Question

A ray is incident at an angle of incidence $i$ on one surface of a small angle prism(with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu$. then the angle of incidence is nearly equal to:

• A. $\frac {A}{2\mu}$
• B. $\frac {2A}{\mu}$
• C. $\mu A$
• D. $\frac {\mu \,A}{2}$

Answer 1

Answer: (C)

$\mu A$

Answer 2

Light ray emerges from another surface normally, hence e(angle of emergence) = 0
$\Rightarrow r_{2}=0$
$r_{1}+r_{2}=A$
$\Rightarrow r_{1}=A$
Applying Snells law on first surface,
$1. sin\,i=\mu\,sin\,r_{1}$
For small angle, $sin\,\theta\, \approx\,\theta$ Hence,
$i=\mu\,A$