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In a Young's double-slit setup the slit separation is d = 3 mm and the screen is D = 1 m away. Microwaves of wavelength lambda = 1 mm are incident normally on the slits. Find the distance of the first maximum on the screen from the central maximum, and the total number of maxima observable on the screen.

1. First maximum at 1/3 m from centre; total 7 maxima
2. First maximum at 1/3 m from centre; total 5 maxima
3. First maximum at 1 m from centre; total 7 maxima
4. First maximum at 1/6 m from centre; total 3 maxima

Correct answer: First maximum at 1/3 m from centre; total 7 maxima

Solution

Approximate first-maximum position: y1 = lambda*D/d = (1 mm)(1 m)/(3 mm) = 1/3 m. For the total count, use the exact condition d*sin(theta) = n*lambda -> sin(theta) = n*lambda/d = n/3. Since |sin(theta)| <= 1, n can be -3, -2, -1, 0, 1, 2, 3, i.e. 7 values (n = +-3 gives sin theta = +-1, grazing). Hence there are 7 maxima, with the first one at about 1/3 m from the centre.

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