A perfectly reflecting hollow conical surface is placed with its axis parallel to an incident collimated light beam. The entire beam of power 30 W strikes the inner conical surface and is specularly reflected. The semi-vertical angle of the cone is 30°. Take c = 3×10⁸ m·s⁻¹. If the net force on the cone along its axis is N×10⁻⁸ N, find N.
Physics · Photoelectric effect and dual nature of matter · question based on photoelectric effect
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Question

A perfectly reflecting hollow conical surface is placed with its axis parallel to an incident collimated light beam. The entire beam of power 30 W strikes the inner conical surface and is specularly reflected. The semi-vertical angle of the cone is 30°. Take c = 3×10⁸ m·s⁻¹. If the net force on the cone along its axis is N×10⁻⁸ N, find N.

Physics · Photoelectric effect and dual nature of matter · question based on photoelectric effect

G1 Physics · Accepted Answer

For a specularly reflecting cone whose axis is parallel to the incident beam, the axial momentum change of reflected radiation gives F = 2P sin²α ÷ c, where α is the semi-vertical angle. Here, P = 30 W, α = 30°, sin30° = 1 ÷ 2. Thus, F = 2×30×(1 ÷ 2)² ÷ (3×10⁸) = 60×1 ÷ 4 ÷ (3×10⁸) = 15 ÷ (3×10⁸) = 5×10⁻⁸ N. Hence N = 5.