Two identical narrow slits separated by a distance d are illuminated by monochromatic light of wavelength λ and the interference pattern is observed on a distant screen.
(i) Define (a) path difference (Δx) and (b) phase difference (ϕ) between the two interfering waves at an arbitrary point on the screen.
(ii) Establish the mathematical relation connecting ϕ and Δx.
(iii) Using this relation, state the condition for (a) constructive and (b) destructive interference in terms of path difference.
(iv) Explain, with proper reasoning, why points on the screen corresponding to Δx=nλ appear bright while those at Δx=(2n−1)λ/2 appear dark.