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

`(1)/(f) = (n-1) [(1)/(infty) - ( (1)/(-R) ) ] `
and `(1)/(f) = ((3)/(2) - 1) ((1)/(R )) = (1)/(2R)`
`rArr " " f = 2R rArr R = (f)/(2)`
Now, `(1)/(f_(1)) = (n_(l) - 1) ( (1)/(-R) - (1)/(infty) )`
`(1)/(f_(1)) = (-(n_(l) -1))/(R ) rArr (1)/(f_(l)) = (-2(n_(l) -1))/(f ) `
Again `(1)/(f_(eq)) = (1)/(f_(1)) + (1)/(f_(2))`
`rArr (1)/(2f) = (1)/(f) + (1)/(f_(l)) rArr (1)/(2f) = (1)/(f) - (2(n_(l) - 1))/(f)`
`n_(l) = (5)/(4) = 1.25`.