Question

Two coherent point sources $S_1$ and $S_2$ vibrating in phase emit light of wavelength $\lambda$0 the separation between the sources is $2\lambda .$ consider a line passing thrrough $S_2$ and perpendicular to the line$S_1{S}_2$ What is the smallest distance from $S_2$ where is the smallest distance from $S_2$ where a minimum of intensity occurs?

Answer 1

For minimum intensity
$\therefore S_{1}P-S_{2}P=x=(2n+1)\frac{\lambda }{2}$
Thus, we get
$\Rightarrow \sqrt{Z^2+(2\lambda {)}^2}-Z=(2n+1)\frac{\lambda }{2}\Rightarrow Z^2+4{\lambda }^2=Z^2(2n+1{)}^2\frac{{\lambda }_2}{4}+2Z(2n+1)\frac{\lambda }{2}\Rightarrow Z=\frac{4{\lambda }^2-(2n+1)\frac{2{\lambda }^2}{4}}{(2n+1)\lambda }=\frac{163{\lambda }^2-(2n+1{)}^2{\lambda }^2}{4(2n+1)\lambda \cdots }$
Putting $n=0\Rightarrow z=\frac{15\lambda }{4}n=-1\Rightarrow Z=\frac{-15\lambda }{4}n=1=\Rightarrow Z=\frac{7\lambda }{12}n=2\Rightarrow Z=\frac{-9\lambda }{20}$
$\therefore Z=\frac{7\lambda }{12}$ is the smallest distance for there will be minimum intensity.