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(C) The condition for minima in a single slit diffraction is given by $a \sin 	heta = n\lambda$. For small angles, $\sin 	heta \approx 	an 	heta =

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$2D\lambda/a$

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(C) The condition for minima in a single slit diffraction is given by $a \sin 	heta = n\lambda$. For small angles, $\sin 	heta \approx 	an 	heta = y_n/D$, so the position of the $n^{th}$ minima is $y_n = nD\lambda/a$. For the $1^{st}$ minima $(n=1)$, the position is $y_1 = D\lambda/a$. For the $3^{rd}$ minima $(n=3)$, the position is $y_3 = 3D\lambda/a$. The linear separation between the $1^{st}$ and $3^{rd}$ minima is $|y_3 - y_1| = 3D\lambda/a - D\lambda/a = 2D\lambda/a$.

$A$ slit of width $a$ is illuminated by light of wavelength $\lambda$. The linear separation between $1^{st}$ and $3^{rd}$ minima in the diffraction pattern produced on a screen placed at a distance $D$ from the slit system is . . . . . . .

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