Final answer:
Destructive interference in a double slit experiment occurs when the path-length difference is a half-integral multiple of the wavelength.
Step-by-step explanation:
In physics, particularly in the study of wave interference, destructive interference occurs when two waves of the same frequency and wavelength meet out of phase, resulting in a decreased amplitude of the resultant wave. For a double slit experiment, this happens when the difference in path length, Δd, traveled by two waves from the slits to a point on a screen is a half-integral multiple of their wavelength (λ). Specifically, Δd = (m + ½)λ, where m is an integer, such as 0, 1, -1, 2, -2, etc. For constructive interference, on the other hand, the path-length difference must be an integral multiple of the wavelength, such that Δd = mλ.