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 $\frac{d^2}{D}=9\lambda$
$\therefore \lambda =\frac{d^2}{9D}$