Question

A ray of light passes through an equilateral prism such that the angle of incidence is equal to angle of emergence and each of these angles is equal to \( \frac{1}{3} \)rd the angle of prism. The angle of deviation is

• A. 35°
• B. 40°
• C. 20°
• D. 30°

Hint:

In a prism, the angle of deviation depends on the angle of incidence, angle of emergence, and the angle of the prism.

Answer 1

The Correct Option is D

Step 1: Understanding the angle of deviation.
The angle of deviation \( D \) for a prism is given by the relation: \[ D = i + e - A \] where \( i \) is the angle of incidence, \( e \) is the angle of emergence, and \( A \) is the angle of the prism.
Step 2: Using the given values.
It is given that \( i = e = \frac{A}{3} \), so we can substitute into the formula for \( D \): \[ D = \frac{A}{3} + \frac{A}{3} - A = \frac{2A}{3} - A = 30° \] Step 3: Conclusion.
Thus, the angle of deviation is 30°, which corresponds to option (D).