A ray of light is propagating in a horizontal direction close to the earth's surface where the gradient of the refractive index is 
= 3 × 10 –8 m –1 (z = height above the earth's surface). The refractive index of air = 1.0 at the surface and radius of earth = 6400 km.
(i) Find the radius of curvature of the ray of light.
(ii) For what value of the gradient would the ray of light propagate all the way round the earth?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Let us consider a vertical wavefront whose lower end is a height z and the upper end is at a height z + δ z . In a short time δ t, the upper end will move by (v + dv) δ t and lower end by v δ t .
So the angle through which the wavefront has turned is
θ = 
= 
θ = 
δ t
Now R = radius of curvature = 
= 
⇒ R = 
= 
= 
× 10 8 m
If radius of curvature = R earth , the ray would propagate all around the earth.
= 6.4 × 10 6 ⇒ 
= 
= 1.56 × 10
–7 m –1
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