Question

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^th maximum is at a distance of $y_{2}$ from its central maximum. The ratio $\frac{y_{1}}{y_{2}}$ is

• A. $\frac{2 \lambda _{1}}{\lambda _{2}}$
• B. $\frac{2 \lambda _{2}}{\lambda _{1}}$
• C. $\frac{\lambda _{1}}{2 \lambda _{2}}$
• D. $\frac{\lambda _{2}}{2 \lambda _{1}}$

Answer 1

Answer: (A)

Position of fringe from central maxima
$y_{1}=\frac{n\lambda _{1} D}{d}$
Given, $n=10$
$$ $y_{1}=\frac{10 \lambda _{1} D}{d}$ ……….(i)
For second source
$y_{2}=\frac{5 \lambda _{2} D}{d}$ ........... (ii)
$$ $\frac{y_{1}}{y_{2}}=\frac{\frac{10 \lambda _{1} D}{d}}{\frac{5 \lambda _{2} D}{d}}$
$\frac{y_{1}}{y_{2}}=\frac{2 \lambda _{1}}{\lambda _{2}}$