Two coherent point sources S_1 and S_2 vibrat | vedclass

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(C) From the figure,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

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$\sqrt{3} D$

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(C) From the figure,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 $\lambda$ (since they are in phase).From the geometry of the setup,the path difference can be approximated as $\Delta x = d \cos 	heta$,where $d = 2 \lambda$ is the separation between the sources.Thus,$2 \lambda \cos 	heta = \lambda$.$\cos 	heta = \frac{1}{2}$,which implies $	heta = 60^{\circ}$.From the right-angled triangle formed by the screen,$	an 	heta = \frac{OP}{D} = \frac{x}{D}$.Since $	heta = 60^{\circ}$,$	an 60^{\circ} = \sqrt{3}$.Therefore,$\frac{x}{D} = \sqrt{3}$,which gives $x = \sqrt{3} D$.

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