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

Q. For what value of refractive index `mu`, the thin beam can be focussed at centre of sphere.

Options

A. 1.5
B. 2
C. 2.5
D. none of these

Answer

d.

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)