Question

Tow monochromatic coherent source of wavelength $5000\mathring{A}$ are placed along the line normal to the screen as shown in the figure.
(a) Determine the condition for maxima at the point $P$.
(b) Find the order of the centre bright fringe if $d=0.5mm,D=1m$

Answer 1

(a) The optical path difference at $P$ is
$p=S_{1}P-S_{2}P=d\cos \theta$
Since. $\cos \theta =1\frac{{\theta }^2}{2}$, where is small,
Therefore, $p=d(1-\frac{{\theta }^2}{2})$
$=d[1-\frac{y^2}{2D^2}]$ where $D+d\approx D$ and $\theta =y/D$
For $nth$ maxima, $p=n\lambda$
$\therefore y=D\sqrt{2(1-\frac{n\lambda }{d})}$
(b) At the central maxima, $\theta =0$
$\therefore p=d=n\lambda$
or $n=\frac{d}{\lambda }=\frac{0.5}{0.5\times {10}^{-3}}=1000$