Two coherent narrow slits emitting light of wavelength in the sam… - Vidyadip

Question

Two coherent narrow slits emitting light of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $3 \lambda$. The light is collected on a screen $S$ which is placed at a distance $D (>> \lambda)$ from the slits. The smallest distance $x$ such that the $P$ is a maxima.

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Answer

In this case path difference is $\mathrm{d} \cos \theta$

so $n \lambda=\lambda=3 \lambda \cos \theta \Rightarrow \cos \theta=\frac{1}{3}$

$\Rightarrow \frac{D}{\sqrt{D^{2}+y^{2}}}=\frac{1}{3} \Rightarrow 3 D=\sqrt{D^{2}+Y^{2}}$

$\Rightarrow y=\sqrt{8} D=2 \sqrt{2} D$

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