Explain why the pattern of maxima and minima observed in single-slit diffraction differs from that observed in double-slit interference, even when the slit separation and wavelength are the same.

In double‑slit interference the two slits are essentially point sources, so the path difference between the two waves at a screen point is


d = dsin heta

where d is the slit separation. Constructive interference occurs when dsin heta = mlambda, giving equally spaced bright fringes of equal intensity.

In single‑slit diffraction the slit has a finite width a. Huygens’ principle shows that each point across the slit acts as a secondary source. The path difference between the extreme parts of the slit is asin heta. Destructive interference occurs when asin heta = mlambda (m≠0), so the minima are at the same angles as the double‑slit condition, but the intensity between minima is not constant. The central maximum is twice as wide as the secondary maxima, and the intensity of successive maxima decreases because the contributions from different parts of the slit add with varying phase.

Thus the single‑slit pattern is a diffraction envelope that modulates the double‑slit interference fringes. Where the envelope has a minimum, the interference fringes are suppressed or absent, and the remaining fringes have reduced intensity.