Destructive Interference

Waves from the two sources as before arrive simultaneously but with the crest (trough) of one superposed on trough (crest) of the other. Then according to the superposition principle the resultant amplitude is zero, hence the intensity will be zero. The point on the screen where this occurs will be dark. This type of interference is called destructive interference.

The condition for destructive interference is that the optical path difference 'D' should be odd integral multiple of half the wave length, (see figure.2).

       i.e. D = (2K + 1) l_/2 : K = 0, 1, 2, 3, ----------(2)

Figure 2

Note :1) S₁ & S₂ are the "Sources" of light
2) Air is the medium through which waves travel from S₁ & S₂ to P
3) Optical path difference in air = S₂P - S₁P
4) If in the path of light, an object like a glass plate of width 'd' and refractive index, m is interposed, then the optical path would be augumented by factor d ( m - 1 )

Figure 3

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Index

18.1 Interference of light
18.2 Diffraction of Light
18.3 Polarization of light

Chapter 19