Question

In a Newton's ring experiment the diameter of 15^( th ) dark ring is 0.59cm . Find the diameter of 5^( th ) and 20^( th ) ring.

Answer 1

Given Info : In a Newton's ring experiment the diameter of 15^( th ) dark ring is 0.59cm.

To find : The diameters of 5th and 20th dark ring are...

solution : using formula, $D_n^2=4n\lambda R$

here $D_n$ is diameter of nth dark ring, λ is wavelength and R is radius of curvature.

for similar conditions,

R and λ remain constant.

so, $D_n^2$ ∝ n

⇒$\frac{D_{n_1}^2}{D_{n_2}^2}=\frac{n_1}{n_2}$

here D₁₅ = 0.59 cm , D₅ = ?

so, (0.59cm)²/D₅² = 15/5 = 3

⇒D₅ = 0.59/√3 = 0.34 cm

again, D₁₅ = 0.59 cm, D₂₀ = ?

(0.59cm)²/D₂₀² = (15/20) = 0.75

⇒D₂₀ = 0.59/√(0.75) = 0.68 cm

Therefore the diameters of 5th and 20th dark ring are 0.34 cm and 0.68 cm respectively.