A thin converging lens has a focal length 'f' in air. If it is completely immersed in a liquid, briefly explain, how the focal length of the lens will vary ?

Explanation

The focal length of a converging lens is given by:
`1/f = (n/n_(m)-1) (1/R_(1)+1/R_(2))`
where n = refractive index of lens and `n_(m)` = refracting index of the surrounding medium.
Hence in air
`1/f = (n-1) (1/R_(1) + 1/R_(2))` and in a given liquid medium `=1/f. = (n/n_(m)-1) (1/R_(1)+1/R_(2))`
`f. = ((n-1)n_(m)f)/(n-n_(m))`
Following two cases are important here :
(i) If `n_(m) lt n`, then `f.` is +ve and has a value greater than f i.e., focal length of the lens increases when immersed in given liquid medium but even now the lens behaves as a converging lens.
(ii) If `n_m gt n`, then f. is -ve i.e., the lens will begin to behave as a diverging lens.