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

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 384 × 108 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? difference in travel time: | 5.75 ×10-0

Explanation / Answer

Given,

Total distance d = 50 km = 50000 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)

= 50000*(1/(2.99704*10^8) - 1/(2.99792*10^8))

= 50000*10^-8*(9.7942*10^-5)

= 4.8971*10^-8 s

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