A clear transparent glass sphere `(mu=1.5)` of radius R is immersed in a liquid of refractive index 1.25. A parallel beam of light incident on it will converge to a point. The distance of this point from the center will be

Options

A. `-3R`
B. `+3R`
C. `-R`
D. `+R`

Answer

b.

Explanation

`(mu_(1))/(-u)+(mu_(2))/(v)=(mu_(2)-mu_(1))/(R)`
`(1.25)/(-(oo))+(1.5)/(v)=(1.5-1.25)/(R)` or `(1.5)/(v)=(0.25)/(R)`
or `v=(1.5R)/(0.25)=6R`
Again, `(mu_(2))/(-u)+(mu_(1))/(v)=(mu_(1)-mu_(2))/(R)`
`(1.5)/(-4R)+(12.5)/(v)=(1.25-1.5)/(-R)`
or `(1.25)/(v)=(1)/(4R)+(1.5)/(4R)=(2.5)/(4R)`
`=(1.25xx4R)/(2.5)=(5R)/(2.5)`
or `v=2R`
Distance from the center `=3R`