Answer to Question #122085 in Physics for Mio

Question #122085
What is the reason for total internal reflections? What are the conditions for it to occur?
1
Expert's answer
2020-06-15T10:35:06-0400

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 θ1\theta_1 and refraction θ2\theta_2 of light when it falls on the boundary between two mediums, are connected according to the Snell's law:


sinθ1sinθ2=n2n1\dfrac{\sin{\theta_1 }}{\sin{\theta_2}} = \dfrac{n_2}{n_1}

where n1n_1 and n2n_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

θ2>θ1\theta_2>\theta_1

if

n1>n2n_1>n_2

.

Obviously, the refraction angle can not exceed 90 degrees. Thus, in the limit case θ2=90°\theta_2 = 90\degree , the angle of incident will be:


θ1=arcsin(n2n1)\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 n1>n2n_1>n_2, otherwise we get asine of the number that is greater then 1.


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