A ray of light is falling on a glass sphere of μ = 3 such that the incident ray and the emergent ray, when produced, intersect at a point on the surface of the sphere. The angle of incidence in degr

Question

A ray of light is falling on a glass sphere of μ = 3 ​ such that the incident ray and the emergent ray, when produced, intersect at a point on the surface of the sphere. The angle of incidence in degrees is found to be k 2 π ​ . Find the value of k .

TestHub · Accepted Answer

∠ ABC = π − 2 ( i ^ − r ^ ) 2∠ ABC = ∠ AOC [ half angle theorem] 2 π − 4 i ^ + 4 r = ( π + 2 r ) 2 i ^ − r = z π ​ ⇒ r = 2 i ^ − 2 π ​ 1 sin i ^ = μ sin r ^ sin i ^ = μ sin ( 2 i ^ − 2 π ​ ) sin i ^ = 2 3 ​ ​ ⇒ i ^ = 3 π ​ ⇒ 6 2 π ​ ⇒ k = 6

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