Question

The focal length of a convex lens of `R.I. 1.5` is `f` when it is placed in air. When it is immersed in a liquid is behaves as a converging lens its focal length becomes `xf(x gt 1)`. The refractive index of the liquid
A. `gt 3//2`
B. `lt (3//2)` and `gt 1`
C. `lt 3//2`
D. All of these

Answer 1

`1//f=(n-1)((1)/(R_(1))+(1)/(R_(2)))`
`rArr 1//f=((1.5)/(1)-1)((1)/(R_(1))+(1)/(R_(2)))` when the lens is placed in air and
`1//xf=((1.5)/(y)-1)((1)/(R_(1))+(1)/(R_(2)))` when the lens is places in the liquid.
where `y=R.I.` of the liquid
On solving, we get
`y=(3)/(2+1//x)`