A lens is made of flint glass (refractive index `=1.5`). When the lens is immersed in a liquid of refractive index `1.25` , the focal length:

Options

A. increases by a factor of `1.25`
B. increases by a factor of `1.2`
C. decreases by a factor of `1.2`
D. increases by a factor of `2.5`

Answer

D

Explanation

Lens - Maker's formula is given by
`(1)/(f)=(._(a)mu_(g)-1)((1)/(R_(1))-(1)/(R_(2)))` ....(i)
where `._(a)mu_(g)` is refractive index of glass w.r.t. air, `R_(1)` and `R_(2)` radii of curvature of two surfaces of lens and `f` is focal length of the focal length of the lens.
If the lens is immersed in a liquid of refractive index `mu_(l)` then
`(1)/(f_(1))=(._(l)mu_(f)-1)((1)/(R_(1))-(1)/(R_(2)))` ...(ii)
Here, `._(l)mu_(g)` is refractive index of glass w.r.t. liquid.
Dividing Eq. (i) by Eq. (ii) , we have
`(f_(1))/(f)=((._(a)mu_(g)-1))/((._(l)mu_(g)-1))implies(f_(1))/(f)=((1.5-1)/((1.5)/(1.25)-1))`
`implies(f_(1))/(f)=(0.5xx1.25)/(0.25)=2.5`
Hence, the angle of prism `P_(2)` is `3^(@)`.