Question

The focal length of a convex lens of = 1.5 if 'f' when it is placed in air. In a liquid, its focal length becomes f (x > 1). The refractive index of liquid is .

Answer 1

Answer:

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

The focal length increases in water.