Q. In an experiment of Newton’s rings, the diameter of the 20$^{th}$ dark ring was found to be $5.82\ mm$ and that of the 10$^{th}$ ring $3.36\ mm$. If the radius of the plano-convex lens is $1\ m$, the wavelength of light used is
A) $5646\ \mathring{\mathrm{A}}$
B) $5896\ \mathring{\mathrm{A}}$
C) $5406\ \mathring{\mathrm{A}}$
D) $5900\ \mathring{\mathrm{A}}$
Explanation
(a) In the Newton’s Ring interference experiment the diameter of the $n^{th}$ dark ring is given by $D_{n} = 2\sqrt{n.\lambda.R}$ where $R$ is the radius of curvature of the lens and $\lambda$ is the wavelength
Using the formula we have
$\lambda = \frac{D_{n + m}^{2} - D_{n}^{2}}{4m.R} = \frac{D_{20}^{2} - D_{10}^{2}}{4(20 - 10)R}$
$= \frac{\left( 5.82 \times 10^{- 3} \right)^{2} - \left( 3.36 \times 10^{- 3} \right)^{2}}{4 \times 10 \times 1} = 5646\lbrack\mathring{\mathrm{A}}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.