Optics Problem: Find Smallest Refractive Index of Slab

[arpon]

Homework Statement

Light falls on the surface AB of a rectangular slab from air. Determine the smallest refractive index n that the material of the slab can have so that all incident light emerges from the opposite face CD.

Homework Equations

The Attempt at a Solution

Let's think about this case:

There must be total internal reflection at Q and S.
That means, $90-r>\theta _c$ [$\theta _c$ is the critical angle]
$sin(90-r)>sin \theta _c$
$cos r > \frac{1}{n}$ [$sin \theta _c = \frac {1}{n}$]
$n>sec(r)$
But, the maximum value of $sec(r)$ is infinite.
That means n should be infinite.
But that is not the answer.

 

[DEvens]

Try it again. Write down the maximum $r$ in terms of arc-sin of something. Write down $\theta_C$ in terms of arc-sin of something. Then write down $90-r > \theta_C$ in terms of these arc-sin formulas. Don't forget that air has an index of refraction very close to 1. See what you get.

 

[arpon]

I have got the answer. :)

 

[emroz92]

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