Two point sources separated by d = 5, mu m em | vedclass

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(D) Let the two sources be $S_1$ and $S_2$ separated by $d = 5\, \mu m$. The distance between them is $d = 5\, \mu m$ and wavelength $\lambda = 2\, \m

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Points $A$ and $C$ are bright and points $B$ and $D$ are dark.

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(D) Let the two sources be $S_1$ and $S_2$ separated by $d = 5\, \mu m$. The distance between them is $d = 5\, \mu m$ and wavelength $\lambda = 2\, \mu m$.At point $A$ (and $C$),the path difference $\Delta x = \sqrt{R^2 + (d/2)^2} - \sqrt{R^2 + (d/2)^2} = 0$. Since the sources are in phase,$\Delta x = 0$ corresponds to constructive interference (bright).At point $B$,the path difference is $\Delta x = (R + d/2) - (R - d/2) = d = 5\, \mu m$.Since $\Delta x = 5\, \mu m$ and $\lambda = 2\, \mu m$,$\Delta x = 2.5\lambda$. This corresponds to destructive interference (dark).At point $D$,the path difference is $\Delta x = (R - d/2) - (R + d/2) = -d = -5\, \mu m$,which is also $2.5\lambda$ in magnitude,resulting in destructive interference (dark).Thus,points $A$ and $C$ are bright,and points $B$ and $D$ are dark.

Two point sources separated by $d = 5\, \mu m$ emit light of wavelength $\lambda = 2\, \mu m$ in phase. $A$ circular wire of radius $R = 20\, \mu m$ is placed around the sources as shown in the figure. Determine the nature of interference at points $A, B, C,$ and $D$.

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