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Two monochromatic coherent sources of wavelength 5000 A are placed along line normal to screen as shown. Then the condition for maxima at the point P is :

$(a)\;y = D \sqrt {\frac{2n \lambda}{d}} \\ (b)\;y=D \sqrt { 2 \bigg(1- \frac{n \lambda}{d} \bigg)} \\ (c)\;y=D \sqrt {1- \frac{n \lambda}{d}} \\ (d)\;None $

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1 Answer

The optical path difference at P is
$P= S_1 P -S_2 P = d\cos \theta$
Since $\cos \theta=1 - \large\frac{\theta^2}{2}$
When $\theta$ is small
$\therefore P=d \bigg[1- \large\frac{\theta^2}{2}\bigg]$
$\qquad= d \bigg[ 1- \large\frac{y^2}{2D^2}\bigg]$
Where $D +d =D$
For nth maxima , $P=n \lambda$
$\therefore y=D \sqrt { 2 \bigg(1- \frac{n \lambda}{d} \bigg)}$
Hence b is the correct answer.
answered Feb 20, 2014 by meena.p

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