Question

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

• A. ${42}^o$
• B. ${45}^o$
• C. ${50}^o$
• D. ${52}^o$

Answer 1

Answer: (B)

${45}^o$

Given,

Refracting angle is ${60}^{\circ }$ Devaition is ${30}^{\circ }$

Using relation:

$\mu =\frac{\sin \left(\frac{1}{2}\right(A+{\delta }_m\left)\right)}{\sin \frac{1}{2}A}=\frac{\sin \left(\frac{60+30}{2}\right)}{\sin \frac{60}{2}}=\sqrt{2}$

$\Rightarrow \frac{1}{\sin i_c}=\sqrt{2}$ Where $i_c$ is the crictical angle

Thus $i_c={45}^{\circ }$