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Two coherent monochromatic point sources S1 and S2 of wavelength lambda = 600 nm are placed symmetrically about the centre of a circle, separated by d = 1.8 mm. They produce interference fringes seen as alternating bright and dark spots on the circle's circumference. Let P1 be on the perpendicular bisector of S1S2 and P2 on the line of S1S2. The angular separation between consecutive bright spots is delta-theta. Which statement(s) is/are correct?

1. A dark spot will be formed at the point P2
2. The angular separation between two consecutive bright spots decreases as we move from P1 to P2 along the first quadrant
3. At P2 the order of the fringe will be maximum
4. The total number of fringes produced between P1 and P2 in the first quadrant is close to 3000

Correct answer: At P2 the order of the fringe will be maximum

Solution

This is a multiple-correct question. Path difference at angle phi from the source axis is delta = d cos(phi). At P2 (on the axis) delta = d, giving the maximum order, so 'order maximum at P2' is correct. Maximum order = d/lambda = 1.8e-3/600e-9 = 3000, so the number of fringes between P1 and P2 is close to 3000 (also correct). The angular spacing of fringes is not uniform and changes from P1 to P2. The canonical key chosen here is 'At P2 the order of the fringe will be maximum.'

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