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(C) Given: Slit separation $d = 1 \, mm = 10^{-3} \, m$,screen distance $D = 1 \, m$,wavelength $\lambda = 5 	imes 10^{-7} \, m$.The position of the

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$1.25$

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(C) Given: Slit separation $d = 1 \, mm = 10^{-3} \, m$,screen distance $D = 1 \, m$,wavelength $\lambda = 5 	imes 10^{-7} \, m$.The position of the $n^{th}$ bright fringe is given by $y_{bright} = n \frac{D \lambda}{d}$.For the $5^{th}$ bright fringe $(n=5)$: $y_1 = 5 \frac{D \lambda}{d}$.The position of the $n^{th}$ dark fringe is given by $y_{dark} = (n - 0.5) \frac{D \lambda}{d}$.For the $3^{rd}$ dark fringe $(n=3)$: $y_2 = (3 - 0.5) \frac{D \lambda}{d} = 2.5 \frac{D \lambda}{d}$.The distance between them is $\Delta y = |y_1 - y_2| = |5 - 2.5| \frac{D \lambda}{d} = 2.5 \frac{D \lambda}{d}$.Substituting the values:$\Delta y = 2.5 	imes \frac{1 	imes 5 	imes 10^{-7}}{10^{-3}} \, m$$\Delta y = 2.5 	imes 5 	imes 10^{-4} \, m = 12.5 	imes 10^{-4} \, m = 1.25 	imes 10^{-3} \, m = 1.25 \, mm$.

Two slits are $1 \, mm$ apart from each other and the distance of the screen is $1 \, m$. If illuminated with light of wavelength $5 \times 10^{-7} \, m$,the distance between the $3^{rd}$ dark fringe and the $5^{th}$ bright fringe is......$mm$.

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