Question

Find the value of angle of emergence for a emergent ray from the prism in the figure given below (assume a ray entering a $60^\circ$ equilateral prism at a specific angle). (refractive index $\mu = \sqrt{3}$ and air $\mu = 1$).

• A. 60°
• B. 45°
• C. 30°
• D. 90°

Hint:

In symmetric cases (minimum deviation), the light ray travels parallel to the base of the prism.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Refraction through a prism follows Snell's Law: $\mu_1 \sin i = \mu_2 \sin r$. The total deviation depends on the prism angle ($A$) and the angles of incidence and emergence.
Step 2: Detailed Explanation:
For many standard physics problems involving $\mu = \sqrt{3}$, at minimum deviation in an equilateral prism ($A = 60^\circ$): $\mu = \frac{\sin[(A + \delta_m)/2]}{\sin(A/2)}$ $\sqrt{3} = \frac{\sin[(60 + \delta_m)/2]}{\sin(30)}$ $\sqrt{3} \times 0.5 = \sin[(60 + \delta_m)/2] \implies \sin(60^\circ) = \frac{\sqrt{3}}{2}$. So, $(60 + \delta_m)/2 = 60 \implies \delta_m = 60^\circ$. At minimum deviation, $i = e$. $i = (A + \delta_m)/2 = (60+60)/2 = 60^\circ$.
Step 3: Final Answer:
The angle of emergence is 60°.