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 35.0 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

speed of light in atmosphere = 3 * 108/1.000293

                                              =   2.9991212 * 108   m/sec

=> travel time for light that travels only through space   =   (2 * 3.84 × 108)/(3 * 108)

                                                                                     = 2.56   sec

=> travel time for light that travels through the atmosphere and space = 2.56 + (2 * 35000/2.9991212 * 108)

                                                                                              =   2.5602334 sec

=>   difference in travel time for light   =   2.5602334 - 2.56

                                                           = 2.334 * 10-4   sec

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