Question

In a double slit experiment, $5th$ dark fringe is formed opposite to one of the slits, the wavelength of light is

• A. $\frac{d^{2}}{6D}$
• B. $\frac{d^{2}}{5D}$
• C. $\frac{d^{2}}{15D}$
• D. $\frac{d^{2}}{9D}$

Answer 1

Answer: (D)

For dark fringe,
$\frac{xd}{D} =\left(2m-1\right) \frac{\lambda}{2}$
Here, $m=5,\,\, x=\frac{d}{2}$
$\therefore \frac{d}{2} \cdot \frac{d}{D}=(2 \times 5-1) \frac{\lambda}{2}$
or $\frac{d^{2}}{D}=9 \lambda$
$\therefore \lambda=\frac{d^{2}}{9 D}$