Question

In a double slit experiment, the distance between the slits is $d$. The screen is at a distance $D$ from the slits. If a bright fringe is formed opposite to one of the slits, its order is

• A. $\frac{d}{\lambda}$
• B. $\frac{\lambda^{2}}{dD}$
• C. $\frac{D^{2}}{2\lambda d}$
• D. $\frac{d^{2}}{2D\lambda}$

Answer 1

Answer: (D)

When a bright fringe is formed opposite to one of the slits, $x = \frac{d}{2}$
Path difference $ = \frac{xd}{D} $
$= \frac{d}{2} \times \frac{d}{D} = \frac{d^2}{2D}$
If it is $n^{th}$ order bright fringe,
Path differnce, $n\lambda = \frac{d^2}{2D}$ or $ n = \frac{d^2}{2D\lambda}$