Question

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

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

Answer 1

Answer: (D)

For dark fringe,
$\frac{Y d}{D}=\left(2 m - 1\right)\frac{\lambda }{2}$


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