On the Moon\'s surface, lunar astronauts placed a corner reflector, of which a l

Question

On the Moon's surface, lunar astronauts placed a corner reflector, of which a laser beam is periodically reflected. the distance to the Moon is calculated from the round-trip time. the Earth's atmosphere slows down light. Assume the distance to the Moon is precisely 3.84 times 10^8 m. and Earth's atmosphere (which varies in density with altitude) is equivalent to a layer 25.0 km thick with a constant index of refraction n = 1.000293. What is the difference in travel time for light that travels only through space to the moon and back and light that travels through the atmosphere and space?

Explanation / Answer

Here ,

distance between moon and earth , d = 3.84 *10^8 m

for the light reflected through the space to the moon

t = 3.84 *10^8/(3 *10^8)

t = 1.28 s

Now, for the time taken

t = (25 *10^3/(3 *10^8/1.000293)) + (3.84 *10^8 - 25 *10^3)/(3 *10^8)

t = 1.280000024417 s

difference in time = 1.28- 1.280000024417

difference in time = 2.442 *10^-8 s

the difference in time is 2.442 *10^-8 s

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