Question

Two coherent light sources $S_{1}$ and $S_{2}$ each of wavelength $\lambda$ are separated by a distance $d=2 \lambda$. The number of minima formed on the screen as shown in the figure is ______.

Answer 1

Here, path difference of point $P$ is

For minima, $d \sin \theta=(2 m-1) \frac{\lambda}{2}$
or $2 \lambda \sin \theta=(2 m-1) \frac{\lambda}{2}$
or $ \sin \theta=\frac{(2 m-1)}{4}$
$-1<\sin \theta<1$
or $-1<\frac{(2 m-1)}{4}<1$
or $-4<(2 m-1)<4$
or $-3<2 m<5$
or $-1.5 < m < 2.5$
$\therefore m=-1,0,1,2$
Thus number of minima is $4$