Question

A liquid is placed in a hollow prism of angle ${60}^o$. If angle of the minimum deviated 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

The correct option is A $1.41$

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

$IE\parallel AC$

$i=e$

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

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

$x+\gamma =60$

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

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

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

$\begin{array}{cc}\left(1\right)\sin us& =\mu \sin 30\\ \mu & =\sqrt{2}=1.41\end{array}$

option (A) is correct