A transparent with film of uniform thickness and refractive index `n_(1)=1.4` is coated on the convex spherical surface of radius `R` at one end of a long solid glass cylinder of refractive index `n_(2)=1.5` as shown in figure. Rays of light of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance `f_(1)` from the film, while rays of light traversing from glass to air get focused at distance `f_(2)` from the film. then

Options

A. `|f_(1)|=3R`
B. `|f_(1)|=2.8R`
C. `|f_(2)|=2R`
D. `|f_(2)|=1.4R

Answer

C

Explanation

`(1)/(f_(film))=(n_(1)-1)((1)/(R)-(1)/(R)) rArr f_(film)=infty` (inf inite)
`therefor` No effect of presence of film.
For Air to glass
Using single spherical Refraction :-
`(n_(2))/(v)-(1)/(u)=(n_(2)-1)/(R)`
`(1.5)/(v)-(1)/(infty)=(1.5-1)/(R) rArr v=3R`
`therefore f_(1)=3R`
For Glass to Air `( :-)/`
`(1)/(v)-(n_(2))(u)=(1-n_(2))/(-R)`
`rArr (1)/(v)-(1.5)/(infty)=(1-1.5)/(-R)`
`rArr v=2R`
`therefore f_(2)=2R`