Halliday, Resnick & Walker — Interference: Problem 68

68 In Fig. 35-36, two isotropic point sources \(S_1\) and \(S_2\) emit light in phase at wavelength \(\lambda\) and at the same amplitude. The sources are separated by distance \(2d = 6.00\lambda\). They lie on an axis that is parallel to an \(x\) axis, which runs along a viewing screen at distance \(D = 20.0\lambda\). The origin lies on the perpendicular bisector between the sources. The figure shows two rays reaching point \(P\) on the screen, at position \(x_P\). (a) At what value of \(x_P\) do the rays have the minimum possible phase difference? (b) What multiple of \(\lambda\) gives that minimum phase difference? (c) At what value of \(x_P\) do the rays have the maximum possible phase difference? What multiple of \(\lambda\) gives (d) that maximum phase difference and (e) the phase difference when \(x_P = 6.00\lambda\)? (f) When \(x_P = 6.00\lambda\), is the resulting intensity at point \(P\) maximum, minimum, intermediate but closer to maximum, or intermediate but closer to minimum?