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)|=1.4 R`

Answer

A, C

Explanation

`(1)/(f_("film"))=(n_(1)-1)((1)/(R)-(1)/(R))`
`rArr f_("film")=infty` (infinite)
No effect of presence of film
From Air to Glass :
Using single spherical Refraction :-
`(n_(2))/(v)-(1)/(u)=(n_(2)-1)/(R),(1.5)/(v)-(1)/(prop)=(1.5-1)/(R)`
`v=3R f_(1)=3R`
From Glass to Air : -