Question

Which condition is necessary for total internal reflection?

Answer 1

Answer:

The index of refraction of the first medium must be higher than the index of refraction of the second medium

Explanation:

Snell's law describes the behaviour of light at the boundary between two mediums:

$n_1 sin \theta_1 = n_2 sin \theta_2$

where

n1 and n2 are the index of refraction of the two mediums

$\theta_1, \theta_2$ are the angle between the direction of the light ray and the normal to the interface

We can rewrite the condition as:

$sin \theta_2 = \frac{n_1}{n_2} sin \theta_1$

Let's assume now that the light is travelling in the first medium with a very large angle with respect to the normal to the surface, i.e. $\theta_1 = 90^{\circ}$, so that $sin \theta_1=1$. In this case, we have

$sin \theta_2 = \frac{n_1}{n_2}$

We notice that if $n_1 > n_2$, the ratio on the right is larger than 1, and so the term $sin \theta_2$ should be also larger than 1: but this is not possible of course, since the sine function is always less than 1. Therefore, in this case total internal reflection occurs, because no refracted ray is produced.