Two coherent point sources A and B are in phase and form the endpoints of the diameter of a semicircle. Their separation is AB = 6λ. An observer moves along the open semicircular arc from A to B, with the endpoints excluded. How many positions of maximum intensity occur on the arc?
Physics · Wave Optics · interferece of light and huygen principle
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Question

Two coherent point sources A and B are in phase and form the endpoints of the diameter of a semicircle. Their separation is AB = 6λ. An observer moves along the open semicircular arc from A to B, with the endpoints excluded. How many positions of maximum intensity occur on the arc?

Physics · Wave Optics · interferece of light and huygen principle

G1 Physics · Accepted Answer

Along the open semicircular arc, the signed path difference PA−PB changes continuously through values strictly between −6λ and +6λ. For maxima, Δ = nλ. Since the endpoint values ±6λ are excluded, the allowed integers are n = −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5. That gives 11 positions. Hence the answer is 11.