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(B) The path difference $\Delta x$ at any point on the screen is given by $\Delta x = d \cos 	heta$,where $d = 2 \lambda$ is the distance between the

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$3$

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(B) The path difference $\Delta x$ at any point on the screen is given by $\Delta x = d \cos 	heta$,where $d = 2 \lambda$ is the distance between the sources and $	heta$ is the angle with the line joining the sources.For maxima,the path difference must be an integer multiple of $\lambda$,i.e.,$\Delta x = n \lambda$.Since the screen is perpendicular to the line joining the sources,the range of $	heta$ is from $0$ to $90^\circ$ (or $0$ to $\pi/2$ radians).Thus,$\Delta x = 2 \lambda \cos 	heta$.As $	heta$ varies from $0$ to $90^\circ$,$\cos 	heta$ varies from $1$ to $0$.Therefore,the path difference $\Delta x$ varies from $2 \lambda$ to $0$.The possible values for $n$ in $\Delta x = n \lambda$ are $n = 0, 1, 2$.For $n = 2$,$\Delta x = 2 \lambda$ (at $	heta = 0$,the point on the screen closest to the sources).For $n = 1$,$\Delta x = \lambda$ (at $\cos 	heta = 0.5$,i.e.,$	heta = 60^\circ$).For $n = 0$,$\Delta x = 0$ (at $	heta = 90^\circ$,i.e.,at infinity).Since the screen is symmetric on both sides of the line joining the sources,we have:- At $	heta = 0$: $1$ central maxima $(n=2)$.- For $	heta > 0$: $2$ maximas for $n=1$ (one on each side) and $2$ maximas for $n=0$ (one on each side at infinity).However,the question typically asks for finite points on the screen. At $	heta = 90^\circ$,the path difference is $0$,which corresponds to the point at infinity. Excluding the points at infinity,we have $n=2$ (one point) and $n=1$ (two points),totaling $3$ maximas.

Two coherent sources are kept at a distance of $d = 2 \lambda$. $A$ large screen is placed perpendicular to the line joining the sources. Determine the total number of maximas observed on the screen. (Here,$\lambda$ is the wavelength of light.)

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