Question

The refractive index of a prism with apex angle \( A \) is \( \cot \frac{A}{2} \). The angle of minimum deviation is:

• A. \( \delta_m = 180^\circ - A \)
• B. \( \delta_m = 180^\circ - 3A \)
• C. \( \delta_m = 180^\circ - 4A \)
• D. \( \delta_m = 180^\circ - 2A \)

Answer 1

The Correct Option is D

Given:

\[ \mu = \frac{\sin \left( \frac{A + \delta_m}{2} \right)}{\sin \frac{A}{2}} \]

Using the relation:

\[ \cos \frac{A}{2} = \sin \left( \frac{A + \delta_m}{2} \right) \]

We get:

\[ \delta_m = \pi - 2A \]

Therefore:

\[ \delta_m = 180^\circ - 2A \]