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

1 Answer
Feb 2, 2017

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#