Find the curvature radius of a ray of light propagating in a horizontal direction close to the Earth's surface where the gradient of the refractive index in air is equal to approximately `3.10^(-8) m^(-1)`. At what value of that gradient would the ray of light propagate all the way round the Earth?

Explanation

From the above problem
`(1)/(rho) = (1)/(n) hatp.oversetrarr(Delta) n~~ hatp. Delta ~~ |Deltan| = 3 xx 10^(-8)m^(-1)`
(since `hatp ||oversetrarr(Delta)n` both being vertical). So `rho = 3.3 xx 10^(7) m`
For the ray of light to propagate all the way round the earth we must have
`rho = R = 6400 km = 6.4 xx 10^(6)m`
Thus `|Delta n| = 1.6 xx 10^(-7) m^(-1)`