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 40.0 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

Extra time will be same as extra time taken to travell 40 km twice
d = 80 km = 80000 m
speed of light in vacuum,
v1 = 2.99792*10^8 m/s
v2 = (2.99792*10^8)/(1.000293) = 2.99704*10^8 m/s

extra time = d*(1/v2- 1/v1)
=80000*(1/(2.99704*10^8) - 1/(2.99792*10^8))
= 80000*10^-8*(9.7942*10^-5)
= 7.835*10^-8 s
Answer: 7.835*10^-8 s

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