Question

A light ray is incident a glass sphere at an angle of incidence of ${45}^o$ as shown in figure. Find the total deviation suffered by ray of two successive reflection.

• A. ${45}^o$
• B. ${30}^o$
• C. ${60}^o$
• D. ${120}^o$

Answer 1

The correct option is B ${30}^o$

Now from a above image

At First reflection

$1\times Sin{45}^{\circ }=\sqrt{2}Sinr$

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

Since

$r=i$ (Both are symmetric)

Show at second reflection

$\sqrt{2}Sini=1\times Sin{r}^{\prime }$

$r^{\prime }={45}^{\circ }$

Now consider quadrilateral A O B C

$\angle A+\angle O+\angle B+\angle C$ = 360

$45+120+45+\angle C=360$

$\angle C=150$

Now $\angle C+S=180$

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

Hence (B) is correct answer