A ray of light is falling on a glass sphere of `mu=sqrt(3)` such that the incident ray and 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 degree).

Answer

60

Explanation

Form the figure it is clear that
`angleABC=pi-2(i-r)`
So, `angleAOC(external)=2pi-{pi-2r}`
`=pi+2r`
Form the property of circle,
`2angleABC=angleAOC`
`:. 2{pi-2(i-r)}=pi+2r`
This gives, `2i-r=(pi)/(2)rArr r=(2i-(pi)/(2))`
`:.mu=(sini)/(sinr)`
As `mu=sqrt(3)` given `rArr sqrt(3)=(sini)/(sin[2i-(pi)/(2)]`
or ` sqrt(3)=(sini)/(-cos2i)` or `sqrt(3)=(sini)/(2sin^(2)i-1)`
`2sqrt(3)sin^(2)i-sqrt(3)=sini`
Solving the avove equation, we get `sini=sqrt(3)/(2)rArr i=60^@`