Question

A ray incident at an angle ${53}^o$ on a prism emerges at an angle at ${37}^o$ as shown. If the angle of incidence is made ${50}^o$, which of the following is a possible value of the angle of emergence.

• A. ${35}^o$
• B. ${42}^o$
• C. ${40}^o$
• D. ${38}^o$

Answer 1

The correct option is D ${38}^o$

By snell's law of refraction

$\mu =\frac{sin{53}^0}{sin{r}_1}$ at first refraction on surface AB

$\mu =\frac{sin{37}^0}{sin{r}_2}$ at surface AC

when $\angle i$ decreases it means angle $\angle r_1$ also decreases because refractive index is constant.

from the following reason we can conclude that

$\angle r_1+\angle r_2={180}^0-A$

when $\angle r_1$ decreases then angle $\angle r_2$ must increase.

therefore if $\angle r_2$ increases then $\angle e$ also increases.

In short we can say that if $\angle i$ slightly decreases then $\angle e$ slightly increases and vice versa

By solving equation 1 and 2 we get,

if angle of incidence become 50 degree then angle of emergence become 38 degree.

Option D is correct.