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

Question

On the Moon's surface, lunar astronauts placed a corner reflector, off 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 × 108 m, and Earth's atmosphere (which varies in density with altitude) is equivalent to a layer 20.0 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 , d = 3.84 *10^8 m

t = 20 km = 2 *10^4 m

n = 1.000293

difference in travel time = (t/(c/n) + (d-t)/c)- d/speed of light

difference in travel time = (20 *10^3/(3 *10^8/1.000293) + (3.84 *10^8 - 2 *10^4)/(3 *10^8)) - 3.84 *10^8/(3 *10^8)

difference in travel time = 1.9533 *10^-8 s

the difference in travel time is 1.9533 *10^-8 s

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