Answer to Question #122085 in Physics for Mio

Question

What is the reason for total internal reflections? What are the conditions for it to occur?

Answer 1

The reason for total internal reflections is that the wave can not pass through the boundary of two mediums, when comes to it at some slanting enough angle from the medium with greater refractive indices. The geometric optics provides the following explanation and the condition for this phenomenon.

The angles of incident $\theta_1$ and refraction $\theta_2$ of light when it falls on the boundary between two mediums, are connected according to the Snell's law:

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

where $n_1$ and $n_2$ are refractive indices of the initial medium, where light propagated before the incidence and the second one respectively.

One can notice from here that the greater the angle of incident, the greater the refraction angle should be, but also holds

$$\theta_2>\theta_1$$

if

$$n_1>n_2$$

.

Obviously, the refraction angle can not exceed 90 degrees. Thus, in the limit case $\theta_2 = 90\degree$ , the angle of incident will be:

$$\theta_1 = \arcsin\left(\dfrac{n_2}{n_1}\right)$$

This is the limit angle for total internal reflections. As one can note, this angle exists only in case $n_1>n_2$, otherwise we get asine of the number that is greater then 1.