In Young's double slit experiment, the path difference between two interfering light waves at a point on the screen is Δx = 3.5 λ (where λ is the wavelength). What type of interference occurs at this point, and what is the corresponding phase difference?
Answer and explanation
Correct answer: A. Destructive interference (dark fringe), phase difference Δφ = 7π radians
.
- Step 1: The relationship between phase difference and path difference is: .
- Step 2: Substitute :
- Step 3: For constructive interference, the path difference must be an integer multiple of wavelength (, phase difference ).
- Step 4: For destructive interference, the path difference must be an odd half-integral multiple of wavelength: , and phase difference must be an odd multiple of : .
- Step 5: Since is an odd multiple of and , this point experiences completely destructive interference (a dark fringe).
Answer
Destructive interference (dark fringe), phase difference Δφ = 7π radians
Why not the others: 'Constructive interference, phase difference 7π' confuses odd multiples of (which produce cancellation: ) with even multiples (); 'Phase difference 3.5π' forgets the factor of 2 in ; 'Destructive interference, phase difference 3.5π' has the correct nature but an incorrect phase calculation.
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