Question

In Young's double slit experiment, the distance of the $n^{th}$ dark fringe from the centre is-

• A. $n\left(\frac{\lambda D}{2D}\right)$
• B. $n\left(\frac{2d}{\lambda D}\right)$
• C. $(2n-1)\left(\frac{\lambda D}{2d}\right)$
• D. $(2n-1)\left(\frac{4d}{\lambda D}\right)$

Answer 1

The correct option is C $(2n-1)\left(\frac{\lambda D}{2d}\right)$

For $n^{th}$ dark fringe path difference is
$\Delta x=(2n-1)\frac{\lambda }{2}=\frac{dy}{D}$
$y=(2n-1)\frac{D\lambda }{2d}$