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(B) The fringe width $\beta$ is given by the formula $\beta = \frac{\lambda D}{d}$.Given: $\lambda = 5890 \, 	ext{Å} = 5890 	imes 10^{-10} \, m$, $D

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$1178 	imes 10^{-6} \, m$

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(B) The fringe width $\beta$ is given by the formula $\beta = \frac{\lambda D}{d}$.Given: $\lambda = 5890 \, 	ext{Å} = 5890 	imes 10^{-10} \, m$, $D = 0.5 \, m$, and $d = 0.5 \, mm = 0.5 	imes 10^{-3} \, m$.Substituting the values: $\beta = \frac{5890 	imes 10^{-10} 	imes 0.5}{0.5 	imes 10^{-3}} = 5890 	imes 10^{-7} \, m = 589 	imes 10^{-6} \, m$.The distance between the $n^{th}$ and $m^{th}$ bright fringe is $(n-m) \beta$.For the first and third bright fringe, the distance is $(3-1) \beta = 2 \beta$.Distance $= 2 	imes 589 	imes 10^{-6} \, m = 1178 	imes 10^{-6} \, m$.

In Young's double slit arrangement, slits are separated by a gap of $0.5 \, mm$, and the screen is placed at a distance of $0.5 \, m$ from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of $5890 \, \text{Å}$ is

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