In Young's double slit experiment, the $10^{\text {th }}$ maximum of wavelength ' $\lambda_1$ ' is at a…

In Young's double slit experiment, the $10^{\text {th }}$ maximum of wavelength ' $\lambda_1$ ' is at a distance of ' $\mathrm{Y}_1$ ' from the central maximum. When the wavelength of the source is changed to ' $\lambda_2$ ', $5^{\text {th }}$ maximum is at a distance ' $Y_2$ ' from the central maximum. The ratio $\frac{\mathrm{Y}_1}{\mathrm{Y}_2}$ is
  1. $\frac{2 \lambda_1}{\lambda_2}$
  2. $\frac{\lambda_2}{2 \lambda_1}$
  3. $\frac{2 \lambda_2}{\lambda_1}$
  4. $\frac{\lambda_1}{2 \lambda_2}$

Solution

$\begin{aligned} & Y_1=\frac{10 \lambda_1 D}{d}, Y_2=\frac{5 \lambda_2 D}{d} \\ & \therefore \frac{Y_1}{Y_2}=\frac{10 \lambda_1}{5 \lambda_2}=\frac{2 \lambda_1}{\lambda_2}\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 1)

Practice more Wave Optics questions on Aicharya