When the sun appears to be just on horizon, it is in fact below the horizon. This is because the light from the sun bends when it enters the earth’s atmosphere. Let us assume that atmosphere is uniform and has index of refraction equal to `mu`. It extends upto a height `h (lt lt R =` radius of earth) above the earth’s surface. In absence of atmosphere how late would we see the sunrise compared to what we see now? Take time period of rotation of earth to be T. Calculate this time for following data
`R = 6400km, mu = 1.0003, h = 20 km, T = 24hr`.

Answer

`Deltat =(T)/(2pi) [sin^(-1) ((muR)/(R+h)) -sin^(-1) ((R)/(R+h))] = 0.9` minute.