Physics - Wave Optics Question with Solution | TestHub

Newton's ring arrangement is used for determining the wavelength of monochromatic light. For this the diameter of $n^{\text{th }}$ dark ring $\left(D_n\right)$ and $(n+p{)}^{\text{th }}$ dark ring $\left({\mathrm{D}}_{\mathrm{n}+\mathrm{p}}\right)$ are measured then $D_{(\mathrm{n}+\mathrm{p})}^2=4(\mathrm{n}+\mathrm{p})\lambda \mathrm{R}$ and ${\mathrm{D}}_{\mathrm{n}}^2=4\mathrm{n}\lambda \mathrm{R}$ $\Rightarrow \lambda =\frac{D_{n+p}^2-D_n^2}{4pR}$ Here, $n=10,n+p=20$ $\therefore p=10;R=1m,D_{10}=3.96\times 10^{-3}\mathrm{m}$, $D_{20}=5.82\times 10^{-3}\mathrm{m}$ $\therefore \lambda =\frac{D_{20}^2-D_{10}^2}{4\mathrm{pR}}$ $=\frac{{\left(5.82\times 10^{-3}\right)}^2-{\left(3.36\times 10^{-3}\right)}^2}{4\times 10\times 1}$ $=5646\mathring{A}$