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QPages 365-366: Q11: HC Verma: Concepts of Physics - Volume 2 Photoelectric Effect and Wave-Particle Duality Pages 365-366: Q11 Solution: A sphere of radius 1.00 cm is placed in the path of a parallel…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume the force equals the incident momentum flux $I A/c$ regardless of absorption. However, reflected photons reverse their momentum, giving a change of $2p$ per photon. Thus the total force is $F=(I A/c)(1+r)$, where $r$ is the reflectivity. Only the incident part is independent of absorption; the total force is not.

A sphere of radius 1.00 cm is placed in the path of a parallel beam of light of large aperture. The intensity of the light is 0.5 W cm−20.5 \text{ W cm}^{-2}. If the sphere completely absorbs the radiation falling on it, show that the force on the sphere due to the light falling on it is the same even if the sphere is not perfectly absorbing.

Step-by-Step Verified Solution

**Answer:** The force is independent of the absorption property. **Step-by-Step Explanation:** For a perfectly absorbing sphere, F=IAcF = \frac{IA}{c}. For a perfectly reflecting sphere, F=2IAcF = \frac{2IA}{c}. For a partially absorbing/reflecting sphere, F=IAc(1+r)F = \frac{IA}{c}(1 + r), where rr is the reflection coefficient. In all cases, the force depends only on the power intercepted, not on the nature of absorption. Hence, the force is the same for a given cross-sectional area.

All Questions in this Chapter

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