Two coherent point sources A and B are in phase and are separated by 3.6λ. A circular path is centred at the midpoint of AB and has radius greater than AB ÷ 2, so that both sources lie inside the circle. An observer moves once around the complete circle. How many positions of maximum intensity are encountered?
Physics · Wave Optics · interferece of light and huygen principle
JEE Mains NEET JEE Advanced

Question

Two coherent point sources A and B are in phase and are separated by 3.6λ. A circular path is centred at the midpoint of AB and has radius greater than AB ÷ 2, so that both sources lie inside the circle. An observer moves once around the complete circle. How many positions of maximum intensity are encountered?

Physics · Wave Optics · interferece of light and huygen principle

G1 Physics · Accepted Answer

The signed path difference on the circle ranges between values near −3.6λ and +3.6λ. For maxima, Δ = nλ. Allowed integers are −3, −2, −1, 0, 1, 2, 3. There are seven allowed signed path-difference values. Each intersects the circular observation path at two points. Therefore, number of maxima = 7×2 = 14. Hence the answer is 14.