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` and `f_(1)` becomes negative
B. `f_(1)`and `f_(2)` both become negative
C. `f_(1) = f_(2) lt f`
D. `f_(1) gtf ` and `f_(2)` becomes negative

Answer

4

Explanation

`f_(m)/f = ((mu-1))/((mu/mu_(in) -1)) `
`f_(1)/f = (3/2 -1 )/((3//2 - 1)/(5//3) - 1) = 4`
`implies f_(1) = 4f`
`f_(2)/f = (3/2 - 1)/((3//2)/(5//3) - 1) implies f_(2)lt0`