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In a two-slit interference pattern, dark fringes (destructive interference) occur where the path difference between the two waves is:
A$n\lambda$, with $n = 0, 1, 2, \dots$
B$(2n-1)\dfrac{\lambda}{2}$, with $n = 1, 2, 3, \dots$
C$n\dfrac{\lambda}{4}$
D$(2n+1)\lambda$
Answer & Solution
Correct answer: B. $(2n-1)\dfrac{\lambda}{2}$, with $n = 1, 2, 3, \dots$
Bright fringes occur when the path difference is an integer multiple of the wavelength ($n\lambda$), giving constructive interference. Dark fringes occur when the path difference is an odd multiple of half a wavelength, $(2n-1)\lambda/2$, producing complete destructive interference between waves of equal amplitude.
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