Question

In Young's double slit experiment the ${10}^{th}$ 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 $\frac{y{}_1}{y{}_2}$

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

Position fringe from central maxima:
$y_1=\frac{n{\lambda }_{1}D}{d}$
Given, $n=10$
$\therefore y_1=\frac{10{\lambda }_{1}D}{d}$ .. (i)

For second source:
$y_2=\frac{5{\lambda }_{2}D}{d}$ .. (ii)
$\therefore \frac{y_1}{y_2}=\frac{\frac{10{\lambda }_{1}D}{d}}{\frac{5{\lambda }_{2}D}{d}}$
$\Rightarrow \frac{y_1}{y_2}=\frac{2{\lambda }_1}{{\lambda }_2}$