At the second minimum of a single-slit diffraction pattern, what is the phase difference between the

Question

At the second minimum of a single-slit diffraction pattern, what is the phase difference between the Huygens' wavelet originating from the extreme edge of the slit and the wavelet from the exact midpoint of the slit?

Professor PC Thomas Classes · Answer

(a) : For the $n$-th minimum in a single slit diffraction, the path difference between wavelets from the two extreme edges of the slit is $\Delta x_{total} = n\lambda$. For the second minimum ($n=2$), the total path difference is $2\lambda$. The path difference between a wavelet from the edge and a wavelet from the midpoint is half of this, which is $\Delta x = \lambda$. The corresponding phase difference is $\Delta \phi = \frac{2\pi}{\lambda} \Delta x = \frac{2\pi}{\lambda} 	imes \lambda = 2\pi \mathrm{~radian}$.