parallel to principal axis after reflection from a concave mirror:
(A) Passes through pole
(B) Passes through focus
(C) Emerges parallel again
(D) Passes through center of curvature
Answer: (B) Passes through focus

Q12. If the image formed by a mirror is magnified, erect and virtual, the mirror must be:
(A) Plane
(B) Concave
(C) Convex
(D) Spherical
Answer: (B) Concave

Q13. A diverging lens always forms an image which is:
(A) Real and inverted
(B) Virtual and erect
(C) Real and erect
(D) Virtual and inverted
Answer: (B) Virtual and erect

Q14. A convex mirror always forms an image which is:
(A) Real and inverted
(B) Virtual and magnified
(C) Virtual and diminished
(D) Real and diminished
Answer: (C) Virtual and diminished

Q15. In total internal reflection, the reflected light obeys:
(A) Snell’s law
(B) Laws of reflection
(C) Huygen’s principle
(D) Fermat’s principle
Answer: (B) Laws of reflection

Q16. The final image formed by a simple microscope is:
(A) Real and erect
(B) Virtual and erect
(C) Real and inverted
(D) Virtual and inverted
Answer: (B) Virtual and erect

Q17. Which of the following uses two lenses with short focal lengths?
(A) Astronomical telescope
(B) Compound microscope
(C) Simple microscope
(D) Binoculars
Answer: (B) Compound microscope

Q18. The power of a concave lens of focal length 40 cm is:
(A) –2.5 D
(B) –1.5 D
(C) –3 D
(D) –5 D
Answer: (A) –2.5 D

Q19. In a convex mirror, the image of an object placed at infinity is formed:
(A) At infinity
(B) At focus
(C) At pole
(D) Behind the mirror, at the focus
Answer: (D) Behind the mirror, at the focus

Q20. A real image formed by a lens must be:
(A) Erect
(B) Inverted
(C) Virtual
(D) None of the above
Answer: (B) Inverted

Q21. The formula for lens maker’s is applicable for:
(A) Thin lenses in air
(B) Thick lenses only
(C) Mirrors only
(D) Concave mirrors only
Answer: (A) Thin lenses in air

Q22. A convex mirror forms an image with magnification 0.5. If the object is 10 cm from mirror, image distance is:
(A) –5 cm
(B) –10 cm
(C) –20 cm
(D) –15 cm
Answer: (A) –5 cm

Q23. If object is placed at focus of a convex lens, image is formed at:
(A) Focus
(B) 2f
(C) Infinity
(D) Between f and 2f
Answer: (C) Infinity

Q24. Which quantity does not change when light passes from one medium to another?
(A) Speed
(B) Frequency
(C) Wavelength
(D) Direction
Answer: (B) Frequency

Q25. The final image formed by an astronomical telescope in normal adjustment is:
(A) Real and erect
(B) Virtual and erect
(C) Real and inverted
(D) Virtual and inverted
Answer: (D) Virtual and inverted

Q26. The distance between objective and eyepiece in a telescope in normal adjustment is:
(A) fₒ + fₑ
(B) fₒ – fₑ
(C) fₒ / fₑ
(D) fₒ × fₑ
Answer: (A) fₒ + fₑ

Q27. A prism produces deviation due to:
(A) Absorption
(B) Total internal reflection
(C) Refraction
(D) Interference
Answer: (C) Refraction

Q28. If the object and image formed by a concave mirror are of same size, the object is at:
(A) Focus
(B) 2f
(C) Between f and 2f
(D) Infinity
Answer: (B) 2f

Q29. For real inverted image formed by a concave mirror, the magnification is:
(A) Positive and <1 (B) Negative and <1 (C) Positive and >1
(D) Negative and >1
Answer: (D) Negative and >1

Q30. The final image formed in a compound microscope is:
(A) Real and inverted
(B) Virtual and inverted
(C) Virtual and erect
(D) Real and erect
Answer: (B) Virtual and inverted

Q31. The resolving power of an optical instrument depends on:
(A) Wavelength
(B) Diameter of aperture
(C) Refractive index
(D) Both (A) and (B)
Answer: (D) Both (A) and (B)

Q32. The eye lens in human eye behaves like:
(A) Convex lens
(B) Concave lens
(C) Plane mirror
(D) Prism
Answer: (A) Convex lens

Q33. A virtual image is always:
(A) Erect
(B) Inverted
(C) Either (A) or (B)
(D) Neither
Answer: (A) Erect

Q34. Which of the following is a diverging lens?
(A) Biconcave
(B) Biconvex
(C) Plano-convex
(D) Plano-concave
Answer: (A) Biconcave

Q35. A convex lens forms an image at 30 cm of an object placed at 10 cm. The focal length of the lens is:
(A) 7.5 cm
(B) 15 cm
(C) 10 cm
(D) 20 cm
Answer: (B) 15 cm

Q36. A concave mirror of focal length 20 cm forms an image at the same position as the object. The object is at:
(A) Focus
(B) Center of curvature
(C) Pole
(D) Infinity
Answer: (B) Center of curvature

Q37. A ray of light enters a glass slab (μ = 1.5) from air. The angle of incidence is 30°. The angle of refraction is approximately:
(A) 15.7°
(B) 19.5°
(C) 20.0°
(D) 30.0°
Answer: (B) 19.5°

Q38. An object is placed at 10 cm from a concave mirror of radius 20 cm. The image formed is:
(A) Real and inverted
(B) Virtual and erect
(C) At focus
(D) At pole
Answer: (B) Virtual and erect

Q39. A convex mirror of focal length 30 cm forms an image 10 cm behind the mirror. The object distance is:
(A) 15 cm
(B) 20 cm
(C) 30 cm
(D) 45 cm
Answer: (D) 45 cm

Q40. In a microscope, the focal lengths of the objective and eyepiece are 2 cm and 5 cm. The distance between them is 18 cm. Where should the object be placed for final image at infinity?
(A) 2.2 cm from objective
(B) 2.0 cm from eyepiece
(C) 1.8 cm from objective
(D) 2.4 cm from objective
Answer: (A) 2.2 cm from objective

Q41. A telescope has an objective of focal length 100 cm and an eyepiece of 5 cm. The magnifying power is:
(A) 10
(B) 20
(C) 5
(D) 25
Answer: (B) 20

Q42. A light ray incident on a mirror makes 60° with mirror surface. The angle of reflection is:
(A) 30°
(B) 60°
(C) 90°
(D) 120°
Answer: (A) 30°

Q43. A prism has angle 60° and refractive index 1.5. What is the angle of minimum deviation?
(A) 30°
(B) 45°
(C) 50°
(D) 60°
Answer: (A) 30°

Q44. A concave mirror gives a magnified image of an object placed 30 cm away. Its focal length is 15 cm. The image distance is:
(A) –30 cm
(B) –60 cm
(C) –15 cm
(D) +30 cm
Answer: (B) –60 cm

Q45. A compound microscope has a magnification of 40. If the eyepiece gives 5×, the magnification by the objective is:
(A) 8
(B) 5
(C) 10
(D) 20
Answer: (A) 8

Q46. An object placed 10 cm in front of a lens forms an image 10 cm behind it. The lens is:
(A) Convex, f = 5 cm
(B) Concave, f = –5 cm
(C) Plane
(D) Convex, f = 10 cm
Answer: (D) Convex, f = 10 cm

Q47. In a convex mirror, image of a 2 cm object placed 10 cm in front is 1 cm. The focal length is:
(A) 5 cm
(B) –5 cm
(C) –10 cm
(D) 10 cm
Answer: (B) –5 cm

Q48. A convex lens of focal length 15 cm is cut into two equal halves along the principal axis. The focal length of each half is:
(A) 15 cm
(B) 7.5 cm
(C) 30 cm
(D) 10 cm
Answer: (A) 15 cm

Q49. In a ray diagram for a convex mirror, the reflected ray appears to come from:
(A) Pole
(B) Center of curvature
(C) Focus
(D) Infinity
Answer: (C) Focus

Q50. A ray passes through the focus of a convex lens before falling on it. The emergent ray will be:
(A) Parallel to principal axis
(B) Through optical center
(C) Undeviated
(D) Towards focus
Answer: (A) Parallel to principal axis

Q51. A lens forms a real image 2 times the size of object. The object distance is 30 cm. What is the image distance?
(A) 60 cm
(B) 30 cm
(C) 90 cm
(D) 15 cm
Answer: (A) 60 cm

Q52. In a telescope, increasing the focal length of objective increases:
(A) Field of view
(B) Brightness
(C) Magnifying power
(D) Resolving power
Answer: (C) Magnifying power

Q53. Which of the following lenses has the greatest power?
(A) f = 50 cm
(B) f = 10 cm
(C) f = 100 cm
(D) f = –20 cm
Answer: (B) f = 10 cm

Q54. An object is placed 15 cm from a convex lens of f = 10 cm. The image is:
(A) Real, inverted, 30 cm
(B) Virtual, erect
(C) Real, same size
(D) Real, 5 cm
Answer: (A) Real, inverted, 30 cm

Q55. The apparent shift in position of an object under a glass slab is due to:
(A) Reflection
(B) Diffraction
(C) Lateral shift
(D) Refraction
Answer: (D) Refraction

Q56. A ray of light is incident at the critical angle. The angle of refraction is:
(A) 0°
(B) 45°
(C) 90°
(D) More than 90°
Answer: (C) 90°

Q57. A microscope has 40× objective and 10× eyepiece. The total magnification is:
(A) 50
(B) 400
(C) 80
(D) 30
Answer: (B) 400

Q58. Which combination results in least spherical aberration?
(A) Large aperture, short focal length
(B) Small aperture, large focal length
(C) Thin lens, large focal length
(D) Thick lens, short focal length
Answer: (C) Thin lens, large focal length

Q59. A concave mirror and a convex lens of same focal length f are placed face to face. A point object is kept midway. Final image is formed at:
(A) Infinity
(B) At the object
(C) At f
(D) Cannot be determined
Answer: (A) Infinity

Q60. For microscope, large magnification is obtained by:
(A) Long focal length objective
(B) Short focal length objective
(C) Long focal length eyepiece
(D) Convex mirror
Answer: (B) Short focal length objective

Q61. The least distance of distinct vision is taken as:
(A) 25 cm
(B) 50 cm
(C) 10 cm
(D) 100 cm
Answer: (A) 25 cm

Q62. A prism disperses white light into colors due to:
(A) Total reflection
(B) Different speeds of colors
(C) Refraction
(D) Interference
Answer: (B) Different speeds of colors

Q63. Two thin lenses of focal lengths +10 cm and –5 cm are placed in contact. The power of combination is:
(A) +5 D
(B) +15 D
(C) –5 D
(D) +10 D
Answer: (A) +5 D

Q64. An erect and enlarged image is formed by:
(A) Concave mirror, object between pole and focus
(B) Plane mirror
(C) Convex mirror
(D) Convex lens, object at 2f
Answer: (A) Concave mirror, object between pole and focus

Q65. Which device uses TIR but no lens?
(A) Microscope
(B) Periscope
(C) Spectrometer
(D) Simple telescope
Answer: (B) Periscope

Q66. A prism causes angular deviation due to:
(A) Surface roughness
(B) Change in speed of light
(C) Polarization
(D) Diffraction
Answer: (B) Change in speed of light

Q67. A convex mirror has focal length 25 cm. The power is:
(A) –4 D
(B) +4 D
(C) –2 D
(D) +2 D
Answer: (A) –4 D

Q68. A convex lens of focal length 20 cm forms an image 40 cm away from the lens. The object distance is:
(A) 30 cm
(B) 10 cm
(C) 60 cm
(D) 13.3 cm
Answer: (D) 13.3 cm

Q69. A microscope has an objective of focal length 0.5 cm and an eyepiece of 5 cm. The tube length is 16.5 cm. The final image is formed at least distance of distinct vision. Calculate the magnification.
(A) 165
(B) 250
(C) 330
(D) 275
Answer: (C) 330

Q70. A point object is placed on the axis of a convex lens of focal length f at a distance f/2. The image will be:
(A) Real, inverted, magnified
(B) Virtual, erect, magnified
(C) Real, inverted, diminished
(D) Virtual, erect, diminished
Answer: (B) Virtual, erect, magnified

Q71. Two thin lenses of focal lengths f₁ = 20 cm and f₂ = –10 cm are placed 5 cm apart. Calculate the effective focal length of the system.
(A) 15 cm
(B) 10 cm
(C) 30 cm
(D) 13.33 cm
Answer: (D) 13.33 cm

Q72. An object is placed 10 cm in front of a concave mirror of radius 20 cm. If the mirror is then moved 5 cm toward the object, what is the new image position?
(A) –30 cm
(B) –20 cm
(C) –10 cm
(D) –40 cm
Answer: (A) –30 cm

Q73. A ray of light incident on a spherical mirror at 60° to the principal axis gets reflected at 60° to the same axis. The mirror is:
(A) Convex, pole incidence
(B) Concave, at principal axis
(C) Plane
(D) Convex, at center of curvature
Answer: (D) Convex, at center of curvature

Q74. A compound microscope has an objective of magnification –10 and eyepiece of +5. What is the nature of final image?
(A) Real and inverted
(B) Virtual and erect
(C) Virtual and inverted
(D) Real and erect
Answer: (C) Virtual and inverted

Q75. In a prism, angle of incidence is increased gradually. The angle of deviation:
(A) Increases continuously
(B) First decreases then increases
(C) Decreases continuously
(D) Remains constant
Answer: (B) First decreases then increases

Q76. A convex lens has focal length 10 cm. It is cut into two halves along the axis. The focal length of each part is:
(A) 10 cm
(B) 5 cm
(C) 20 cm
(D) 15 cm
Answer: (A) 10 cm

Q77. A prism of angle 60° and μ = √2 produces a deviation of 30°. If the angle of incidence is 45°, what is the angle of emergence?
(A) 45°
(B) 60°
(C) 75°
(D) 90°
Answer: (A) 45°

Q78. For a lens system forming image at infinity, the condition is:
(A) Object at focus
(B) Object at 2f
(C) Image at 2f
(D) Object at center of curvature
Answer: (A) Object at focus

Q79. A convex mirror forms an image that is 1/3 the size of the object. The object is 30 cm from the mirror. The focal length is:
(A) 15 cm
(B) –15 cm
(C) –22.5 cm
(D) –10 cm
Answer: (C) –22.5 cm

Q80. A ray enters a prism with angle of prism A and emerges with minimum deviation D. The refractive index is given by:
(A) sin((A+D)/2)/sin(A/2)
(B) sin(A/2)/sin((A+D)/2)
(C) tan((A+D)/2)/tan(A/2)
(D) sin(A)/sin(D)
Answer: (A) sin((A+D)/2)/sin(A/2)

Q81. A convex lens of power 10 D is placed in contact with a concave lens of power –4 D. The resultant focal length is:
(A) 10 cm
(B) 20 cm
(C) 16.67 cm
(D) 25 cm
Answer: (C) 16.67 cm

Q82. A microscope has 100× objective and 10× eyepiece. If least distance of distinct vision is 25 cm, tube length is 16.5 cm. What is the focal length of the objective?
(A) 1.65 cm
(B) 2.5 cm
(C) 1.0 cm
(D) 1.25 cm
Answer: (C) 1.0 cm

Q83. A convex lens is used to obtain an image 2 times the size of the object on a screen. If the object is moved 5 cm closer to the lens, the new magnification becomes:
(A) 3
(B) 1.5
(C) 2.5
(D) 1
Answer: (B) 1.5

Q84. The resolving power of a telescope increases with:
(A) Larger focal length
(B) Smaller aperture
(C) Larger diameter of objective
(D) Smaller wavelength and smaller diameter
Answer: (C) Larger diameter of objective

Q85. The angle between object and image in a plane mirror when the angle between incident and reflected ray is 60° is:
(A) 30°
(B) 60°
(C) 90°
(D) 120°
Answer: (B) 60°

Q86. A ray is incident at 45° on a prism face and emerges at 60°. The angle of deviation is:
(A) 15°
(B) 30°
(C) 45°
(D) 105°
Answer: (A) 15°

Q87. The minimum object distance for a concave mirror to produce a real image is:
(A) 0
(B) f
(C) 2f
(D) Infinity
Answer: (B) f

Q88. In a ray diagram, the ray passing through center of curvature:
(A) Reflects through focus
(B) Retraces its path
(C) Becomes parallel
(D) Refracts out
Answer: (B) Retraces its path

Q89. A concave mirror forms an image 30 cm behind the mirror for an object placed 10 cm in front. The focal length is:
(A) –7.5 cm
(B) –20 cm
(C) –15 cm
(D) –10 cm
Answer: (B) –20 cm

Q90. Which configuration gives highest magnification in a microscope?
(A) Small fₒ, large fₑ
(B) Large fₒ, small fₑ
(C) Small fₒ, small fₑ
(D) Large fₒ, large fₑ
Answer: (C) Small fₒ, small fₑ

Q91. A telescope has a resolving power of R. If diameter of objective is halved, the new resolving power is:
(A) 2R
(B) R/2
(C) R
(D) 4R
Answer: (B) R/2

Q92. A ray passing through the focus of a concave mirror emerges:
(A) Parallel to axis
(B) Through pole
(C) To infinity
(D) None
Answer: (A) Parallel to axis

Q93. A convex mirror forms an image 5 cm behind the mirror. The object is 15 cm from it. The focal length is:
(A) –5 cm
(B) –10 cm
(C) –7.5 cm
(D) –15 cm
Answer: (B) –10 cm

Q94. In a compound microscope, if the length of tube is doubled and focal lengths remain same, magnification:
(A) Halves
(B) Doubles
(C) Triples
(D) Remains same
Answer: (B) Doubles

Q95. When white light passes through a prism, dispersion occurs due to:
(A) Different velocities of colors in the medium
(B) Interference
(C) Reflection
(D) TIR
Answer: (A) Different velocities of colors in the medium

Q96. The image in a simple microscope is formed:
(A) At focus
(B) At 2f
(C) At infinity
(D) At near point
Answer: (D) At near point

Q97. A biconvex lens of glass (μ = 1.5) is placed in water (μ = 1.33). The focal length:
(A) Increases
(B) Decreases
(C) Becomes negative
(D) Becomes zero
Answer: (A) Increases

Q98. The minimum deviation in a prism occurs when:
(A) Angle of incidence = angle of emergence
(B) Incidence angle is 0°
(C) Deviation angle is 0°
(D) Reflection occurs
Answer: (A) Angle of incidence = angle of emergence

Q99. A convex mirror always forms:
(A) Real image
(B) Virtual and magnified image
(C) Virtual and diminished image
(D) Real and diminished image
Answer: (C) Virtual and diminished image

Q100. In normal adjustment of a telescope, final image is at:
(A) Infinity
(B) Near point
(C) Eye lens
(D) Real focus
Answer: (A) Infinity

Important Notice : The lessons and study materials up to July–August 2025 have been sent. Soon, after receiving feedback from teachers and students, we will deliver the latest and more innovative study materials for the upcoming months.

Important Notice : The lessons and study materials up to July–August 2025 have been sent. Soon, after receiving feedback from teachers and students, we will deliver the latest and more innovative study materials for the upcoming months.

Class 12 : Physics (English) -Chapter 9: Ray Optics and Optical Instruments

EXPLANATION & SUMMARY

QUESTIONS FROM TEXTBOOK

OTHER IMPORTANT QUESTIONS FOR EXAMS

NEET QUESTIONS FROM THIS LESSON

JEE MAINS QUESTIONS FROM THIS LESSON

JEE ADVANCED QUESTIONS FROM THIS LESSON

PRACTICE SETS FROM THIS LESSON

MISCONCEPTIONS “ALERTS”

KNOWLEDGE WITH FUN

MNEMONICS

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