Question

Newton’s rings are formed by light reflected normally from a plano convex lens and a plane glass plate with liquid between them. The diameter of nth ring is 2.18 mm and that of (n+10)th ring is 4.51 mm. Calculate the RI of the liquid, given that the radius of curvature of the lens is 90 cm and wavelength of light is 5893 A°

Answer 1

→Newton's rings are formed as a result of interference between the light waves reflected from the top and bottom surfaces of the air film formed between the lens and glass sheet. ... When a ray is incident on the surface of the lens, it is reflected as well as refracted.

Answer 2

The refractive index of the liquid is μ = 1.701

Step-by-step Explanation:

Given: Diameter of nth ring = 2.18 mm

Diameter of (n+10)th ring = 4.51 mm

Radius of the curvature (R) = 90 cm

The wavelength (λ) of the monochromatic light = 5893 A°

To Find: The refractive index of the liquid

Solution:

• Finding the refractive index (μ) of the liquid in Newton's ring

The refractive index of the liquid for the diameters of the nth and (n+m)th dark rings and wavelength λ of the light is,

$\mu = \frac{4m \lambda R}{d^{2}_{n+m} - d^{2}_{n}}$

For the given question, m = 10. Now, substituting the given values in the above formula to get-

$\mu = \frac{4 \times 10 \times 5893 \times 10^{-10} \times 0.9}{ (4.51 \times 10^{-3})^2 - (2.18 \times 10^{-3})^2} = 1.701$

Hence, the refractive index of the liquid is μ = 1.701