# Problem on optics

1. Jun 9, 2015

### arpon

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution

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.

2. Jun 9, 2015

### 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.

3. Jun 9, 2015

### arpon

I have got the answer. :)

4. Jun 9, 2015

### emroz92

..

Last edited: Jun 9, 2015