Mirrors and Plane Refraction — Part 2: Refraction, apparent depth and total internal reflection: visual lesson, ISC Class 12 Physics

Lesson

Refraction at Plane Surfaces

Part 2 — light bending at flat boundaries: Snell’s law, slabs, apparent depth and total internal reflection.

In this lesson you will

Apply Snell’s law and relative refractive indices to rays crossing several parallel media, and find the lateral shift through a slab
Calculate real and apparent depth and the apparent shift through a slab or liquid
Relate the critical angle to refractive index and explain total reflecting prisms and optical fibres

Concept

Refraction and Snell’s law

When light crosses from one medium into another it changes speed and, unless it meets the boundary normally, its direction. Laws of refraction: (1) the incident ray, the refracted ray and the normal lie in one plane; (2) Snell’s law: $n_1\sin i = n_2\sin r \qquad\text{or}\qquad \dfrac{\sin i}{\sin r} = {}_1n_2$

Absolute refractive index $n = c/v$ : the speed in vacuum over the speed in the medium.
Into a denser medium (larger n) the ray bends towards the normal; into a rarer one, away from it.
Frequency does not change; speed and wavelength fall by the factor n.

Concept

Relative refractive index

The refractive index of medium 2 relative to medium 1: ${}_1n_2 = \dfrac{\sin i}{\sin r} = \dfrac{n_2}{n_1} = \dfrac{v_1}{v_2}$

Reversibility: ${}_2n_1 = \dfrac{1}{{}_1n_2}$ (a ray retraces its path).
Example: ${}_an_w = 1.33$ , ${}_an_g = 1.50$ , so ${}_wn_g = \dfrac{1.50}{1.33} = 1.13$ .

Table of refractive indices of air, water, crown glass and diamond with the speed of light in each, equal to c divided by n
Medium	Refractive index n	Speed of light (× 10⁸ m s⁻¹)
Air	1.0003 (taken as 1)	3.00
Water	1.33	2.26
Crown glass	1.52	1.97
Diamond	2.42	1.24

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