Question

A light ray is incident on a glass sphere at angle of incidence ${60}^0$ as shown. Then the total deviation after two refraction is

• A. ${30}^0$
• B. ${60}^0$
• C. ${90}^0,$
• D. ${20}^0,$

Answer 1

The correct option is B ${60}^0$

$\begin{array}{c}Applyingsnel{l}^{\prime }slaw\\ 1\sin {60}^0=\sqrt{3}\sin r\\ \Rightarrow r={30}^0\\ Forsymmetry{r}^{\prime }=r={30}^0\\ Againapplyingsnel{l}^{\prime }slawat\sec ondsurface\\ 1\sin e=\sqrt{3}\sin r\\ r={60}^0\\ Divationatfirstsurface=i=r={60}^0-{30}^0={30}^0\\ Deviationat\sec ondsurface=e-r={60}^0-{30}^0={30}^0\\ \therefore totaldeviation={60}^0\\ Hence,theoptionBisthecorrectanswer.\end{array}$