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 30.0 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?

Answer 1

Answer:

a) space only    t = 1.28 s

b) space+ atmosphere   t_ {total} = 1.28000003 s

Explanation:

The speed of light in each material medium is constant, which is why we can use the uniform motion relations

           v= x / t

           

a) let's look for time when it only travels through space

          t = x / c

          t = 3.84 10⁸/3 10⁸

          t = 1.28 s

b) we look for time when it travels part in space and part in the atmosphere

space

as it indicates that the atmosphere has a thickness of e = 30 10³ m

           t₁ = (D-e) / c

           t₁ = (3.84 10⁸ - 30.0 10³) / 3 10⁸

           t₁ = 1.2799 s

           

atmosphere

             

we use the refractive index

           n = c / v

           v = c / n

we substitute in the equation of time

           t₂ = e n / c

           t₂ = 30 10³   1,000293 /3 10⁸

           t₂ = 1.000293 10⁻⁴ s

therefore the total travel time is

           t_ {total} = t₁ + t₂

           t_ {total} = 1.2799+ 1.000293 10⁻⁴

           t_ {total} = 1.28000003 s

we can see that the time increase due to the atmosphere is very small