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)
$\frac{y_1}{y_2}=\frac{\frac{10{\lambda }_{1}D}{d}}{\frac{5{\lambda }_{2}D}{d}}$
$\frac{y_1}{y_2}=\frac{2{\lambda }_1}{{\lambda }_2}$