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 `2.25`
C. increases by a factor of `1.2`
D. decreases by a factor of `1.2`

Answer

B

Explanation

Let f be focal length of lens. `(1)/(f)=(""^(u)u_(g)1)((1)/(R_(1))-(1)/(R_(2)))=(1.5-1)((1)/(R_(1))-(1)/(R_(2)))`
or,`(1)/(f)=0.5((1)/(R_(1))-(1)/(R_(2))) or, (1)/(R_(1))-(1)/(R_(2))=(1)/(0.5f)....(i)`
Let f, be focal length of the lens when immeresed in a liquid.
`(1)/(f)=(""^(u)u_(g)-1)((1)/(R_(1))-(1)/(R_(2)))=((1.5-1)/(1.25)-1)((1)/(R_(1))-(1)/(R_(2)))`
`=((0.25)/(1.25))((1)/(R_(1))-(1)/(R_(2)))=(0.25)/(2.5f)` (using (i))
`(1)/(f)=(1)/(2.5f) or f'=2.5 f`
i.e., focal lenght of lens when immeresed in a liquid is increases by a factor of 2.5