Question

A convex lens of focal length 10 cm with refractive index 1.5 is immersed in water of 1.33

Answer 1

If the focal length of a double convex lens is 20cm, then what is its focal length in water?

Refractive index of glass w.r.t. air = μg

Refractive index of the liquid w.r.t. air = μl = 2μg

If a lens made of glass of refracive index μg is immersed in a liquid of refractive index μl then its focal length fl is given by

1fl=(μlg−1)×(1R1−1R2)

If f is the focal length of the lens in air then

120=(μag−1)×(1R1−1R2)

Therefore

fl20=(μag−1)(μ1g−1)

=(μag−1)(μagμal−1)

=(μg−1)(μgμl−1)

The liquid is water.

μl=μw=1.33

μg≈1.5>μw

fw20=(1.5−1)(1.51.33−1)

=0.5(1.13−1)=3.846fw=3.846×20

fw=76.92