A rectangular glass slab ABCD of refractive index n1 is immersed in water of refractive index n2 (n1 > n2).

Q: A rectangular glass slab ABCD of refractive index n1 is immersed in water of refractive index n2 (n1 > n2). A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence αmax, such that the ray comes out only from the other surface CD, is given by

Numerical

(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

n1 sin⁡C= n2 sin⁡90°  ⇒ sin⁡C = n2/n1

Applying Snell’s law at face AB

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

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

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

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

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

 

Author: Rajesh Jha

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