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

Answer

A, C

Explanation

As thickness of film is uniform, the effective power of the film is zero. Therefore, we can consider refraction at glass air interface.
In case I : Refraction from air to glass
`-(mu_(1))/(u) + (mu_(2))/(v) = (mu_(2) - mu_(1))/(R )`
`-(1)/(oo) + (1.5)/(f_(1)) = (1.5 - 1)/(R )` or `f_(1) = 3 R`
In case II : Refraction from denser to rarer
`-(mu_(2))/(u) + (mu_(1))/(v) = (mu_(1) - mu_(2))/(R )`
`-(1.5)/(oo) + (1)/(f_(2)) = (1 - 1.5)/(R )` or `f_(2) = 2 R`
Choice (a) and ( c) are correct.