Concerning the absorption of sunlight in the atmosphere.

Question

The amount of sunlight absorbed by the Earth’s atmosphere is approximately proportional to the length of air through which it travels to reach to the Earth. Which of the following is closest to the ratio of the absorption of sunlight during sunset relative to the absorption when the Sun is exactly at the center of the sky? The effective height of the atmosphere is about 10 km

Answer 1

Let $R$ be the radius of the earth in kilometres, then the ratio between the distances the light travels through the atmosphere is $$\frac{\sqrt{(R+10)^2-R^2}}{10}=\frac{\sqrt{20R+100}}{10}\approx\frac{\sqrt{20R}}{10}=\frac{\sqrt{5R}}{5}$$ Since you didn't give any choices this is approximately the answer.

Answer 2

I think you are talking about the albedo effect.

I found this article with interesting maps:

http://curry.eas.gatech.edu/Courses/6140/ency/Chapter9/Ency_Atmos/Reflectance_Albedo_Surface.pdf

and also

https://wattsupwiththat.com/2015/06/08/the-daily-albedo-cycle/

and this one in spanish but with an interesting graph of albedo variation as function of time

http://blog.aterrageo.com/tag/albedo/

Hope it helps.