Question

A ray of light is incident on one of the faces of the prism with an angle ${40}^{\circ }$ with the surfaces. The angle of the prism is ${60}^{\circ }$. The emergent ray deviates through an angle ${38}^{\circ }$ then, the angle of emergence is:

• A. ${38}^{\circ }$
• B. ${48}^{\circ }$
• C. ${52}^{\circ }$
• D. ${58}^{\circ }$

Answer 1

The correct option is D ${58}^{\circ }$

We know that

$f=i_1+i_2-A$

where,

$A=$ Angle of prism $={60}^o$

$f=$ angle of deviation $={38}^o$

$i_1=$ angle of incidence $={40}^o$

$i_2=$ energence angle . So,

${30}^o={40}^o+i_2-{60}^o$

${38}^o-{40}^o+{60}^o=i_2$

$\Rightarrow i_2={58}^o$

Option $D$ is correct