Question

A ray is incident at an angle of incidence $i$ on one 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 $i$ is nearly equals to :

• A. $\mu A/2$
• B. $A/2\mu$
• C. $\mu A$
• D. $A/\mu$

Answer 1

The correct option is C $\mu A$

Given data:
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 is $\mu$.
For a small angle prism, angle of deviation, $\delta =(\mu -1)A$ .......(i)

Since, the ray emerges normally, $\therefore e=0$

By the relation,

$A+\delta =i+e$

We have, $i=A+\delta$

or $\delta =(i-A)$ .........(ii)

From Eqs. (i) and (ii)

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

$\Rightarrow i=\mu A$.