Question

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

• A. $\frac{2y_1}{y_2}$
• B. $\frac{2y_2}{y_1}$
• C. $\frac{y_1}{2y_2}$
• D. $\frac{y_2}{2y_1}$

Answer 1

The correct option is C $\frac{y_1}{2y_2}$

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