Question

In the 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,
$\frac{Yd}{D}=\left(2m-1\right)\frac{\lambda }{2}$


Here, $m=5,Y=\frac{d}{2}$
$\therefore \frac{d}{2}\frac{d}{D}=\left(2\times 5-1\right)\frac{\lambda }{2}$
Or $\frac{d^2}{D}=9\lambda$
$\therefore \lambda =\frac{d^2}{9D}$