Determination of refractive index of a liquid by Newton's rings

Theory of Newton's rings:

7)Determination of refractive index of a liquid by Newton's rings:

           First Newton's rings are ontaobta when there is an air film  between  the  glass  plate  and  the plano-convex lens. The system is placed in a metal container.  Measure  the  diameter  of  nth  and (n+p)the dark  ring  with  the  help  of  traveling microscope.

For air film:

Dₙ² = 4nλR

D²ₙ₊ₚ = 4(n+p)λR

.•. D²ₙ₊ₚ - Dₙ² = 4pλR    .....(1)

              Now pour the liquid whose refractive index is to be calculated in the container without disturbing the arrangement. The air film is now replaced by liquid. Now measure the diameter of nth and (n + p)th  dark  ring with  the  help  of traveling microscope.

For liquid film :

Let μ is the R.I. of the liquid

D'ₙ² = 4nλR
             μ

D'²ₙ₊ₚ = 4( n+p)λ.R
                      μ

.•. D'²ₙ₊ₚ - D'ₙ² = 4pλR      ......(2)
                               μ

Eq. (1) / eq. (2) gives

μ = D²ₙ₊ₚ - Dₙ²
      D'²ₙ₊ₚ - D'ₙ²                  .....(3)

           Eq. (3) gives the refractive index of the liquid by knowing the diameters of nth and ( n+p )th dark rings with and without liquid.