Use the exact values you enter in previous answer(s) to make later calculation(s

Question

Use the exact values you enter in previous answer(s) to make later calculation(s). The Sun appears red when it is on the horizon due to scattering of light by molecules in the atmosphere (see figure below). The Sun does not appear as reddish in color when it is overhead because the thickness of the atmosphere through which sunlight must travel is smaller when the Sun is overhead than when it is near the horizon. Take the approximate thickness of the atmosphere to be 1.5 times10^5 m. What distance through the atmosphere must light travel to reach us when the Sun is at the horizon? M Calculate the ratio of the distances that sunlight travels through the atmosphere in these two cases.  L_horizon/L_overhead=

Explanation / Answer

when the Sun is on the horizon we can form a right triangle with sides Re and L, and hypotenuse Re + t. This implies the distance (L) the light must travel through the atmosphere is given by:

RE 2 + L2 = (RE + t)2

Solving for L, and inserting values, including the radius of the Earth

L = (RE + t)2 – RE 2
L = (6.38 × 10 6 m + 2.0 × 105 m) 2 – (6.38 × 106 m)

L = 1.6 × 106 m

When the Sun is directly overhead, it travels just through
the thickness of one atmosphere.
Taking the ratio between the answer in above and the thickness of the
atmosphere gives:

L horizon/Loverhead = 1.6*10^6/2 × 105 m = 8

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