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)| = 2R`
D. `|f_(2)| = 1.4R`

Answer

AC

Explanation

When rays are moving from air to glass,

`(1.5)/(f_(1)) = ((1.4 -1))/(+R) + ((1.5 - 1.4))/(+R)`
`(1.5)/(f_(1)) = (0.4)/(R) + (0.1)/(R) = (0.5)/(R)`
`|f_(1)| = 3R`
When rays are moving from glass to air ,
`(1)/(F_(2)) = ((1 - 1.4))/(-R) + ((1.4 - 1.5))/(-R) = (0.5)/(R)`
`|f_(2)| = 2R`