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(D) For constructive interference (maxima),the path difference $\Delta x = d \sin 	heta = n\lambda$,where $n$ is an integer.Since the maximum path di

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$3, 0, \pm 75 \, cm$

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(D) For constructive interference (maxima),the path difference $\Delta x = d \sin 	heta = n\lambda$,where $n$ is an integer.Since the maximum path difference is $d = 5 \, cm$ and $\lambda = 3 \, cm$,the possible values for $n$ are determined by $|n| \le d/\lambda = 5/3 \approx 1.66$.Thus,$n$ can take values $0, \pm 1$.For $n = 0$,$\sin 	heta = 0 \implies y = 0$.For $n = \pm 1$,$\sin 	heta = \pm \lambda/d = \pm 3/5 = \pm 0.6$.Using the relation $y = D 	an 	heta$,we find $	an 	heta = \frac{\sin 	heta}{\sqrt{1 - \sin^2 	heta}} = \frac{0.6}{\sqrt{1 - 0.36}} = \frac{0.6}{0.8} = 0.75$.Therefore,$y = D 	an 	heta = 100 	imes 0.75 = \pm 75 \, cm$.The positions of the maxima are $y = 0$ and $y = \pm 75 \, cm$. There are $3$ maxima in total.

Young's double-slit experiment is performed using microwaves of wavelength $\lambda = 3 \, cm$. The distance between the plane of the slits and the screen is $D = 100 \, cm$,and the distance between the slits is $d = 5 \, cm$. Find $(a)$ the number of maxima and $(b)$ their positions on the screen.

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