Question

In an experiment on Newton’s rings, the diameter of the 20${}^{th}$ dark ring was found to be 5.82mm 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. $5646\mathring{A}$
• B. $5896\mathring{A}$
• C. $5406\mathring{A}$
• D. $5900\mathring{A}$

Answer 1

Answer: (A)

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