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# Monochromatic light from narrow slits produce a interference pattern of fridge width $\beta$ , for a certain slit separation. When the slit separation is doubled and distance between screen and slit distance between screen and slit is made $\large\frac{1}{3}$ rd the fringe width

$(a)\;becomes \; 6\;times \\ (b)\;becomes \; \frac{1}{6} th\;times \\ (c)\;becomes \; 3\;times \\ (d)\;becomes \; \frac{1}{3} rd\;times$

Fringe width $= \beta =\large\frac{\lambda}{d}$
$\beta'= \large\frac{\lambda \Large\frac{D}{3}}{2d}$
$\beta'= \large\frac{\lambda D}{6d}$
$\beta' =\large\frac{1}{6}$$\beta$
Hence b is the correct answer.