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(C) The fringe width $\beta$ in Young's double-slit experiment is given by the formula: $\beta = \frac{\lambda D}{d}$,where $\lambda$ is the wavelengt

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$2D$

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(C) The fringe width $\beta$ in Young's double-slit experiment is given by the formula: $\beta = \frac{\lambda D}{d}$,where $\lambda$ is the wavelength of light,$D$ is the distance between the screen and the slits,and $d$ is the separation between the slits.To maintain the same fringe spacing $\beta$,the ratio $\frac{D}{d}$ must remain constant.If the slit separation $d$ is doubled (i.e.,$d' = 2d$),then to keep $\beta$ constant,we must have $\frac{D'}{d'} = \frac{D}{d}$.Substituting $d' = 2d$,we get $\frac{D'}{2d} = \frac{D}{d}$,which implies $D' = 2D$.Therefore,the distance $D$ must be doubled.

In Young's double-slit experiment,if the separation between two narrow slits is doubled,then in order to maintain the same fringe spacing,the distance $D$ of the screen from the slits must be changed to:

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