Question

Three identical monochromatic point sources of light emit light of wavelength $\lambda$ coherently and in phase with each other. They are placed on the x-axis at the points x = -d, 0 and d, find the minimum value of $d/\lambda$ for which there is destructive interference with almost zero resultant intensity at points on the x-axis having x>>d.

Answer 1

Give,

three identical monochromatic point source. $Wavelegth=\lambda$

$\Delta x=(n+\frac{1}{2})\lambda$

$S=\frac{2\pi }{\lambda }\times (n+\frac{1}{2})\lambda$

$I=A^2\left(\frac{si{n}^2\frac{N\delta }{2}}{si{n}^2\frac{\delta }{2}}\right)Since$(N=3)$

$\delta =\left(\frac{2\pi }{\lambda }\right)d$

For destructive interference,

$\delta =2\pi (n+\frac{1}{2})=\frac{2\pi }{\lambda }d$ $n=1$

$\frac{d}{\lambda }=1+\frac{1}{2}=\frac{3}{2}$