A transparent thin 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 the figure. Rays 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)|=1.4R`
D. `|f_(2)|=5.4R`

Answer

A, C

Explanation

There will be no effect of the transparent thin film of uniform thickness and refractive index `n_(1)=1.4`
Therefore,`-(n_(1))/(n)+(n_(2))/(v)=(n_(2)-n_(1))/R) [For case (i)]
`implies`-(1)/(infty)+(1.5)/(f_(1))=(1.5-1)/R``implies``f_(1)=3R` `:'` (a) is a correct option
Again applying `-(n_(1))/(u)+(n_(2))/(v)=(n_(2)-n_(1))/R` [For case (ii)]
`-(1.5)/(infty)+(1)/(f_(2)=(1-1.5)/(-R)` implies` `f_(2)=2R` `:'` (c) is a correct option.