Question

In a Newton's Ring experiment, the diameter of the ${20}^{th}$ dark ring was found to be $5.82mm$ and that the $10th$ ring $3.36mm$. If the radius of the planoconvex lens is $1m$, calculate the wavelength of light used

Answer 1

Diameter of the $20th$ dark ring.
$D_{20}=5.8mm=5.82\times {10}^{-3}m$
Radius of the $20th$ dark ring
$r_{20}=2.91\times {10}^{-3}m$
Diameter of the $10th$ dark ring
$D_{10}=3.36mm=3.36\times {10}^{-3}m$
Radius of the $10th$ dark ring
$r_{10}=1.68\times {10}^{-3}m$
Radius of plano-convex lens $\left(R\right)=1m$
Wavelength of light
$=\frac{r_{n+m}^2-r_n^2}{mR}=\frac{\left[\right(2.91\times {10}^{-3}{)}^2-(1.68\times {10}^{-3}{)}^2]}{10\times 1}$
$=\frac{[8.4681-2.8224]\times {10}^{-6}}{10}$
$=0.5646\times {10}^{-6}=5636\stackrel{o}{A}$.