Question

Find the angle of deviation produced by the prism $(\mu =\sqrt{3})$ for the situation shown in the figure

• A. ${60}^{\circ }$ clockwise
• B. ${75}^{\circ }$ clockwise
• C. ${30}^{\circ }$ clockwise
• D. ${60}^{\circ }$ anticlockwise

Answer 1

The correct option is A ${60}^{\circ }$ clockwise


Applying Snell's law at surface $\text{AB}$ :

$1\times \sin {60}^{\circ }=\sqrt{3}\times \sin r_1$

$\sin r_1=\frac{1}{2}\Rightarrow r_1={30}^{\circ }$

Angle of prism ,$A=r_1+r_2$

$\Rightarrow r_2=60-30={30}^{\circ }$

Applying Snell's law at surface $\text{AC}$:

$\sqrt{3}\times \sin {30}^{\circ }=1\times \sin e$

$\Rightarrow e={60}^{\circ }$

$\Rightarrow$ Angle of deviation , $\delta =i+e-A$

Substituting the data obtained

$\delta ={60}^{\circ }+{60}^{\circ }-{60}^{\circ }$

$\Rightarrow \delta ={60}^{\circ }={60}^{\circ }$ clockwise.

Hence, option (a) is the correct answer.