Question

A glass convex lens of refractive index 1.5 has focal length 8 cm when in air what would be focal length of lens when immersed in water of refractive index 1.33

Answer 1

When a lens is immersed in water , the value of refractive index decrease . Hence , its focal length increases .

Here, it is a convex lens .

Refractive index of lens , ᵃμg = 1.5

Focal length of lens in air , fa  =  8  cm

Refractive index of water , ᵃμw = 1.33

The radius of curvatures are R1 and R2 .

For the lens in air -

1/fa  = (ᵃμg - 1) * [1/R1 - 1/R2]

=>  1/8  = (1.5 - 1) * [1/R1 - 1/R2]

=>  [1/R1 - 1/R2]  =  1/4

When lens is immersed in water

1/fw  = [(ᵃμg/ᵃμw) - 1] * [1/R1 - 1/R2]

where, fw  =  focal length of lens in water

=>  1/fw =  [(1.5/1.33) - 1] * (1/4)

=>  1/fw  = (1/8) * (1/4)

             =  1/32

=>  fw  =  32   cm

Thus, focal length of lens when immersed in water =  32  cm

Answer 2

Given :

Refractive index of lens= 1.5

focal length in air=8cm

from lens makers formula :

1/f= (n-1)[1/R1-1/R2]

1/8= (1.5-1)[1/R1-1/R2]

1/8= 0.5[1/R1-1/R2]

1x10/8 x 5=[1/R1-1/R2]

[1/R1-1/R2]=2/8

[1/R1-1/R2]=1/4-------------------1

when lens in immersed in water of refractive index = 1.33

1/fw=( n1/n2-1)[[1/R1-1/R2]

1/fw=( 1.5/1.33-1)[1/R1-1/R2]

1/fw= 1/8 x 1/4

fw=32

fw=32cm

∴ Focal length of lens in water =32cm