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

The situtaion can be represented as,

For the refraction at point P,
`(sin60^(@))/(sinr^(1))=sqrt3rArrr_(1)=30^(@)`
Since, `r_(2)=r_(1)rArrr_(2)=30^(@)`
For refraction at point Q,`(sinr_(2))/(sini_(2))=1/sqrt3`
When,`r_(2)=30^(@)`,then `i_(2)=60^(@)`
`rArrr_(2)=r'_(2)=30^(@)`
`therefore alpha=180^(@)-(r'_(2)+i'_(2))=180^(@)-(30^(@)+60^(@))=90^(@)`