Question

In Young’s double slit experiment, the ${10}^{th}$ maximum of wavelength ${\lambda }_1$ is at distance $y_1$ from its central maximum and the $5^{th}$ maximum of wavelength ${\lambda }_2$ is at a distance $y_2$ from its central maximum. The ratio $\frac{y_1}{y_2}$ will be

• 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

The correct option is A

$\frac{2{\lambda }_1}{{\lambda }_2}$

We know that $y_n=\frac{n\lambda D}{d}$. Therefore, for wavelength ${\lambda }_1$,

$y_1=\frac{10{\lambda }_{1}D}{d}$

and for wavelength ${\lambda }_2$,

$y_2=\frac{5{\lambda }_{2}D}{d}$

$\therefore \frac{y_1}{y_2}=\frac{2{\lambda }_1}{{\lambda }_2}$