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

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Q. 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.Physics Question Image

Wave Optics

Solution:

$\Delta x=n \lambda$
in this case path difference is $d \cos \theta$.
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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