Q: A rectangular glass slab ABCD of refractive index n_{1} is immersed in water of refractive index n_{2} (n_{1} > n_{2}). A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence α_{max}, such that the ray comes out only from the other surface CD, is given by

(A) $\large sin^{-1}[\frac{n_1}{n_2}cos(sin^{-1}\frac{n_2}{n_1})]$

(B) $\large sin^{-1}[ n_1 cos(sin^{-1}\frac{1}{n_2})]$

(C) $sin^{-1}\frac{n_1}{n_2}$

(D)$ sin^{-1}\frac{n_2}{n_1}$

Ans: (A)

Sol: Let C = critical angle

n_{1} sinC= n_{2} sin90° ⇒ sinC = n_{2}/n_{1}

Applying Snell’s law at face *AB*

$\large \frac{n_1}{n_2} = \frac{sin\alpha_{max}}{sinr}$

$\large \frac{n_1}{n_2} = \frac{sin\alpha_{max}}{sin(90-C)}= \frac{sin\alpha_{max}}{cosC}$

$\large sin\alpha_{max} = \frac{n_1}{n_2}cosC$

$\large \alpha_{max} = sin^{-1}[\frac{n_1}{n_2}cosC]$

$\large \alpha_{max} = sin^{-1}[\frac{n_1}{n_2}cos(sin^{-1}\frac{n_2}{n_1})]$