Question

In Young’s double slit experiment fifth dark fringe is formed opposite to one of the slit. If $D$ is the distance between the slits and the screen and $d$ is the separation between the slits, then the wavelength of light used is

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

Answer 1

Answer: (B)

Position of $n$ th dark fringes in Young's double slit experiment is given,
$x_n=\frac{D}{d}(2n-1)\frac{\lambda }{2}$
$\Rightarrow \lambda =\frac{2x_{n}d}{D(2n-1)}$...(i)
Since, fitth dark fringe is formed opposite to one of the slit,
$\therefore 2x_5=d$ (distance between slits]
Put $n=5$ in Eq. (i), we get
$\lambda =\frac{2x_{5}d}{D(2\times 5-1)}$
$=\frac{d\cdot d}{D(10-1)}$ [since, $2x_5=d$]
$=\frac{d^2}{9D}$