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(C) For a single slit diffraction experiment, the condition for the $n^{th}$ order minima is given by $a \sin 	heta = n \lambda$.For small angles, $\

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$275$

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(C) For a single slit diffraction experiment, the condition for the $n^{th}$ order minima is given by $a \sin 	heta = n \lambda$.For small angles, $\sin 	heta \approx 	an 	heta = \frac{y}{D}$.Thus, the distance of the $n^{th}$ minima from the central maximum is $y_n = \frac{n \lambda D}{a}$.Given: $\lambda = 550 \,nm = 550 	imes 10^{-9} \,m$, $a = 0.20 \,mm = 0.20 	imes 10^{-3} \,m$, $D = 100 \,cm = 1.0 \,m$, and $n = 1$.Substituting these values:$y_1 = \frac{1 	imes 550 	imes 10^{-9} 	imes 1.0}{0.20 	imes 10^{-3}} \,m$$y_1 = \frac{550}{0.20} 	imes 10^{-6} \,m$$y_1 = 2750 	imes 10^{-6} \,m = 275 	imes 10^{-5} \,m$.Comparing this with $x 	imes 10^{-5} \,m$, we get $x = 275$.

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