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*10^8 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?

Question

Deangelo Rivera

Physics

14 February, 14:09

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*10^8 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?

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Corey Watts · Answer 1

The difference in time will be due to travel through atmosphere where speed of light slows down. If t be the thickness of atmosphere and c be the speed of light in space and μ be the refractive index of atmosphere difference in travel time will be as follows.

difference = / frac{2t/mu }{c}-/frac{2t }{c}

=/frac{2t}{c }/left (1-/mu / right)

Now t = 40 x 10³m,μ = 1.000293, c = 3 x 10⁸.

difference = / frac{2t/mu }{c}-/frac{2t }{c}

=/frac{2t}{c }/left (/mu - 1 / right) / /

=/frac{ 2/times 40/times 10^3}{3/times10^3 }/left (1.000293-1 / right) / /

=7.81/times 10^{-3} s