Question

If one face of a prism of prism angle ${30}^o$ and $\mu \sqrt{2}$ is silvered, the incident ray retraces its intial path. The angle of incidence is:

• A. ${60}^o$
• B. ${30}^o$
• C. ${45}^o$
• D. ${90}^o$

Answer 1

The correct option is A ${60}^o$

For incident light ray to retrace it's initial path, it should fall normally on the silvered surface.

Given, prism angle, $A=30{}^{\circ }$

Let the angle of incidence be $i$

From the figure,

$x=90-A=60{}^{\circ }$

$x+r=90{}^{\circ }\Rightarrow \angle r=30{}^{\circ }$

Thus, angle of refraction $\angle r=30{}^{\circ }$

Now, applying Snell's law at the surface DE, we have

$\mu =\frac{Sini}{Sinr}$

$Sini=Sinr\times \mu$

$Sini=Sin30\times \sqrt{2}$

$i=Si{n}^{-1}\left(\frac{\sqrt{2}}{2}\right)$

$i=Si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)$

$i=45{}^{\circ }$

Hence, the answer is OPTION C.