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. \(45^\circ\)
• B. \(42^\circ\)
• C. \(50^\circ\)
• D. \(52^\circ\)

Hint:

Critical angle: \( \sin C = \frac{1}{\mu} \). Always find refractive index first.

Answer 1

The Correct Option is A

Concept: Refractive index of prism in a medium: \[ \mu = \frac{\sin\left(\frac{A + D}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

Step 1: Substitute values.
\[ \mu = \frac{\sin(45^\circ)}{\sin(30^\circ)} = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}} = \sqrt{2} \]

Step 2: Find critical angle.
\[ \sin C = \frac{1}{\mu} = \frac{1}{\sqrt{2}} \Rightarrow C = 45^\circ \]