A parallel beam of light falls on a solid tranparent sphere.

Q. If however thin beam is focussed at A, then find the refractive index of the sphere,

Options

A. 1.5
B. 1.7
C. 2.0
D. 2.5

Answer

c.

Explanation

`(mu)/(y)-(1)/(oo)=(mu-1)/(R)rArr(muR)/(mu-1)`
If beam is focussed at A, than ` y=2R`
`rArr 2R=(muR)/(mu-1)=mu=2`
The above is valid for paraxial rays, hence beam should be thin. If `mugt2` , then `ylt2R` , hence beam can be focussed before A.
For thin beam to be focussed at A, `y=R`.
`rArr R=(muR)/(mu-1)rArr mu=oo` (not possible)