Question:
The refractive index of a prism with apex angle \( A \) is \( \cot \frac{A}{2} \). The angle of minimum deviation is:
The refractive index of a prism with apex angle \( A \) is \( \cot \frac{A}{2} \). The angle of minimum deviation is:
Updated On: Nov 20, 2024
- \( \delta_m = 180^\circ - A \)
- \( \delta_m = 180^\circ - 3A \)
- \( \delta_m = 180^\circ - 4A \)
- \( \delta_m = 180^\circ - 2A \)
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The Correct Option is D
Solution and Explanation
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:
\[ \delta_m = 180^\circ - 2A \]
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