Light — Reflection and Refraction

Why This Chapter Matters

Light chapter is one of the highest-scoring in Class 10 Physics — 10-14 marks in board exams. Mirror formula, lens formula, power of lens, and ray diagrams are tested every year. Numerical problems are essential.

Prerequisites

•Basic ray diagrams from Class 7-8

•Rectilinear propagation of light

•Basic geometry (angles, triangles)

Core Concepts

1. Reflection of Light

Laws of Reflection:

1.Angle of incidence = Angle of reflection (∠i = ∠r)

2.Incident ray, reflected ray, and normal — all lie in the same plane

Terms:

•Normal: Perpendicular to mirror surface at point of incidence

•Angle of incidence (i): Between incident ray and normal

•Angle of reflection (r): Between reflected ray and normal

2. Spherical Mirrors

Types:

•Concave mirror: Reflecting surface is inward-curved (like inside a bowl). Used in torches, headlights, shaving mirrors, dental mirrors.

•Convex mirror: Reflecting surface is outward-curved. Used in rear-view mirrors, security mirrors.

Key terms:

•Centre of curvature (C): Centre of sphere from which mirror is part

•Principal focus (F): Point where parallel rays converge (concave) or appear to diverge from (convex) after reflection

•Focal length (f): Distance from mirror to focus (f = R/2, where R = radius of curvature)

•Pole (P): Centre of mirror surface

Sign convention (New Cartesian):

•All distances measured from pole

•Distances in direction of incident light = positive (+)

•Distances opposite to incident light = negative (−)

•Heights above principal axis = positive (+)

•Heights below = negative (−)

3. Mirror Formula

$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$

Magnification:

$$m = \frac{-v}{u} = \frac{h_i}{h_o}$$

•m positive → virtual, erect image

•m negative → real, inverted image

•|m| > 1 → image enlarged

•|m| < 1 → image diminished

4. Image Formation by Concave Mirror

Object Position	Image Position	Nature	Size

|---|---|---|---|

At infinity	At F	Real, inverted	Point/highly diminished
Beyond C	Between F and C	Real, inverted	Diminished
At C	At C	Real, inverted	Same size
Between C and F	Beyond C	Real, inverted	Enlarged
At F	At infinity	Real, inverted	Highly enlarged
Between P and F	Behind mirror	Virtual, erect	Enlarged

Convex mirror: Always forms virtual, erect, diminished image behind mirror (regardless of object position) — that's why used as rear-view mirror (wider field of view).

5. Refraction of Light

Refraction: Bending of light as it passes from one medium to another.

Cause: Change in speed of light in different media.

Laws of Refraction:

1.Incident ray, refracted ray, and normal — all in same plane

2.Snell's Law: n₁ sin i = n₂ sin r (the ratio is constant)

Refractive index (n):

$$n = \frac{\text{Speed of light in vacuum (c)}}{\text{Speed of light in medium (v)}} = \frac{c}{v}$$

•n > 1 for all media (light slows down in media)

•Higher n = denser medium = more bending

•n of water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42

Light bends TOWARDS normal when entering denser medium, AWAY from normal when entering rarer medium.

6. Lenses

Convex (converging) lens: Thicker in middle, converges parallel rays to a focal point.

Concave (diverging) lens: Thinner in middle, diverges parallel rays.

7. Lens Formula

$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$

Magnification for lens:

$$m = \frac{v}{u}$$

8. Power of Lens

$$P = \frac{1}{f}$$

•f in metres → P in Dioptre (D)

•Convex lens: positive power (positive f)

•Concave lens: negative power (negative f)

•For combination: P_total = P₁ + P₂ + P₃ + ...

9. Image Formation by Convex Lens

Object Position	Image	Nature	Size

|---|---|---|---|

At infinity	At F₂	Real, inverted	Point
Beyond 2F₁	Between F₂ and 2F₂	Real, inverted	Diminished
At 2F₁	At 2F₂	Real, inverted	Same size
Between 2F₁ and F₁	Beyond 2F₂	Real, inverted	Enlarged
At F₁	At infinity	Real, inverted	Very large
Between F₁ and O	Same side as object	Virtual, erect	Enlarged

Solved Examples

Example 1 — Mirror Formula

Q: An object is placed at 30 cm from a concave mirror of focal length 15 cm. Find image position.

u = −30 cm, f = −15 cm (concave mirror)

1/v + 1/u = 1/f

1/v + 1/(−30) = 1/(−15)

1/v = −1/15 + 1/30 = −2/30 + 1/30 = −1/30

v = −30 cm (real, in front of mirror)

Magnification: m = −v/u = −(−30)/(−30) = −1 (same size, inverted, real)

Example 2 — Power of Lens

Q: A lens has focal length +50 cm. What is its power?

f = +50 cm = +0.5 m

P = 1/f = 1/0.5 = +2 D (converging lens)

PYQs

2023

Q: An object is placed at a distance of 15 cm from a convex lens of focal length 10 cm. Find image distance and magnification.

u = −15 cm, f = +10 cm

1/v − 1/u = 1/f

1/v − 1/(−15) = 1/10

1/v = 1/10 − 1/15 = 3/30 − 2/30 = 1/30

v = +30 cm (real, inverted, on other side)

m = v/u = 30/(−15) = −2 (inverted, twice the size)

2022

Q: Why does a ray of light bend when it travels from one medium to another?

Light travels at different speeds in different media. When light enters a denser medium (glass from air), it slows down and bends towards the normal. When entering a rarer medium, it speeds up and bends away from the normal.

2021

Q: Define focal length of a concave mirror. What is the relationship between focal length and radius of curvature?

Focal length = distance between pole and principal focus of mirror.

Relationship: f = R/2 (focal length is half the radius of curvature).

MCQ Practice

Q1. Which mirror is used as a rear-view mirror in vehicles?

(A) Plane (B) Concave (C) Convex ✓ (D) Cylindrical

[Convex — provides wider field of view]

Q2. Power of a concave lens is:

(A) Positive (B) Zero (C) Negative ✓ (D) Infinite

[Concave = diverging = negative focal length = negative power]

Q3 (Hard). Object placed 20 cm from concave mirror, image 30 cm behind mirror. Focal length?

u = −20 cm, v = +30 cm (behind mirror → virtual → positive)

1/f = 1/v + 1/u = 1/30 + 1/(−20) = 2/60 − 3/60 = −1/60

f = −60 cm (concave mirror → focal length negative)

Revision Notes

MIRROR FORMULA: 1/v + 1/u = 1/f
LENS FORMULA:   1/v − 1/u = 1/f

SIGN CONVENTION (New Cartesian):
  Everything from pole/optical centre
  Direction of incident light = positive
  Against incident light = negative

CONCAVE MIRROR: f negative, real focus
CONVEX MIRROR: f positive, virtual focus
CONVEX LENS: f positive, converging
CONCAVE LENS: f negative, diverging

MAGNIFICATION:
  Mirror: m = −v/u
  Lens: m = v/u
  m positive = virtual, erect
  m negative = real, inverted

POWER: P = 1/f(m)   Unit: Dioptre (D)
Combined lenses: P = P₁ + P₂

REFRACTIVE INDEX: n = c/v = sin i/sin r
Denser medium: light bends towards normal, n > 1, slower speed

Common Mistakes:

❌ Mirror formula same as lens formula — they're DIFFERENT (check signs)

❌ Forgetting to use metres in power calculation (P = 1/f requires f in metres)

❌ Convex mirror always forms virtual image — but forgetting it's also always diminished and erect

Light - Reflection and Refraction