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

Answer

A, B, C, D

Explanation

`(1)/(f)=((3)/(2)-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f)=(1)/(2x)rArr f=2x` here `((1)/(x)=(1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f_(1))=((3//2)/(4//3)-1)(1)/(x)`
`(1)/(f_(2))=((3//2)/(5//3)-1)((1)/(x)): rArr f_(2)` is iegative
`(1)/(f_(1))=(1)/(8x)=(1)/(4(2x))=(1)/(4f)`
`rArr f_(1)=4f`
Analytically, If a lense is inserted in a denser sourrounding the sing of focal length changes changes and if lens is inserted in a rarer sourrounding, the sign of focal length remain same.
If lense is inserted in rarer medium the focal length increases.