Light — Propagation, Reflection and Refraction; Mirrors and Lenses

Overview

Light is a fundamental topic in the MAHA TET Paper II Science section, forming the basis for understanding optical phenomena that students encounter daily—shadows, mirror images, bending of objects in water, and how spectacles work. This topic carries consistent weightage and tests both conceptual understanding and numerical problem-solving ability.

For the exam, you must master three core areas: how light travels (propagation), how it bounces off surfaces (reflection), and how it bends when passing between media (refraction). Questions typically involve ray diagrams, mirror and lens formulas, and real-life applications. The pedagogy angle often asks how to demonstrate these concepts using simple classroom experiments.

Understanding light also connects to other syllabus topics like the human eye, solar energy, and optical instruments, making it a high-value area for integrated learning.

Key Concepts

**Light travels in straight lines** (rectilinear propagation) — this explains shadow formation, eclipses, and pinhole cameras.

**Speed of light** in vacuum is approximately 3 × 10⁸ m/s; it slows down in denser media like water or glass.

**Reflection** occurs when light bounces off a surface; the angle of incidence equals the angle of reflection (measured from the normal).

**Plane mirrors** produce virtual, erect, laterally inverted images of the same size as the object, located at the same distance behind the mirror.

**Spherical mirrors** (concave and convex) form images based on the position of the object relative to the focus and centre of curvature.

**Refraction** is the bending of light when it passes from one medium to another due to change in speed.

**Refractive index** (n) = speed of light in vacuum / speed of light in medium; higher n means denser medium.

**Lenses** (convex and concave) refract light to converge or diverge rays, forming real or virtual images depending on object position.

Formulas / Key Facts

**Mirror Formula:** 1/v + 1/u = 1/f (v = image distance, u = object distance, f = focal length)

**Lens Formula:** 1/v − 1/u = 1/f (same symbols; sign convention must be applied)

**Magnification (mirrors and lenses):** m = h'/h = −v/u (h' = image height, h = object height; negative m means inverted image)

**Snell's Law of Refraction:** n₁ sin i = n₂ sin r (n = refractive index, i = angle of incidence, r = angle of refraction)

**Refractive Index:** n = c/v = real depth / apparent depth

**Relationship between f and R (spherical mirrors):** f = R/2 (R = radius of curvature)

**Power of a Lens:** P = 1/f (in metres) Unit: Dioptre (D); convex lens has positive power, concave has negative.

**Sign Convention (New Cartesian):**

All distances measured from the pole/optical centre.
Distances in direction of incident light are positive.
Heights above principal axis are positive.

Worked Examples

### Example 1: Plane Mirror **Q:** A boy stands 2 m in front of a plane mirror. How far is his image from him?

**Solution:** Image distance behind mirror = object distance = 2 m Total distance from boy to image = 2 + 2 = **4 m**

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### Example 2: Concave Mirror **Q:** An object is placed 30 cm from a concave mirror of focal length 15 cm. Find image position and nature.

**Solution:** Using mirror formula: 1/v + 1/u = 1/f Sign convention: u = −30 cm, f = −15 cm (concave mirror)

1/v + 1/(−30) = 1/(−15) 1/v = −1/15 + 1/30 = (−2 + 1)/30 = −1/30 v = −30 cm

Image is at 30 cm in front of the mirror (same side as object). m = −v/u = −(−30)/(−30) = −1

**Nature:** Real, inverted, same size as object (formed at centre of curvature).

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### Example 3: Refraction and Snell's Law **Q:** Light passes from air (n = 1) into glass (n = 1.5) at an angle of incidence of 30°. Find the angle of refraction.

**Solution:** n₁ sin i = n₂ sin r 1 × sin 30° = 1.5 × sin r 0.5 = 1.5 × sin r sin r = 0.5/1.5 = 1/3 ≈ 0.333 r = sin⁻¹(0.333) ≈ **19.5°**

Light bends towards the normal when entering a denser medium.

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### Example 4: Lens Power **Q:** A convex lens has a focal length of 25 cm. Find its power.

**Solution:** P = 1/f (f must be in metres) f = 25 cm = 0.25 m P = 1/0.25 = **+4 D**

Common Mistakes

**Confusing focal length signs:** Students often forget that for concave mirrors and convex lenses, f is taken as negative and positive respectively under the New Cartesian convention used in Indian textbooks. → Always write sign convention first before solving.

**Measuring angles from the surface instead of the normal:** Both reflection and refraction laws define angles from the normal (perpendicular), not the mirror or boundary surface. → Draw the normal first in every ray diagram.

**Mixing up mirror and lens formulas:** Mirror formula has a plus sign (1/v + 1/u), lens formula has a minus sign (1/v − 1/u). → Remember: "Mirror mein milao" (add in mirror).

**Ignoring units in power calculation:** Focal length must be converted to metres before calculating power in dioptres. → A lens with f = 50 cm has P = 2 D, not 0.02 D.

**Assuming all images from convex lenses are real:** When the object is between the lens and focus, a convex lens forms a virtual, erect, magnified image (like a magnifying glass). → Learn image formation for all object positions.

Quick Reference

Light travels in straight lines; speed in vacuum = 3 × 10⁸ m/s.
Angle of incidence = Angle of reflection (always from normal).
Concave mirror: converging; Convex mirror: diverging, always virtual image.
Convex lens: converging; Concave lens: diverging, always virtual image.
Snell's Law: n₁ sin i = n₂ sin r; light bends towards normal in denser medium.
Power (D) = 1/f (m); positive for convex lens, negative for concave lens.

Light