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:
[tex]n_1 sin \theta_1 = n_2 sin \theta_2[/tex]
where
n1 and n2 are the index of refraction of the two mediums
[tex]\theta_1, \theta_2[/tex] are the angle between the direction of the light ray and the normal to the interface
We can rewrite the condition as:
[tex]sin \theta_2 = \frac{n_1}{n_2} sin \theta_1[/tex]
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. [tex]\theta_1 = 90^{\circ}[/tex], so that [tex]sin \theta_1=1[/tex]. In this case, we have
[tex]sin \theta_2 = \frac{n_1}{n_2}[/tex]
We notice that if [tex]n_1 > n_2[/tex], the ratio on the right is larger than 1, and so the term [tex]sin \theta_2[/tex] 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.
