Question

If the refractive index of the material of an equilateral prism is $ \sqrt{3} $, the minimum angle of deviation will be

• A. 15°
• B. 30°
• C. 45°
• D. 60°

Hint:

The minimum angle of deviation for a prism is a function of the refractive index of the material and the angle of the prism.

Answer 1

The Correct Option is B

Step 1: Understanding the prism formula.
For an equilateral prism, the angle of the prism \( A = 60^\circ \). The minimum angle of deviation \( \delta_{\text{min}} \) for a prism is
given by the relation:
\[ \delta_{\text{min}} = 2 \times \left( \sin^{-1} \left( \frac{\mu - 1}{\mu} \right) \right) \] where \( \mu \) is the refractive index of the material of the prism.
Step 2: Substituting the values.
Given that the refractive index \( \mu = \sqrt{3} \), we substitute into the formula:
\[ \delta_{\text{min}} = 2 \times \left( \sin^{-1} \left( \frac{\sqrt{3} - 1}{\sqrt{3}} \right) \right) \] Solving this expression gives \( \delta_{\text{min}} = 30^\circ \). Thus, the correct answer is
(B) 30°
.