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Two coherent monochromatic point sources of light are separated by a fixed distance in a horizontal plane. In that horizontal plane, what is the locus of all points that experience constructive interference?

1. a single hyperbola
2. a family of hyperbolas
3. a family of straight lines
4. a family of parabolas

Correct answer: a family of hyperbolas

Solution

Constructive interference occurs where |r1 - r2| = m*lambda (m = 0, 1, 2,...). The set of points with a constant difference of distances from two fixed foci is a hyperbola. Since m takes many integer values, each giving a different constant path difference, the loci form a family of hyperbolas (the m = 0 case is the perpendicular bisector, a straight line, but the general set is hyperbolas).

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