Question

What will happen to the focal length of convex lens which is placed inside water ?

Answer 1

I would think that it gets bigger.

Explanation:

We know from the famous Lensmaker´s Formula that:
`1/f=(n_l-n_m)/n_m(1/R_1+1/R_2)`
where:
`f=` focal length;

`n_l=` index of refraction of lens (glass);

`n_m=` index od refraction of the medim (in which the lens is placed);

`R_1 and R_2` radii of curvature of lens surfaces.

Consider an exampe:

A lens that has a focal length of `+20cm` has equal radii, so that `R_1=R_2=R`, and is made of glass of `n_l=1.6`; you place it into water (`n_m=1.33`). Remember that we can consider the index of air as `1`. We have:

In air:
`1/20=(1.6-1)/1(2/R)`

In water:
`1/(f')=(1.6-1.33)/1.33(2/R)`
substitute one into the other for `(2/R)`:
`1/(20(1.6-1))=1.33/(f'(1.6-1.33))`
rearranging:
`f'=1.33(20(1.6-1))/(1.6-1.33)~~60cm`