1. The refractive index of the Earth’s atmosphere is(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Refractive index question - light beam around the world

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