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. Find the value of angle of incidence in degrees.
As shown in the figure, refraction occurs at points A and B on the glass sphere.
Both the angles of refraction have to be same, since they are angles opposite to the equal sides of the triangle ABC.
This gives ∠DAB=i−r and ∠DBA=i−r
In triangle ABC, ∠ACB=π−2r
Hence, ∠AEB=π2−r
In triangle ABD, ∠ADB=π−2(i−r)
Sum of opposite angles of a cyclic quadrilateral is π.
∠ABD+∠AEB
2i−r=π2
Using snell's law at point A gives, sini=μsinr
Hence i=60∘