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(B) In Young's double slit experiment,the fringe width (fringe separation) $\beta$ is given by the formula:$\beta = \frac{\lambda D}{d}$Since the wave

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$0.5$

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(B) In Young's double slit experiment,the fringe width (fringe separation) $\beta$ is given by the formula:$\beta = \frac{\lambda D}{d}$Since the wavelength $\lambda$ is related to the frequency $f$ by $\lambda = \frac{c}{f}$,where $c$ is the speed of light,we can substitute this into the formula:$\beta = \frac{cD}{fd}$Assuming the distance between the slits $d$ and the distance to the screen $D$ remain constant,the fringe width is inversely proportional to the frequency:$\beta \propto \frac{1}{f}$Given that the initial fringe separation $\beta_1 = 1.0 \,mm$ at frequency $f_1 = f$,when the frequency is doubled $(f_2 = 2f)$,the new fringe separation $\beta_2$ will be:$\beta_2 = \beta_1 	imes \frac{f_1}{f_2} = 1.0 \,mm 	imes \frac{f}{2f} = 0.5 \,mm$Therefore,the new separation of the bright fringes is $0.5 \,mm$.

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