**Applications of Newton’s rings**

(i) Using the method of Newton’s rings, the wavelength of a given monochromatic source of light can be determined. The radius of nth dark ring and (n+m)the dark ring are given by

r_{n}^{2 }= nRλ and r^{2}_{n+m} = (n+m) Rλ

r_{n+m}^{2} – r_{n}^{2} = mRλ

so,** λ = [r _{n+m}^{2} – r_{n}^{2}] / mR**

Knowing r_{n+m}, r_{n} and R, the wavelength can be calculated.

(ii) Using Newton’s rings, the refractive index of a liquid can calculated. Let λ_{a} and λ_{m} represent the wavelength of light in air and in medium (liquid). If r_{n} is the radius of the n^{th} dark ring in air and if r_{n} is the radius of the n^{th} dark ring in liquid, then

r_{n}^{2} = nRλ_{a}

r`_{n}^{2} = nRλ_{m} = nRλ_{a}/μ

**so, μ = r _{n}^{2}/ r`_{n}^{2}**