Question

A convex lens has a focal length of 0.3 m is in air. Calculate its focal length

when it is immersed in water. Given that refractive index of water = 4/3 and

refractive index of glass = 3/2.​

Answer 1

Given:

Focal length of convex lens = 0.3m = 30 cm

Refractive index of water = 4/3

Refractive index of glass = 3/2

To find:

The focal length when the convex lens is immersed in water.

Solution:

When lens was in air:

According to lens maker's formula:

1/f₁ = (μ₂/μ(air)- 1) [1/R₁ - 1/R₂]

Since μ(air ) = 1

μ₂ is the refractive index of glass.

On putting the values we get:

1/30 = (3/2 - 1) [1/R₁ - 1/R₂]

1/R₁ - 1/R2 = 2/30 = 1/15

When the lens is immersed in water:

μ₁ is the refractive index of water.

1/f₂ = (μ₂/ μ₁ -1) [1/R₁ - 1/R₂]

1/f₂ = {[(3/2) / (4/3)] - 1} [1/15]

1/f₂ = (9/8 - 1) [1/15]

1/f₂ = 1/8 * 1/15

1/f₂ = 1/120

f₂ = 120 cm = 1.2 m

Therefore, the required focal length is 1.2 m.