Two coherent point sources S_1 and S_2 vibrat | vedclass

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(C) The path difference between the waves reaching point $P$ from $S_1$ and $S_2$ is given by $\Delta x = S_1 P - S_2 P$.For the first bright fringe,

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$\sqrt{3} D$

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(C) The path difference between the waves reaching point $P$ from $S_1$ and $S_2$ is given by $\Delta x = S_1 P - S_2 P$.For the first bright fringe, the path difference must be equal to the wavelength, so $\Delta x = \lambda$.From the geometry of the setup, the path difference can also be expressed as $\Delta x = d \cos 	heta$, where $d = 2 \lambda$ is the separation between the sources.Thus, $2 \lambda \cos 	heta = \lambda$.This simplifies to $\cos 	heta = \frac{1}{2}$, which means $	heta = 60^{\circ}$.From the right-angled triangle formed by the screen, we have $	an 	heta = \frac{OP}{D}$.Substituting $	heta = 60^{\circ}$, we get $	an 60^{\circ} = \frac{OP}{D}$.Since $	an 60^{\circ} = \sqrt{3}$, we have $\sqrt{3} = \frac{OP}{D}$.Therefore, $OP = \sqrt{3} D$.

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