Question

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

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

Answer 1

The correct option is A $\frac{d^2}{2\lambda D}$

path difference is $\sqrt{(}{D}^2+d^2)-D=n\lambda$ (as bright fringe is formed )
so ,
$D(1+\frac{d}{D}{)}^{\frac{1}{2}}-D=n\lambda$

$D+\frac{d^2}{2D}-D=n\lambda$

$n\lambda =\frac{d^2}{2D}$

$n=\frac{d^2}{2\lambda D}$
option $A$ is correct