Question

a convex lens has 20 cm focal length in air . what will be its focal length in water

Answer 1

Heya Dear ☺

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)1fl=(μgl−1)×(1R1−1R2)

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

120=(μag−1)×(1R1−1R2)120=(μga−1)×(1R1−1R2)

Therefore

fl20=(μag−1)(μ1g−1)fl20=(μga−1)(μg1−1)

=(μag−1)(μagμal−1)=(μga−1)(μgaμla−1)

=(μg−1)(μgμl−1)=(μg−1)(μgμl−1)
 
 The liquid is water. 
μl=μw=1.33μl=μw=1.33

μg≈1.5>μwμg≈1.5>μw
fw20=(1.5−1)(1.51.33−1)fw20=(1.5−1)(1.51.33−1)
 =0.5(1.13−1)=3.846fw=3.846×20=0.5(1.13−1)=3.846fw=3.846×20

fw=76.92

Hope it helps you ☺