Question

A ray of light is incident on one face of a prism $(\mu =1.5)$ at an angle of ${60}^{\circ }.$ The refracting angle of the prism is also ${60}^{\circ }.$ Find the angle of emergence & angle of deviation?
$(\sin {25}^{\circ }=0.42,\sin {39}^{\circ }=0.63)$

• A.
  ${39}^{\circ },{39}^{\circ }$
• B.
  ${39}^{\circ },{60}^{\circ }$
• C.
  ${60}^{\circ },{39}^{\circ }$
• D.
  ${25}^{\circ },{39}^{\circ }$

Answer 1

The correct option is A

${39}^{\circ },{39}^{\circ }$

Given, angle of incidence, $\angle i={60}^{\circ }$

At point P, using Snell's Law we get,

${\mu }_{air}\times \sin {60}^{\circ }=\mu \times \sin r_1$

$\Rightarrow \sin r_1=\frac{1}{\sqrt{3}}\Rightarrow r_1={35}^{\circ }$

Using, $A=r_1+r_2$

$\Rightarrow r_2=A-r_1={60}^{\circ }-{35}^{\circ }={25}^{\circ }$

At point $Q,$ using Snell's law we get,

$\therefore \mu \times \sin r_2={\mu }_{air}\times \sin e$

$\Rightarrow \sin e=1.5\sin \left({25}^{\circ }\right)=0.63$

$\therefore e={39}^{\circ }$

Angle of deviation ,

$\delta =(i+e)-A={60}^{\circ }+{39}^{\circ }-{60}^{\circ }$

$\therefore \delta ={39}^{\circ }$

Hence, option (a) is the correct answer.

Why this question ? To understand the basic relations between different angles in case of prism.