Question

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is ${30}^o$. One of the two refracting surface of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is?

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

Answer 1

The correct option is D ${45}^o$

Using $A=r_1+r_2$

$30=r_1+0$

so $r_1=30$

Using Snell's Law, $1\times sini=\mu \times sinr$

$1\times sini=\sqrt{2}\times sin30=\sqrt{2}3/2$

$sini=1/\sqrt{2}$

$i={45}^o$

option 4 is correct