In a double-slit arrangement, the two slits are separated by d=0.50mm and the interference pattern is observed on a screen D=2.0m away. The light used has wavelength λ=650nm.
(i) Derive an expression for the path difference Δx between the two waves reaching a point on the screen that is at a transverse distance y from the central bright fringe.
(ii) Using your result from part (i), obtain the corresponding expression for the phase difference ϕ at that point in terms of y, d, D and λ.
(iii) If the phase difference at some point is 3π, calculate the value of y for that point.
(iv) State whether this point corresponds to a bright fringe or a dark fringe and indicate its fringe order with respect to the central maximum.