Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

$ D_{(n+p)}^2 - D_n^2 = \frac{4pλR}{μ} $

For air film, μ = 1

For 12$^{th}$ and 4$^{th}$ dark rings:

$ D_{12}^2 - D_4^2 = 4 \times 8 \times λ \times R $ ………………………………..(1)

For 20$^{th}$ and 4$^{th}$ dark rings:

$ D_{20}^2 - D_4^2 = 4 \times 16 \times λ \times R $ ……………………………….(2)

Dividing equation 1 and 2

$ \frac{(D_{20}^2 - D_4^2)}{(D_{12}^2- D_4^2 )} = \frac{4 \times 16 \times λ \times R}{4 \times 8 \times λ \times R} $

$ \frac{(D_{20}^2 - 0.4^2)}{(0.7^2- 0.4^2 )} = 2 $

D$_{20}$ = 0.906 cm