Question

A light ray is incident on a glass sphere at an angle of incidence ${60}^{o}asshown.Thentheangles$r, r, e$ and the total deviation after two refraction are

• A. ${30}^o,{30}^o{60}^o$ and ${60}^o$
• B. ${60}^o,{60}^o{30}^o$ and ${30}^o$
• C. ${60}^o,{30}^o{60}^o$ and ${30}^o$
• D. ${30}^o,{60}^o{30}^o$ and ${60}^o$

Answer 1

The correct option is A ${30}^o,{30}^o{60}^o$ and ${60}^o$

Applying snell's law

$\begin{array}{c}{n}_1\sin i=n_2\sin r\\ n_1\sin {60}^{\circ }=\sqrt{3}\sin r\\ n_1\frac{\sqrt{3}}{2}=\sqrt{3}\sin r\\ \sin r=\frac{1}{2}\\ r={30}^{\circ }\\ fromsymmetryr={30}^{\circ }\end{array}$

Again applying Snell's law at the second surface

$\begin{array}{c}\sin e=\sqrt{3}\sin r\\ \sin e=\sqrt{3}\frac{1}{2}=\frac{\sqrt{3}}{2}\\ e={30}^{\circ }\end{array}$

Deviation at first surface $=i-r={60}^{\circ }-{30}^{\circ }={30}^{\circ }$

Deviation at second surface $=i-r={60}^{\circ }-{30}^{\circ }={30}^{\circ }$

Total deviation $={60}^{\circ }$

Option A.