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

1 Answer
Gió
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

Related questions
See all questions in Curved Mirrors
Impact of this question
5803 views around the world
You can reuse this answer
Creative Commons License