Question

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

Answer 1

Correct Answer - c.
`(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)