Two coherent microwave emitters oscillate at the same frequency and are aimed so that their beams overlap in a large, open laboratory space. At a point P in the overlap region, the electric fields from the two waves can be expressed in complex form as E1=E0eiωt and E2=E0ei(ωt+ϕ), where ϕ is the phase difference produced by the difference in path lengths traveled by the waves.
The following four independent situations are investigated by adjusting the apparatus so that the indicated phase difference ϕ occurs at point P:
(a) For each listed value of ϕ, classify the resulting interference at point P as constructive, destructive, or neither completely constructive nor completely destructive. Provide clear reasoning grounded in the relationship between phase difference and superposition of the electric fields.
(b) Convert each of the four phase differences to an equivalent path-length difference expressed as an exact multiple or fraction of the wavelength λ of the microwaves.
(c) For cases (iii) and (iv), explain qualitatively why the resultant intensity at P is identical even though the numerical values of ϕ differ.
(d) A student claims that any phase difference that is an integer multiple of π must always give complete cancellation. Evaluate the validity of this claim using the examples above and a concise explanation.