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 indices `(4)/(3)` and `(5)/(3)`, it has the focal lengths `f_1` and `f_2` respectively . The correct relation between the focal lengths is ,

Options

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

Answer

C

Explanation

Focal length of thin convex lens
`f=(r)/(2(mu-1))=(R )/(2((3)/(2)-1))=R`
Refractive index of lens `mu=(3)/(2)=1.5=""_(a)mu_(g)`
Now this lens immersed in liquid having refractive index `mu_(1)=4//3=1.34`, which is lower than the converging lens, the actual focal length in liquid is

`f_(1)=(R)/(2(""_(1)mu_(g)-1))`
`=(R )/(2((3//2)/(4//3)-1))`
`=(R )/(2xx((9)/(8)-1))`
`=(R )/(1//4)=4R`
`rArr" "=4f`
Again immersedin liquid, `mu_(2)=(5)/(3)=1.67`

which is greater than refrqaction index of the material of converging lens, the nature of lens will change to become diverging.
`f_(2)=(R )/((""_(2)mu_(g)-1))`
`f_(2)=(R )/((""_(2)mu_(g)-1))`
`=(R)/(((3//2)/(5//3)-1))`
`=(R )/(((9)/(10)-1))=-10R`
`rArr" "f_(2)=-10f`