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QPage 363: Q3: HC Verma: Concepts of Physics - Volume 2 Photoelectric Effect and Wave-Particle Duality Page 363: Q3 Solution: What is the speed of a photon with respect to another photon if …

⚠️ Common Exam Traps & Conceptual Pitfalls

Many students mistakenly think that two photons always have a relative speed of $c$, regardless of their directions. In special relativity the velocity‑addition formula must be used: for photons moving in the same direction $v_{ ext{rel}}=rac{c-c}{1-c^2/c^2}=0$, while for opposite directions $v_{ ext{rel}}=rac{c+c}{1+c^2/c^2}=c$. Thus the relative speed is zero for co‑moving photons and $c$ for counter‑moving photons, not $2c$ or always $c$.

What is the speed of a photon with respect to another photon if a) the two photons are going in the same direction and b) they are going in opposite directions?

Step-by-Step Verified Solution

**Answer:** (a) 0 (b) c. **Step-by-Step Explanation:** (a) In relativity, the relative speed of two objects moving in the same direction with speeds

u

and

v

is given by

v_{rel} = \frac{u - v}{1 - uv/c^2}

. For photons,

u = c

and

v = c

, so

v_{rel} = 0

. (b) For objects moving in opposite directions,

v_{rel} = \frac{u + v}{1 + uv/c^2}

. For photons,

u = c

and

v = c

, so

v_{rel} = c

.

All Questions in this Chapter

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