The focal length of a plano-convex lens is `f` and its refractive index is 1.5 it is kept over a plane galss plate with its curved surface touching the glass plate. The gap between the lens and the glass plate is filled by a liquid. As a result the effective focal length of the combination becomes `2f`. Then the refractive index of the liquid is

Options

A. `1.5`
B. 2
C. `1.25`
D. `1.33`

Answer

C

Explanation

According to lens maker.s formula
The focal length of plano convex lens is
`1/f=(n-1)((1)/(oo)-(1)/(-R))`
`1/f=(3/2-1)(1/R)=(1)/(2R)`
or `R=f/2` . . . (i)
The focal length of liquid lens is
`(1)/(f_(1))=(n_(1)-1)((1)/(-R)-(1)/(oo))`
`(1)/(f_(1))=-((n_(1)-1))/(R)`
`(1)/(f_(1))=-(2(n_(1)-1))/(f)" (Using (i))"`
Effective focal length of the combination is
`(1)/(2f)=(1)/(f)+(1)/(f_(1))`
`(1)/\(2f)=(1)/\(f)-(2(n_(1)-1))/(f),2(n_(1-1))=1-(1)/(2)=1/2`
`n_(1)-1=1/4`
`n_(1)=(5)/(4)=1.25`