Question

K 2. Point Source Interference Pattern

Consider a two-dimensional x-y space in which there are two identical and synchronized point sources located at y=±D/2 emitting waves of wavelength λ. The sources are said to constructively interfere at any location if the phase difference between waves received from the two sources at that location differ by an integral multiple of 2π. Equivalently, the distances from the location to the two sources differ by an integral number of wavelengths. Derive the complete set of locations in x-y space for constructive interference, not simply the asymptotic limits far from the sources. Important: since you already know the answer from class, you will be graded not on the answer, but on the correctness of the process you use to reach that answer. An incorrect process that somehow ends up with the correct answer will not be credited.

Answer 1

Solution:

S₁ and S₂ are two syncronized point sources at y = D/2 and y = - D/2.

P (x, y) is a point of constructive interference of light from S₁ and S₂.

At point P phase difference between light waves from S1 and S2 must have phase difference of

S₂P - S₁P = n

For Different values of n, locus of all points of constructive interference is a family of hyperbolas as show in next image.