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

Answer: 4

Here, path difference of point $P$ is

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