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(D) The position of the $n^{th}$ order bright fringe in Young's double slit experiment is given by $y_n = \frac{n \lambda D}{d}$.Given:Slit separation

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$4 	imes 10^{-4} 	ext{ m}$

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(D) The position of the $n^{th}$ order bright fringe in Young's double slit experiment is given by $y_n = \frac{n \lambda D}{d}$.Given:Slit separation $d = 3 	ext{ mm} = 3 	imes 10^{-3} 	ext{ m}$.Distance to screen $D = 2 	ext{ m}$.Order $n = 5$.Wavelengths $\lambda_1 = 480 	ext{ nm} = 480 	imes 10^{-9} 	ext{ m}$ and $\lambda_2 = 600 	ext{ nm} = 600 	imes 10^{-9} 	ext{ m}$.The position of the $5^{th}$ bright fringe for $\lambda_1$ is $y_1 = \frac{5 	imes 480 	imes 10^{-9} 	imes 2}{3 	imes 10^{-3}} = 1600 	imes 10^{-6} 	ext{ m} = 1.6 	imes 10^{-3} 	ext{ m}$.The position of the $5^{th}$ bright fringe for $\lambda_2$ is $y_2 = \frac{5 	imes 600 	imes 10^{-9} 	imes 2}{3 	imes 10^{-3}} = 2000 	imes 10^{-6} 	ext{ m} = 2.0 	imes 10^{-3} 	ext{ m}$.The separation between the two fringes is $\Delta y = |y_2 - y_1| = (2.0 - 1.6) 	imes 10^{-3} 	ext{ m} = 0.4 	imes 10^{-3} 	ext{ m} = 4 	imes 10^{-4} 	ext{ m}$.

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