Question

Two harmonic waves of monochromatic light y₁ = a cos ωt and y₂ = a cos (ωt + Φ) are superimposed on each other. Show that maximum intensity in interference pattern is four times the intensity due to each slit. Hence write condition for constructive and destructive interference in terms of the phase angle Φ.

Answer 1

The result displacement will be given by
y = y₁ +y₂ = a cos ωt + a cos (ωt + Φ)
a[cos  ωt  + cos (ωt + Φ)]
2a cos (Φ/2) cos (ωt + Φ2)
The amplitude of the resultant displacement is 2a cos (Φ/2).
The intensity of light is directly proportional to the square of amplitude of the wave. The resultant intensity will be given by