A thin convex lens made from crown glass `(mu = 3//2)` has focal length `f`. When it is measured in two different liquids having refractive indiced `4//3` and `5//3`, it has the focal length `f_(1)` and `f_(2)` respectively. The correct ralation between the focal lengths is

Options

A. `f_(2) gt f , f_(1)` becomes negative
B. `f_(1)` and `f_(2)` both becomes negative
C. `f_(1) = f_(2) lt f`
D. `f_(1) gt f` and `f_(2)` becomes negative.

Answer

D

Explanation

From lens Maker's formula
`(1)/(f) = ((mu_(g))/(mu_(a)) - 1)((1)/(R_(1)) - (1)/(R_(2)))`
`= ((3)/(2) - 1)((1)/(R_(1)) - (1)/(R_(2))) = (1)/(2)((1)/(R_(1)) - (1)/(R_(2)))`
`(1)/(f_(1)) = ((3//2)/(4//3) - 1)((1)/(R_(1)) - (1)/(R_(2))) = (1)/(8)((1)/(R_(1)) - (1)/(R_(2)))`
and `(1)/(f_(2)) = ((3//2)/(5//3) - 1)((1)/(R_(1)) - (1)/(R_(2)))`
`= -(1)/(10)((1)/(R_(1)) - (1)/(R_(2)))`
Clearly, `(1)/(f_(1)) lt (1)/(f) or f_(1) gt f`
and `f_(2)` is negative.
Choice (d) is correct.