Question

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

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

Answer 1

The correct option is C $\mu A$


Given:
The angle of incidence = $i$
The angle of the prism = $A$
The angle of emergence = $e$
The refractive index of the material of the prism = $\mu$
For thin prism, angle of deviation, $\delta =(\mu -1)A$----(1)
Since, the ray emerges normally, $e=0$
By the relation,
$\delta =i_1+i_2-A$
$\Rightarrow \delta =i+e-A$
or $\delta =i-A$-------(2)
From equation (1) and (2)
$(i-A)=(\mu -1)A$
$i=\mu A$