A ray incident at a point at an angle of incidence of `60^(@)` enters a glass sphere with refractive index `sqrt(3)` and it is reflected and refracted at the farther surface of the sphere. The angle between the reflected and refracted rays at this surface is:

Options

A. `50^(@)`
B. `60^(@)`
C. `90^(@)`
D. `40^(@)`

Answer

C

Explanation

Reftraction at P,
`(sin60^(@))/(sinr_(1))=sqrt3`
`sinr_(1)=(1)/(2)`
or `r_(1)=30^(@)`
Since, `r_(2)=r_(1), :. r_(2)=30^(@)`
Refraction at Q, `(sinr_(2))/(sini_(2))=(1)/(sqrt(3))` or `(sin30^(@))/(sini_(2))=(1)/(sqrt(3))`
or `i_(2)=60^(@)`
At point Q, `r_(2)^(.)=r_(2)=30^(@)`
`:. alpha=180^(@)-(r_(2)^(.)=r_(2))=180^(@)-(30^(@)+60^(@))=90^(@)`