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(B) Given: Distance between slits $d = 1 \,mm = 10^{-3} \,m$, wavelength $\lambda = 6.5 	imes 10^{-7} \,m$, distance of screen $D = 1 \,m$.For the $n

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$1.625$

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(B) Given: Distance between slits $d = 1 \,mm = 10^{-3} \,m$, wavelength $\lambda = 6.5 	imes 10^{-7} \,m$, distance of screen $D = 1 \,m$.For the $n^{th}$ dark fringe, the position is given by $y_n = (n - 0.5) \frac{\lambda D}{d}$.For the $3^{rd}$ dark fringe $(n=3)$: $y_3 = (3 - 0.5) \frac{6.5 	imes 10^{-7} 	imes 1}{10^{-3}} = 2.5 	imes 6.5 	imes 10^{-4} = 16.25 	imes 10^{-4} \,m$.For the $n^{th}$ bright fringe, the position is given by $y_n = \frac{n \lambda D}{d}$.For the $5^{th}$ bright fringe $(n=5)$: $y_5 = \frac{5 	imes 6.5 	imes 10^{-7} 	imes 1}{10^{-3}} = 32.5 	imes 10^{-4} \,m$.The distance between the $3^{rd}$ dark fringe and the $5^{th}$ bright fringe is $\Delta y = y_5 - y_3 = 32.5 	imes 10^{-4} - 16.25 	imes 10^{-4} = 16.25 	imes 10^{-4} \,m = 1.625 \,mm$.

Two slits separated by a distance of $1 \,mm$ are illuminated with light of wavelength $6.5 \times 10^{-7} \,m$. The interference fringes are observed on a screen placed at $1 \,m$ from the slits. The distance between the third dark fringe and the fifth bright fringe is equal to (in $\,mm$)

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