Question

A ray is incident at a small angle of incidence $i$ on one face of a prism with angle of prism $6^{\circ }$ and emerges from the second face. If the prism is dipped in transparent liquid of refractive index $1.2$ and angle of deviation is $2^{\circ }$, then what is the refractive index of prism material?

• A. $1.20$
• B. $1.82$
• C. $1.60$
• D. $1.98$

Answer 1

The correct option is C $1.60$

The angle of deviation by thin prism is given by,

$\delta ={(}^1{\mu }_2-1)\text{A}$

$\Rightarrow 2^{\circ }=(\frac{\mu }{1.2}-1)\times 6^{\circ }$

$\Rightarrow \frac{2}{6}=\frac{\mu }{1.2}-1$

$\Rightarrow \frac{\mu }{1.2}=\frac{1}{3}+1=\frac{4}{3}$

$\Rightarrow \mu =\frac{4\times 1.2}{3}=1.60$