1.

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.

Answer»

1.5
2
2.5
none of these

Solution : `(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`.
`rArrR=(muR)/(mu-1)rArr mu=oo`(not possible)


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