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In a modified double-slit setup, two coherent point sources S1 and S2 (wavelength 600 nm) lie in the x-y plane, separated by d = 0.6003 mm. The screen is placed parallel to the x-z plane (for z > 0) at a distance D = 3 m from the midpoint of S1S2. The origin O is where the screen meets the line joining S1 and S2. Which statement(s) about the intensity pattern on the screen is/are correct?

1. Hyperbolic bright and dark bands with foci placed symmetrically about O along the x-direction
2. Concentric semicircular bright and dark bands centred at O
3. The region very close to O will be dark
4. Straight bright and dark fringes parallel to the x-axis

Correct answer: Hyperbolic bright and dark bands with foci placed symmetrically about O along the x-direction

Solution

The set of points with constant path difference |r1 - r2| from two point sources forms hyperboloids whose foci are S1 and S2. When the screen is oriented along the line of the sources (parallel to x-z plane here, with the S1S2 line in the plane), the fringes are hyperbolas with foci symmetric about O along the x-direction. At O, the path difference equals d = 0.6003 mm = 1000.5 * 600 nm, a half-integer multiple of lambda, so O is a dark point (this also makes the third statement true in the original multi-answer item). The geometric character of the bands is hyperbolic.

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