In Young's double slit experiment, the $10^{\text {th }}$ maximum of wavelength $\lambda_1$ is at a distance of $y_1$ from the central maximum. When the wavelength of the source is changed to $\lambda_2, 5^{\text {th }}$ maximum is at a distance of $y_2$ from its central maximum. The ratio $\left(\frac{y_1}{y_2}\right)$ is

• A

  $\frac{2 \lambda_1}{\lambda_2}$
• Correct answer
  B

  $\frac{2 \lambda_2}{\lambda_1}$
• C

  $\frac{\lambda_1}{2 \lambda_2}$
• D

  $\frac{\lambda_2}{2 \lambda_1}$

Solution

Position fringe from central maxima $y_1=\frac{n \lambda_1 D}{d}$ Given, $n=10$
For second source
$\therefore \quad \frac{y_1}{y_2}=\frac{\frac{10 \lambda_1 D}{d}}{\frac{5 \lambda_2 D}{d}}$ $\Rightarrow \quad \frac{y_1}{y_2}=\frac{2 \lambda_1}{\lambda_2}$

Hence, the correct answer is option: 'B'.