A parallel beam of monochromatic light of wavelength $\lambda$ is incident normally on a single narr

Question

A parallel beam of monochromatic light of wavelength $\lambda$ is incident normally on a single narrow slit. In the resulting diffraction pattern formed on a screen, the phase difference between the light rays originating from the two extreme edges of the slit at the position of the first secondary maximum is

Professor PC Thomas Classes · Answer

(a) : In a single slit Fraunhofer diffraction pattern, the geometric condition for the $n$-th secondary maximum dictates a path difference of $\Delta x = (2n + 1)\frac{\lambda}{2}$ between the waves emanating from the extreme edges of the slit. For the very first secondary maximum ($n=1$), this path difference is exactly $\Delta x = \frac{3\lambda}{2}$. The corresponding phase difference is calculated as $\Delta \phi = \frac{2\pi}{\lambda} 	imes \Delta x = \frac{2\pi}{\lambda} 	imes \frac{3\lambda}{2} = 3\pi$.