Class 10 : Science (In English) – Lesson 9. Light: Reflection and Refraction

EXPLANATION & SUMMARY

🔵 Detailed Explanation (rendering corrected; copy-safe)
🌟 Introduction: What light does

🔵 Light travels in straight lines (rays) and lets us see objects.

🟢 When light meets a surface or a new medium, two key effects occur: reflection (bouncing back) and refraction (bending).

✨ These ideas power mirrors, lenses, spectacles, cameras and many scientific instruments.

🪞 Reflection of Light (plane mirrors and basics)
🔴 Law 1: Incident ray, reflected ray and the normal at the point of incidence lie in one plane.

🟡 Law 2: Angle of incidence i = angle of reflection r.

🌿 Regular reflection (smooth surface) gives clear images; diffuse reflection (rough surface) scatters light.

✏️ Note: The image in a plane mirror is virtual, erect, same size as the object, and laterally inverted.

🟣 Spherical Mirrors (concave and convex)
🟠 Concave mirror (converging): focuses parallel rays at a point.
🟤 Convex mirror (diverging): spreads rays; appears to focus behind the mirror.

Key terms (copy-safe):
🧠 Pole (P): centre of mirror surface.
🌍 Principal axis: line through P and centre of curvature.

🎯 Centre of curvature (C): centre of the sphere of which the mirror is a part.
⭐ Focus (F): point where parallel rays meet (concave) or appear to meet (convex).
📏 Focal length (f): PF (distance from pole to focus).

Sign convention (Cartesian):
Take the pole P as origin on the principal axis.
Distances measured towards the incident light (usually to the left) are negative.
Heights above principal axis are positive; below are negative.

Mirror formula (copy-safe):
1/f = 1/v + 1/u
(u = object distance, v = image distance, f = focal length)

Magnification for mirrors:
m = h_i / h_o = − v / u
(h_i = image height, h_o = object height)

Concave mirror image summary (textual ray guide):
🔵 Object beyond C → image between C and F (real, inverted, diminished).

🟢 Object at C → image at C (real, inverted, same size).

🟡 Object between C and F → image beyond C (real, inverted, magnified).

🔴 Object at F → image at infinity (highly enlarged).

🟣 Object between F and P → image behind mirror (virtual, erect, magnified).

Convex mirror image:
🧠 For any object position, image forms between P and F, virtual, erect, diminished.

Applications:
⚡ Concave: headlights, shaving/dentist mirrors, solar furnaces.
🚗 Convex: vehicle rear-view (wide field of view).

💧 Refraction of Light (bending across media)
🔵 Refraction is bending of light due to change in speed when it enters a different medium (air → glass or water → air).

🟢 Rays bend towards the normal when entering an optically denser medium; away from the normal when entering a rarer medium.
Snell’s law (copy-safe):
n = sin i / sin r
(i = angle of incidence, r = angle of refraction, n = refractive index of second medium w.r.t. first)
Absolute refractive index:
n = (speed of light in vacuum) / (speed of light in medium)

💡 Concept: Higher n means light slows more and bends more towards the normal.
✔️ Everyday effects: A pencil in water looks bent; the bottom of a pool looks raised; stars appear to twinkle (atmospheric refraction).

🔎 Refraction through a rectangular glass slab (what to expect)
🌿 The emergent ray is parallel to the incident ray, but laterally displaced (shifted sideways).
✏️ Note: The two refractions (air→glass, glass→air) bend in opposite directions, cancelling the angle but not the path shift.

👓 Spherical Lenses (convex and concave)
🔵 Convex lens (converging): thicker at centre; brings parallel rays to a focus.
🔴 Concave lens (diverging): thinner at centre; makes rays diverge as if from a focus.

Key lens terms:
Optical centre (O), principal axis, focal points F on both sides, focal length f (OF).

Sign convention for lenses (Cartesian):
Object kept on the left of lens → u is negative.
Real image on the right → v positive; virtual image on the left → v negative.
Convex lens has positive f; concave lens has negative f (by convention).

Lens formula (copy-safe):
1/f = 1/v − 1/u

Magnification for lenses:
m = h_i / h_o = v / u

Convex lens image guide:
🌟 Object at infinity → image at F (real, inverted, highly diminished).
🟣 Object at 2F → image at 2F (real, inverted, same size).
🟠 Object between F and 2F → image beyond 2F (real, inverted, magnified).
🟤 Object at F → image at infinity (highly enlarged).
🟡 Object between F and O → image on same side as object (virtual, erect, magnified) → magnifying glass.

Concave lens image:
🧠 For any object position, image forms between O and F on the same side as object (virtual, erect, diminished).

📐 Power of a Lens (for spectacle numbers)
Power P measures how strongly a lens converges or diverges light.
Formula (copy-safe): P = 1/f (when f is in metres; P in dioptre, symbol D)

🔵 Convex lens → positive power; 🔴 Concave lens → negative power.
✨ Combination: P_total = P1 + P2 + … (useful for lens systems).

🧠 Problem-solving essentials (safe equations)
Mirror: 1/f = 1/v + 1/u ; m = − v / u.
Lens: 1/f = 1/v − 1/u ; m = v / u.
Keep units consistent (metre for f in power).
Apply sign convention carefully to avoid mistakes.

🌍 Real-life applications
🚗 Convex mirrors as rear-view mirrors (wide field, smaller image).
🔦 Concave mirrors in torches and headlights (focus a strong beam).
🔍 Convex lenses in magnifiers, cameras, projectors, eye (image formation on retina).
🕳️ Concave lenses in spectacles for myopia (diverge rays to help focus).
✏️ Study tip: When you cannot draw, describe the ray diagram—state object position and resulting image position, nature (real/virtual), orientation (inverted/erect), and size (diminished/same/magnified).

🟢 Summary (quick revision)
🔵 Reflection: i = r; plane mirrors give virtual, erect, same-size images.
🟣 Spherical mirrors: Concave (converging), Convex (diverging); 1/f = 1/v + 1/u; m = − v/u.
💧 Refraction: bending due to speed change; n = sin i / sin r; higher n → more bending.
🔎 Glass slab: emergent ray parallel, but laterally shifted.
👓 Lenses: Convex (converging), Concave (diverging); 1/f = 1/v − 1/u; m = v/u; P = 1/f (m).
🌟 Applications: mirrors in vehicles/torches; lenses in spectacles/cameras.

📝 Quick Recap
✨ Laws of reflection hold for all reflecting surfaces.
🌿 Concave mirror: can give real or virtual images; convex mirror: always virtual, erect, diminished.
💧 Refraction follows n = sin i / sin r; denser medium → bend towards normal.
🔍 Convex lens can magnify (object between F and O); concave lens always shrinks the image.
✔️ Power in dioptres helps choose spectacle lenses.

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QUESTIONS FROM TEXTBOOK

Question 1
Which one of the following materials cannot be used to make a lens?
(a) Water
(b) Glass
(c) Plastic
(d) Clay
Answer
🔵 Lenses must be transparent so that light can pass through.
🟢 Water, glass and plastic are transparent.
🔴 Clay is opaque → cannot form a lens.
✔️ Correct option: (d) Clay

Question 2
The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object?
(a) Between the principal focus and the centre of curvature
(b) At the centre of curvature
(c) Beyond the centre of curvature
(d) Between the pole of the mirror and its principal focus
Answer
🌿 Concave mirror gives a virtual, erect, magnified image only when object is between P (pole) and F (focus).
✔️ Correct option: (d)

Question 3
Where should an object be placed in front of a convex lens to get a real image of the same size as the object?
(a) At the principal focus of the lens
(b) At twice the focal length
(c) At infinity
(d) Between the optical centre of the lens and its principal focus
Answer
🧠 A convex lens forms a real, inverted, same size image when object is placed at 2F.
✔️ Correct option: (b)

Question 4
A spherical mirror and a thin spherical lens have each a focal length of –15 cm. The mirror and the lens are likely to be
(a) both concave
(b) both convex
(c) the mirror is concave and the lens is convex
(d) the mirror is convex but the lens is concave
Answer
🔵 Negative focal length means:
Concave mirror has f < 0.
Concave lens has f < 0.
✔️ Correct option: (a) both concave

Question 5
No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be
(a) only plane
(b) only concave
(c) only convex
(d) either plane or convex
Answer
🌸 Plane mirror → erect, virtual image always.
🌍 Convex mirror → erect, diminished, virtual image always.
Concave mirror → erect only when object within F (not always).
✔️ Correct option: (d) either plane or convex

Question 6
Which of the following lenses would you prefer to use while reading small letters in a dictionary?
(a) A convex lens of focal length 50 cm
(b) A concave lens of focal length 50 cm
(c) A convex lens of focal length 5 cm
(d) A concave lens of focal length 5 cm
Answer
🔎 To magnify small letters, a convex lens with short focal length is required.
✔️ Correct option: (c) A convex lens of focal length 5 cm

Question 7
We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.
Answer
🌿 For concave mirror, erect image occurs only when object is placed between P (pole) and F (focus).
🟢 Distance range: 0 to < 15 cm.
🟡 Nature: Virtual, erect, magnified.
✏️ In diagram (to be drawn in exam): object between P and F → image behind the mirror, larger than object.

Question 8
Name the type of mirror used in the following situations. Support your answer with reason.
(a) Headlights of a car
(b) Side/rear-view mirror of a vehicle
(c) Solar furnace
Answer
(a) 🔦 Concave mirror → produces powerful parallel beam.
(b) 🚗 Convex mirror → gives wide field of view, erect and diminished image.
(c) ☀️ Concave mirror → focuses sunlight at one point to produce heat.

Question 9
One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations.
Answer
🌿 Yes, the lens will form a complete image but with reduced brightness.
🟢 Rays from the uncovered part still converge to form image.
🟡 Experiment: Cover half of lens, place object → image appears, but less bright.

Question 10
An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed.
Answer
🔵 Lens formula: 1/f = 1/v – 1/u
f = 10 cm, u = –25 cm (sign convention)
1/v = 1/10 + 1/25 = (2.5 + 1)/25 = 3.5/25
v = 25/3.5 ≈ 7.14 cm (positive → image on right side).
🟢 Magnification: m = v/u = 7.14 / –25 ≈ –0.29 → image inverted and diminished.
🟡 Image size: h_i = m × h_o = –0.29 × 5 ≈ –1.45 cm (negative → inverted).
✔️ Nature: Real, inverted, diminished.

Question 11
A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.
Answer
🔵 Lens formula: 1/f = 1/v – 1/u
f = –15 cm, v = –10 cm
1/–15 = 1/–10 – 1/u
–1/15 = –1/10 – 1/u
1/u = –1/10 + 1/15 = (–3 + 2)/30 = –1/30
u = –30 cm.
✔️ Object distance = 30 cm (in front of lens).
✔️ Nature: Virtual, erect, diminished.

Question 12
An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.
Answer
🔵 Mirror formula: 1/f = 1/v + 1/u
f = +15 cm (convex mirror), u = –10 cm
1/v = 1/15 – 1/10 = (2 – 3)/30 = –1/30
v = –30 cm (negative → image behind mirror).
✔️ Nature: Virtual, erect, diminished.

Question 13
The magnification produced by a plane mirror is +1. What does this mean?
Answer
🌸 Magnification = h_i / h_o = +1.
🟢 Means image is of same size as object.
🟡 Positive sign → image is virtual and erect.

Question 14
An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.
Answer
🔵 Focal length f = R/2 = 30/2 = 15 cm (convex mirror → +15 cm).
u = –20 cm.
1/v = 1/f – 1/u = 1/15 – (–1/20) = 1/15 + 1/20 = (4 + 3)/60 = 7/60.
v = 60/7 ≈ 8.57 cm (behind mirror).
🟢 Magnification: m = –v/u = –8.57/–20 ≈ +0.43.
🟡 Image size: h_i = m × h_o = 0.43 × 5 ≈ 2.15 cm.
✔️ Image: Virtual, erect, diminished.

Question 15
An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.
Answer
🔵 Mirror formula: 1/f = 1/v + 1/u
f = –18 cm, u = –27 cm
1/v = 1/–18 – 1/–27 = –1/18 + 1/27 = (–3 + 2)/54 = –1/54
v = –54 cm (real image).
🟢 Magnification: m = –v/u = –(–54)/(–27) = –2.
🟡 Image size: h_i = m × h_o = –2 × 7 = –14 cm (negative → inverted).
✔️ Screen at 54 cm. Image is real, inverted, magnified (14 cm).

Question 16
Find the focal length of a lens of power –2.0 D. What type of lens is this?
Answer
🔵 Formula: P = 100/f (f in cm).
f = 100/P = 100 / –2 = –50 cm.
🟢 Negative focal length → lens is concave.
✔️ Focal length = –50 cm, concave lens.

Question 17
A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?
Answer
🔵 f = 100 / P = 100 / +1.5 ≈ 66.7 cm.
🟢 Positive focal length → convex (converging) lens.
✔️ Focal length = +66.7 cm, convex lens.

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OTHER IMPORTANT QUESTIONS FOR EXAMS

Question 1
A concave mirror of focal length 15 cm forms an image at infinity when the object is placed at:
Centre of curvature
Focus
Pole
Between focus and pole
Answer: 2 🌟

Question 2
A convex mirror always forms:
Real and inverted images
Virtual, erect and diminished images
Enlarged images
Real and magnified images
Answer: 2 🟢

Question 3
Magnification produced by a plane mirror is:
+1
–1
0
+2
Answer: 1 🧠

Question 4
Which type of lens is used to correct myopia?
Convex lens
Concave lens
Bifocal lens
Cylindrical lens
Answer: 2 🔵

Question 5
The power of a lens is –4 D. The lens is:
Concave, f = 25 cm
Convex, f = 25 cm
Concave, f = –25 cm
Convex, f = –25 cm
Answer: 3 🌿

Question 6
The unit of focal length is:
Dioptre
Metre
Centimetre
Second
Answer: 2 ✔️

Question 7
When light travels from air to glass:
It bends towards normal
It bends away from normal
It goes undeviated
It reflects completely
Answer: 1 💧

Question 8
A convex lens of focal length 10 cm is used. Its power is:
+10 D
+100 D
+20 D
+5 D
Answer: 3 ✨

Question 9
If an object is at the focus of a concave mirror, the image is formed:
At centre of curvature
At infinity
At focus itself
Between focus and pole
Answer: 2 🌟

Question 10
The image formed by a convex mirror for a real object is always:
Real and inverted
Virtual, erect, diminished
Virtual and magnified
Real and magnified
Answer: 2 🟢

Question 11
A: In a plane mirror, the image is always virtual and erect.
R: Magnification is always +1.
Both A and R true; R correct explanation
Both A and R true; R not explanation
A true; R false
A false; R true
Answer: 1 ✔️

Question 12
A: A convex lens converges light rays to a focus.
R: A convex lens is called a converging lens.
Answer: 1 🌿

Question 13
A: A concave mirror is used in car headlights.
R: It produces powerful parallel rays.
Answer: 1 🔦

Question 14
A: Virtual image formed by concave mirror is always diminished.
R: Object must be between focus and pole.
Answer: 3 ❌ (Virtual image is magnified)

Question 15
A: Power of a convex lens is positive.
R: Its focal length is taken negative.
Answer: 3 ⚡ (f is positive for convex)

Question 16
A: Refraction occurs due to change in speed of light.
R: Light changes its frequency at boundary.
Answer: 3 🟠 (frequency remains same)

Question 17
A: Real images can be obtained on screen.
R: They are always inverted.
Answer: 1 ✔️

Question 18
A: Convex mirror provides wider field of view.
R: Rays diverge after reflection.
Answer: 1 🚗

Question 19
A: A concave lens always forms virtual images.
R: Diverging nature prevents real convergence.
Answer: 1 🟡

Question 20
A: In lens formula, all distances are measured from optical centre.
R: Sign convention decides positive/negative values.
Answer: 1 🧠

Question 21
Define focal length of a concave mirror.
Answer:
🔵 Distance between pole (P) and focus (F).
🟢 Focus is point where parallel rays converge after reflection.

Question 22
What is meant by the power of a lens?
Answer:
🔴 Power = ability of lens to converge/diverge light.
✨ Formula: P (in dioptre) = 100 / f (f in cm).

Question 23
State Snell’s law of refraction.
Answer:
🌿 Ratio sin i / sin r = constant (refractive index).
💧 Incident ray, refracted ray, normal lie in same plane.

Question 24
What type of image is formed by convex mirror?
Answer:
🟢 Always virtual, erect, diminished.
🚗 Hence used as rear-view mirror.

Question 25
Why does a pencil appear bent when placed in water?
Answer:
🔵 Due to refraction of light at air–water interface.
🟡 Light from submerged part bends → apparent shift.

Question 26
What is the magnification of plane mirror?
Answer:
🌍 Magnification = +1.
✨ Image is same size, virtual, erect.

Question 27
List three uses of concave mirrors.
Answer:
🔦 In car headlights and torches.
🦷 As dentist’s mirror (magnified image).
☀️ Solar furnace (concentrates sunlight).

Question 28
An object is placed at 2F of a convex lens. Describe the image.
Answer:
🔵 Image formed at 2F.
🟢 Real, inverted, same size.
🟡 Opposite side of lens.

Question 29
Write differences between real and virtual images (3 points).
Answer:
🟠 Real → on screen; Virtual → not on screen.
🟣 Real → inverted; Virtual → erect.
🟤 Real → formed by actual ray convergence; Virtual → by apparent divergence.

Question 30
State Cartesian sign convention for spherical lenses.
Answer:
🔵 Object always left of lens → u negative.
🟢 Distances to right (real v) positive, left (virtual v) negative.
🟡 Heights above axis positive, below axis negative.

Question 31
Define refractive index. Write its formula.
Answer:
💧 Refractive index = ratio of speed of light in vacuum to that in medium.
Formula: n = c / v.
🌿 Higher n → denser medium.

Question 32
State conditions for image to be erect, magnified by concave mirror.
Answer:
🔵 Object placed between pole and focus.
🟢 Image behind mirror.
🟡 Virtual, erect, magnified.

Question 33
An object 4 cm tall is placed 30 cm from concave lens of f = –10 cm. Find position and size of image.
Answer:
Lens formula: 1/f = 1/v – 1/u
f = –10, u = –30
1/v = 1/–10 + 1/–30 = –0.1 – 0.033 = –0.133 → v = –7.5 cm.
Magnification m = v/u = –7.5 / –30 = 0.25.
Image size = 0.25 × 4 = 1 cm.
✔️ Image: 1 cm tall, erect, diminished, virtual.


Question 34
Explain the image formation in a concave mirror for different object positions with ray diagrams.
Answer
🔵 Object at infinity → image at F; real, inverted, highly diminished.
🟢 Object beyond C → image between C and F; real, inverted, diminished.
🟡 Object at C → image at C; real, inverted, same size.
🔴 Object between C and F → image beyond C; real, inverted, magnified.
🟣 Object at F → image at infinity; highly enlarged.
🟤 Object between F and P → image forms behind the mirror; virtual, erect, magnified.
✏️ Ray guide to draw: one ray parallel to principal axis (reflects through F) and one ray through C (reflects back along its path).

Question 35
Derive the mirror formula 1/f = 1/v + 1/u.
Answer
🔵 Setup: Concave mirror with pole P, focus F (PF = f). Object AB at distance u from P; real image A′B′ at distance v from P.
🟢 Geometry step 1 (similar triangles using heights):
From triangles formed near the pole, magnification m = h_i / h_o = − v / u.
🟡 Geometry step 2 (triangle with focus):
Using ray parallel to principal axis reflecting through F, another through C, similarity gives h_i / h_o = (v − f) / f.
🔴 Eliminate h_i / h_o:
− v / u = (v − f) / f.
🟣 Rearrangement (copy-safe algebra):
Multiply: − v f = u (v − f) → − v f = u v − u f.
Bring terms together: u v − u f + v f = 0.
Divide by u v f: (1/f) − (1/v) + (1/u) = 0 → 1/f = 1/v + 1/u.
✔️ Holds for spherical mirrors with proper sign convention (u negative for real objects in front; v sign depends on image side).

Question 36
Derive the lens formula 1/f = 1/v − 1/u.
Answer
🔵 Setup: Convex lens with optical centre O, principal focus F (OF = f). Object AB at distance u to the left of O; image A′B′ at distance v to the right of O.
🟢 Geometry step 1 (similar triangles): From standard ray diagram (one ray parallel through F, one through O), triangles give h_i / h_o = v / u.
🟡 Geometry step 2 (using focus triangle): A second pair of similar triangles gives h_i / h_o = (v − f) / f.
🔴 Eliminate heights: v / u = (v − f) / f.
🟣 Rearrangement (copy-safe algebra): v f = u (v − f) → v f = u v − u f.
Move terms: u v − v f − u f = 0.
Divide by u v f: (1/f) = (1/v) − (1/u).
✔️ With Cartesian signs: for convex lens f > 0; for concave lens f < 0; u is negative for objects on the left.

Question 37
Case: A student uses a convex lens of focal length 10 cm to form an image of a candle flame.
Answer
(a) 🔵 Image at infinity when object is at F → 10 cm from lens.
(b) 🟢 Real, inverted, same size image when object at 2F → 20 cm from lens.
(c) 🟡 Object at 6 cm (inside F) → image virtual, erect, magnified, formed on same side of lens as the object.
(d) 🔴 Lens formula (copy-safe): 1/f = 1/v − 1/u.

Question 38
Case: A car driver sees vehicles behind using a mirror.
Answer
(a) 🚗 Mirror used: Convex mirror (wide field of view).
(b) 🌿 Nature of image: Virtual and erect.
(c) 🟡 Size: Diminished (helps see more area).
(d) 🧠 Field of view: Wider than concave mirror or plane mirror at same size.

Question 39
Case: A doctor prescribes spectacles of power +2.0 D to a student.
Answer
(a) 🔵 Lens type: Convex (converging), because power is positive.
(b) 🟢 Focal length: f = 100 / P = 100 / 2.0 = 50 cm.
(c) 🟡 Corrected defect: Hypermetropia (long-sightedness).
(d) ✔️ After correction, the eye lens–spectacle system focuses a real, inverted, diminished image on the retina (which we perceive upright due to brain processing).

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MIND MAPS

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