1. The refractive index of the Earth’s atmosphere is n = 1.01 + α(R − r), where α is a constant, r is the radial distance from the Earth’s centre and R = 6.4 × 10^6 m is the Earth’s radius. By considering a path comprising a series of total internal reﬂections or otherwise, ﬁnd a value of α for which a light ray emitted horizontally close to the Earth’s surface would go around the Earth. (The eﬀects of absorption may be ignored and the Earth may be taken to be a perfect sphere of radius R.) 2. Relevant equations n1sin(x1)=n2sin(x2) 3. The attempt at a solution I really have no idea what to do as I understand the refractive index is constantly changing? Don't know where to start, any help would be much appreciated.