A ray of light passing through an equilateral prism is having velocity $$2.12 \times 10^8$$ m/s in the prism material, then the minimum angle of deviation is _______ degrees.

speed of light in medium:

v = c / n

so refractive index:

n = c / v = (3 × 10⁸) / (2.12 × 10⁸) ≈ 1.415

for equilateral prism:

A = 60°

at minimum deviation:

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

$$\sin\left(\frac{A}{2}\right)=\sin30°=0.5$$

so:

$$n=\frac{\sin\left(\frac{60+\delta_m}{2}\right)}{0.5}$$

$$\sin\left(\frac{60+\delta_m}{2}\right)=\frac{n}{2}\approx0.7075$$

$$\frac{60+\delta_m}{2}\approx45°$$

$$60+\delta_m\approx90°$$

$$\delta_m\approx30°$$