Question

According to the quantum theory, a photon of electromagnetic radiation of frequency v has energy E = hv where h is known as planck's constant. According to the theory of relativity, a particle of mass m has equivalent energy E = $m{c}^2$, where c is speed of light. Thus a photon can be treated as a particle having effective mass m $=\frac{hv}{C^2}$. If a flash of light is sent horizontally in earth's gravitational field, then photons while travelling a horizontal distanced would fall through a distance given by

• A. $\frac{g{d}^2}{2c^2}$
• B. $\frac{h}{mc}$
• C. $\frac{mc{d}^2}{h}$
• D. zero

Answer 1

The correct option is A $\frac{g{d}^2}{2c^2}$

Time taken by the photon, t = d/c
$h=0\times t+\frac{1}{2}g{t}^2$
$h=\frac{1}{2}g\frac{d^2}{c^2}$
$h=\frac{g{d}^2}{2c^2}$