Question

A liquid is placed in a hollow prism of angle ${60}^o$. If angle of the minimum deviation is ${30}^o$, what is the refractive index of the liquid?

• A. $1.41$
• B. $1.50$
• C. $1.65$
• D. $1.95$

Answer 1

Answer: (A)

$1.41$

$\text{Minimum deviation condition of a prism}$

$I\in \parallel AC$

$i=e$

${\gamma }_1={\gamma }_2=X$

${\gamma }_1+{\gamma }_2=A=60$

$\gamma +\gamma =60$

$\gamma ={30}^{\circ }$

$\begin{array}{cc}\delta =& i+e-A\\ 30=& 2i-60\\ i=90/2& \\ i={45}^{\circ }& \end{array}$

${\mu }_1\sin i_1={\mu }_2\sin {\gamma }_2$

(1) $\sin 45=\mu \sin 30$

$H=\sqrt{2}=1.41\text{option}A$