5 The refractive index of the material of a glass prism is $$\sqrt{3}$$. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

Refractive index $$\mu = \sqrt{3}$$ and angle of minimum deviation $$\delta_m$$ equals the angle of the prism A.

Use the prism formula at minimum deviation:

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

Given $$\delta_m = A$$:

$$\sqrt{3} = \frac{\sin\left(\frac{A+A}{2}\right)}{\sin\left(\frac{A}{2}\right)} = \frac{\sin A}{\sin(A/2)}$$

Apply double angle formula:

$$\sqrt{3} = \frac{2\sin(A/2)\cos(A/2)}{\sin(A/2)} = 2\cos(A/2)$$

$$\cos(A/2) = \frac{\sqrt{3}}{2}$$

$$A/2 = 30°$$

$$A = 60°$$

The correct answer is Option 1: 60°.