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Two identical narrow slits S1 and S2 are illuminated by light of wavelength lambda from a point source P. Light reaching the slits then falls on a screen point Q. Let l1, l2 be the path lengths from P to S1 and P to S2, and l3, l4 the path lengths from S1 to Q and S2 to Q respectively. For integer n, what is the condition for destructive interference at Q?

1. (l1 - l2) = (2n + 1)*lambda/2
2. (l3 - l4) = (2n + 1)*lambda/2
3. (l1 + l2) - (l3 + l4) = n*lambda
4. (l1 + l3) - (l2 + l4) = (2n + 1)*lambda/2

Correct answer: (l1 + l3) - (l2 + l4) = (2n + 1)*lambda/2

Solution

The two interfering routes are P-S1-Q (length l1 + l3) and P-S2-Q (length l2 + l4). The path difference is (l1 + l3) - (l2 + l4). Destructive interference occurs when this equals an odd multiple of lambda/2, i.e. (2n+1)lambda/2.

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