question_answer

A beam of monochromatic light reflects and refracts at point A, as shown in the diagram. Find the angle of refraction at point A.

A)  \[{{60}^{o}}\]                   

B)  \[{{45}^{o}}\]

C)  \[{{30}^{o}}\]                                   

D)  None of these

Correct Answer: C

Solution :

                By Snells law                 \[\frac{\sin i}{\sin r}=\frac{{{n}_{2}}}{{{n}_{1}}}\]              \[[\because \,\,i=(90-30)]\]                 \[\frac{\sin {{60}^{o}}}{\sin r}=\frac{\sqrt{3}}{1}\]                 \[\frac{\sqrt{3}}{2\sin r}=\frac{\sqrt{3}}{1}\]                 \[\sin r=\frac{1}{2}\]                 \[\sin r=\sin {{30}^{o}}\]                                 \[r={{30}^{o}}\] So, the angle of refraction at point A is \[{{30}^{o}}\].