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(D) In single slit diffraction,the condition for the $n^{th}$ dark band is given by $d \sin 	heta = n \lambda$. For small angles,$\sin 	heta \approx

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$\frac{2\lambda D}{d}$

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(D) In single slit diffraction,the condition for the $n^{th}$ dark band is given by $d \sin 	heta = n \lambda$. For small angles,$\sin 	heta \approx 	an 	heta = \frac{y}{D}$,where $y$ is the distance from the central bright band. Substituting this into the condition,we get $d \left( \frac{y}{D} ight) = n \lambda$. Thus,the distance of the $n^{th}$ dark band from the central bright band is $y_n = \frac{n \lambda D}{d}$. For the second dark band,we set $n = 2$. Therefore,$y_2 = \frac{2 \lambda D}{d}$.

$A$ parallel beam of light of wavelength $\lambda$ is incident normally on a single slit of width $d$. Diffraction bands are obtained on a screen placed at a distance $D$ from the slit. The second dark band from the central bright band will be at a distance given by

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