Question

When a glass prism of refracting angle ${60}^{\circ }$ is immersed in a liquid, its angle of minimum deviation is ${30}^{\circ }$. The critical angle of glass with respect to the liquid medium is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

$\mu =\frac{sin\left(\frac{A+d_M}{2}\right)}{sin\frac{A}{2}}=\frac{sin\left[\frac{60+30}{2}\right]}{sin\left[\frac{60}{2}\right]}\mu =\frac{sin{45}^{\circ }}{sin{30}^{\circ }}=\frac{\left(\frac{1}{\sqrt{2}}\right)}{\left(\frac{1}{2}\right)}=\sqrt{2}sinC=\frac{1}{\mu }=\frac{1}{\sqrt{2}}C={45}^{\circ }$