Two point sources $S_1$ and $S_2$ separated by a distance $10 \mu \mathrm{m}$ emit light waves of wavelength…

Two point sources $S_1$ and $S_2$ separated by a distance $10 \mu \mathrm{m}$ emit light waves of wavelength $4 \mu \mathrm{m}$ in phase. A circular wire of radius $40 \mu \mathrm{m}$ is placed around the sources as shown in figure, then ( $O$ is the centre of the circle and $O S_1=O S_2$ )

1. points $A$ and $B$ are dark and points $C$ and $D$ are bright
2. points $A$ and $B$ are bright and point $C$ and $D$ are dark
3. points $A$ and $C$ are dark and points $B$ and $D$ are bright
4. points $A$ and $C$ are bright and points $B$ and $D$ are dark

Solution

Path difference at point $B$, $ \Delta x_B=S_1 B-S_2 B=0 $ and at point $D$, $ \Delta x_D=S_1 D-S_2 D=0 $ Phase difference, $ \phi=\frac{2 \pi}{\lambda} \times(0)=0 $ So, intensity at points $B$ and $D$ $ I=I_{\max } \cos ^2(\phi / 2)=I_{\max } $
So, points $B$ and $D$ are bright. Path difference at point $A$, $ \Delta x_A=35 \mu \mathrm{m} $ $ [40-5] $ But, figure shows $\Delta x_A=\Delta x_C$ is maximum for given circle. When path difference is maximum, intensity will be minimum. So, points $A$ and $C$ are dark

Asked in: AP EAMCET 2018 (23 Apr Shift 1)

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