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(D) The path difference between the rays coming from the edges of a slit of width $d$ at an angle $	heta$ is given by $\Delta x = d \sin 	heta$.For

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$3\pi$

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(D) The path difference between the rays coming from the edges of a slit of width $d$ at an angle $	heta$ is given by $\Delta x = d \sin 	heta$.For a single slit diffraction pattern,the condition for the $n^{th}$ secondary maximum is given by $d \sin 	heta = (n + \frac{1}{2}) \lambda$,where $n = 1, 2, 3, \dots$.For the first secondary maximum,$n = 1$,so $d \sin 	heta = \frac{3\lambda}{2}$.The phase difference $\phi$ is related to the path difference $\Delta x$ by the formula $\phi = \frac{2\pi}{\lambda} \Delta x$.Substituting the value of path difference for the first secondary maximum: $\phi = \frac{2\pi}{\lambda} 	imes \frac{3\lambda}{2} = 3\pi$.Therefore,the phase difference is $3\pi$.

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