Answer to Question #111767 in Optics for Patrick Kariuki

Question

Differentiate between constructive and destructive interference. Use mathematical expressions.

Answer 1

Constructive interference is when the crests or the troughs of the waves interfere with the other. Therefore their amplitudes of are added to find the total amplitude. The amplitude of constructive interference is always greater than the amplitude of individual waves.

W₁ + W₂ = 2Acos(kx - $\omega$t)

Destructive interference is when a crest and a trough interfere with each other. This results in a lower amplitude than those of the original waves.

W₁ + W₂ = 0