Question

A ray of light is incident at an angle of incidence $i$ on one surface of a thin prism $($with angle of prism $A$$)$ and emerges normally from the other face. If the refractive index of the prism is $n$. then the angle of incidence is nearly equal to :

• A. $nA$
• B. $\frac{2A}{n}$
• C. $\frac{A}{2n}$
• D. $\frac{nA}{2}$

Answer 1

The correct option is A $nA$

Ray diagram for given question,



Given,
Angle of the prism $=A$
Angle of incidence$=i$

Let, the angle of emergence be ${}^{\prime }e{}^{\prime }$ and refractive index of the material of the prism be $n$.

For a small angle of prism,
angle of deviation $\delta$ is given by,
$\delta =(n-1)A......\left(1\right)$

The ray emerges normally,
$\therefore e=0$

By the relation,
$\delta =i+e-A$

we get , $\delta =i-A......\left(2\right)$

From Eqs. $\left(1\right)$ and $\left(2\right)$

$(i-A)=(n-1)A$

$\Rightarrow i=nA$

Hence, option (a) is the correct answer.