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interference of monochromatic light

For the interference of monochromatic light we consider two waves with the same frequency and the same wavenumber: ω1 = ω2 = ω     and     k1 = k2 = k Hence (see page 4) a = ωt - kx + ( φ1 + φ2 )/2      and      b = ( φ1 - φ2 )/2 The sum of the waves can thus be written as u(x,t) = 2Acos( ( φ1 - φ2 )/2 ) sin( ωt - kx + ( φ1 + φ2 )/2 ) The sine part of the above formula contains ωt. Consequently, that part vibrates with the frequency of the light under consideration. For visible light that vibration gives the color of the light. However, the cosine part can be maximum or minimum, according to the phase difference.

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