Two identical narrow slits S1 and S2, separated by a distance d, are illuminated by monochromatic light of wavelength λ. A flat screen is placed at a distance D (with D≫d) from the plane of the slits, and P is a point located at a small distance y above the central line on the screen.
Answer the following questions about the interference pattern produced.
(i) Define the term path difference for the two waves reaching the point P.
(ii) Using suitable geometrical reasoning, obtain an approximate relation between the path difference Δx at P and the distance y (i.e. show that Δx is proportional to y for small angles).
(iii) Hence derive the expressions for the positions of (a) the nᵗʰ bright fringe and (b) the nᵗʰ dark fringe measured from the central maximum.
(iv) State the conditions for constructive and destructive interference in terms of the path difference.