Question

A convex lens has focal length f in air what happens to the focal length of lens if it is immersed in water n=4/3

Answer 1

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

1/fl = (l μg − 1) (1/R1 − 1/R2)

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

1/f = (aμg − 1) (1/R1 − 1/R2)

Therefore

fl/f = (aμg − 1)/(l μg − 1)

   = (a μg − 1) / (a μg / a μl − 1)

   = (μg − 1) / (μg /μl − 1)

The liquid is water.

μl = μw = 1.33

μg ≈ 1.5 > μw

fw/f = (1.5 − 1) / (1.5 /1.33− 1)

= 0.5/(1.13 − 1)

    = 3.846

fw = 3.846 f

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