Wave Interference and Path Difference

How does the path difference between two interfering waves affect the pattern of interference obtained on the screen? For a well distinguished pattern of interference(i.e., good contrast between dark and bright bands) should the path difference be large or small? Please explain
- Anu (age 17)
India

The path difference between two interfering waves, be they electromagnetic, sound or water, makes all the difference.  Many waves can be characterized by a sinusoidal function A = sin(x/2π λ + φ) where  λ is the wavelength and φ is a phase angle.  If there is a path length difference then the phase angles between two waves will be different; Δφ  ₌ Δx/2π λ where Δx is the path length difference and Δφ is the phase difference.  When Δφ is a multiple of 2π then you get constructive interference.   When Δφ is a multiple of 2π plus π then you get destructive interference and the total amplitude goes to zero (or close to it).    The web site   has some nice pictures and explanations.

LeeH

(published on 09/30/2010)