Question

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

• A. $\frac{A}{\mu }$
• B. $\frac{A}{\left(2\mu \right)}$
• C. $\mu A$
• D. $2\mu$

Answer 1

The correct option is C $\mu A$

The angle of incidence $=i$

The angle of prism $=A$

angle of emergence $=e$

The refrative index of the material of the

prism is $\mu$.

For a small angle prism, angle of deviation.

$\delta =(\mu -1)A-\left(1\right)$

Since, the ray emerges normally,

$\therefore e=0$

By the relation,

$A+\delta =i+e$

$\Rightarrow i=A+\delta \to$ (2)

$\delta =(i-A)$

from eqn.

(1) and (2)

$\Rightarrow (\mu -1)A=i-A$

$\therefore \mu A-A=i-A$

$i={\mu }_A$

Hence, (c) is correct option.