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(B) Given: $\lambda = 6.5 	imes 10^{-7} \, m$,$d = 1 \, mm = 10^{-3} \, m$,$D = 1 \, m$.The position of the $n^{th}$ bright fringe is given by $x_{n,

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$1.63$

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(B) Given: $\lambda = 6.5 	imes 10^{-7} \, m$,$d = 1 \, mm = 10^{-3} \, m$,$D = 1 \, m$.The position of the $n^{th}$ bright fringe is given by $x_{n, bright} = n \frac{\lambda D}{d}$.For the $5^{th}$ bright fringe $(n=5)$:$x_{5, bright} = 5 	imes \frac{6.5 	imes 10^{-7} 	imes 1}{10^{-3}} = 32.5 	imes 10^{-4} \, m = 3.25 \, mm$.The position of the $n^{th}$ dark fringe is given by $x_{n, dark} = (2n - 1) \frac{\lambda D}{2d}$.For the $3^{rd}$ dark fringe $(n=3)$:$x_{3, dark} = (2 	imes 3 - 1) 	imes \frac{6.5 	imes 10^{-7} 	imes 1}{2 	imes 10^{-3}} = 5 	imes \frac{6.5 	imes 10^{-4}}{2} = 16.25 	imes 10^{-4} \, m = 1.625 \, mm$.The distance between the $5^{th}$ bright fringe and the $3^{rd}$ dark fringe is:$\Delta x = |x_{5, bright} - x_{3, dark}| = |3.25 - 1.625| \, mm = 1.625 \, mm \approx 1.63 \, mm$.

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