Question

A ray of monochromatic light is incident on the refracting face of a prism (angle ${75}^{\circ }$ It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the prism is $\sqrt{2}$, then the angle of incidence on the first face of the prism is

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${15}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

Answer: (D)

$\sin i_c=\frac{1}{\sqrt{2}}{i}_c={45}^{\circ }$

Now, ${75}^{\circ }=r+{45}^{\circ }$

or $r={30}^{\circ }$

Now, $\frac{\sin i}{\sin {30}^{\circ }}=\sqrt{2}$

or $\sin i=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}$

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