Since our perception is based on the idea that light

Chapter 33, Problem 33.51

(choose chapter or problem)

Since our perception is based on the idea that light travels in straight lines, we perceive the light to be coming from an apparent position that is an angle d above the suns true position. (a) Make the simplifying assumptions that the atmosphere has uniform density, and hence uniform index of refraction n, and extends to a height h above the earths surface, at which point it abruptly stops. Show that the angle d is given by d = arcsina nR R + h b - arcsina R R + h b where R = 6378 km is the radius of the earth. (b) Calculate d using n = 1.0003 and h = 20 km. How does this compare to the angular radius of the sun, which is about one quarter of a degree? (In actuality a light ray from the sun bends gradually, not abruptly, since the density and refractive index of the atmosphere change gradually with altitude.)