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Interference of Light

When two waves of exactly same frequency (coming from two coherent sources) travel in a medium in the same direction simultaneously, then due to their superposition at some points intensity of light is maximum while at some other points intensity is minimum. This phenomenon is called interference of light. It is of following two types:

Constructive interference

When the waves meet a point with same phase, constructive interference is obtained at that point (i.e., maximum light).
  • Phase difference between the waves at the point of observation φ = 0° or 2nπ
  • Path difference between the waves at the point of observation, Δ =  (i.e., even multiple of λ/2)
  • Resultant amplitude at the point of observation will be maximum, Amax = a1 + a2
     
    If a1 = a2 = a0  Amax = 2a0
  • Resultant intensity at the point of observation will be maximum94805.png
     
    If I1 = I2 = I0 ⇒ Imax = 4I0

Destructive interference

When the wave meets a point with opposite phase, destructive interference is obtained at that point (i.e., minimum light).
  • Phase difference φ = 180° or (2n – 1)πn = 1, 2, … or (2n + 1)πn = 0, 1, 2 …
  • Path difference, 94811.png (i.e., odd multiple of λ/2)
  • Resultant amplitude at the point of observation will be minimum, Amin = a1 – a2
     
    If a1 = a2 ⇒ Amin = 0
  • Resultant intensity at the point of observation will be minimum, 94817.png
     
    If I1 = I2 = I0  Imin = 0

Super position of waves of random phase difference

When two waves (or more waves) having random phase difference between them super impose, then no interference pattern is produced. Then the resultant intensity is just the sum of the two intensities. I = I1 +I2




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