A ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and the latter is equal to 3/4th of the angle of prism. The angle of deviation is

CONCEPT:

Angle of Deviation in a Prism

• The angle of deviation is the angle between the incident ray and the emergent ray when light passes through a prism.
• For an equilateral prism, the angle of the prism (A) is 60°.
• If the angle of incidence (i) is equal to the angle of emergence (e) and e = 3/4 A, then we can use these relationships to find the angle of deviation (D).

EXPLANATION:

• Let’s analyze the given conditions:
  • The angle of the prism (A) = 60°.
  • The angle of incidence (i) is equal to the angle of emergence (e).
  • The angle of emergence (e) = (3/4)A = (3/4) × 60° = 45°.
• Using the prism formula:
  • For minimum deviation, i = e and A = 60°.
  • The formula for angle of deviation (D) in a prism is:
    • D = i + e - A
  • Since i = e = 45°:
    • D = 45° + 45° - 60°
    • D = 90° - 60°
    • D = 30°

Therefore, the correct answer is option 4: 30°.