Question

At the first minimum adjacent to the central maximum of a single - slit diffraction pattern, the phase difference between the Huygen's wavelet form the edge of the slit and the wavelet from the midpoint of the slit is:

• A. $\frac{\pi }{8}$ radian
• B. $\frac{\pi }{4}$ radian
• C. $\frac{\pi }{2}$ radian
• D. $\pi$ radian

Answer 1

Answer: (D)

$\pi$ radian

If light from symmetric elements near each edge of the slit travels to the centerline of the slit, as indicated by rays 1 and 2 above, their light arrives in phase and experiences constructive interference.
The first minimum in intensity for the light through a single slit can be visualized in terms of rays 3 and 4. An element at one edge of the slit and one just past the centerline are chosen, and the condition for minimum light intensity is that light from these two elements arrive 180 out of phase, or a half wavelength different in pathlength. If those two elements suffer destructive interference, then choosing additional pairs of identical spacing which progress downward across the slit will give destructive interference for all those pairs and therefore an overall minimum in light intensity.