Question

Falling light. According to general relativity and the equivalence principle, light is bent by gravity. Consider two tall, perfectly reflecting mirrors exactly 8 m apart and facing each other. A beam of light is directed horizontally through a hole in one of the mirrors 11 m above the ground

(a) Determine the time it takes for the light to strike the ground.

(b) The light will undergo N reflections (i.e., N/2 reflections from each mirror) before it strikes the ground. Find N.

Answer 1

The angle of deflection of the light by a gravitation is
θ = 4GM/rc²

where G is the gravitational constant , M the mass curving the path, r the distance from the light beam to the mass distribution and c the speed of light.
In the case of light G=6.67∗10⁻¹¹ m³/kg/s²
M = 5.97∗10²⁴ kg
r = 6371 km is Earth radius (the height of the mirror is negligible)
c = 3∗10⁸ m/s

θ = 2.778∗10⁻⁹ rad
for such small angles  θ = tan(θ) = d/D
d = D∗θ = 8∗2.778∗10⁻⁹ = 2.222∗10^-8 m = 22.22 nm deflection/one reflection

total number of reflections is
n = 11m/22.22nm = 4.95∗10⁸ reflections from each mirror
total travelled distance is
L = n∗D = 8∗4.95∗10⁸ = 39.6∗10⁸ m
time of travel is
t = L/c = 13.2 sec