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(B) The condition for the $n^{th}$ dark fringe in a single slit diffraction pattern is given by $d \sin 	heta = n \lambda$. For small angles, $\sin \

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$2.4 \,mm$

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(B) The condition for the $n^{th}$ dark fringe in a single slit diffraction pattern is given by $d \sin 	heta = n \lambda$. For small angles, $\sin 	heta \approx 	an 	heta = \frac{y_n}{D}$.Thus, the position of the $n^{th}$ dark fringe is $y_n = \frac{n \lambda D}{d}$.Given: $\lambda = 600 \,nm = 600 	imes 10^{-9} \,m$, $D = 2 \,m$, $d = 1 \,mm = 10^{-3} \,m$.For the first dark fringe $(n=1)$:$y_1 = \frac{1 	imes 600 	imes 10^{-9} 	imes 2}{10^{-3}} = 1200 	imes 10^{-6} \,m = 1.2 	imes 10^{-3} \,m = 1.2 \,mm$.The distance between the first dark fringe on either side of the central bright fringe is $2 y_1 = 2 	imes 1.2 \,mm = 2.4 \,mm$.

$A$ beam of light of wavelength $600 \,nm$ from a distant source falls on a single slit $1 \,mm$ wide and the resulting diffraction pattern is observed on a screen $2 \,m$ away. The distance between the first dark fringe on either side of the central bright fringe is

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