The ratio of the intensity at the centre of a | vedclass

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(A) The intensity in an interference pattern is given by $I = 4I_0 \cos^2(\phi/2)$,where $I_0$ is the intensity of each individual source and $\phi$ i

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$2$

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(A) The intensity in an interference pattern is given by $I = 4I_0 \cos^2(\phi/2)$,where $I_0$ is the intensity of each individual source and $\phi$ is the phase difference.At the central bright fringe,the phase difference $\phi = 0$,so the intensity $I_1 = 4I_0 \cos^2(0) = 4I_0$ ... $(i)$.The distance between two successive bright fringes is the fringe width $\beta$. The phase difference corresponding to this distance $\beta$ is $2\pi$ radians.For a point at a distance of $\beta/4$ from the centre,the phase difference is $\phi' = (2\pi / \beta) 	imes (\beta/4) = \pi/2$ radians.The intensity at this point is $I_2 = 4I_0 \cos^2(\pi/4) = 4I_0 	imes (1/\sqrt{2})^2 = 4I_0 	imes (1/2) = 2I_0$ ... $(ii)$.Taking the ratio of $(i)$ and $(ii)$,we get $I_1 / I_2 = (4I_0) / (2I_0) = 2$.

The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringes from the centre is

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