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Light waves just like normal waves can interfere with each other. We are talking about a combination of them. This combination sometimes is visible to us. A soap bubble is an example, where colors are reflected when the bubble is illuminated by sun or some other source. This phenomenon is defined as interference.
The previous example or the colors on a drop of oil engine describe the general character of interference. Physicists tend to specialize interfernece in cases where two waves have the same frequency and fase, although this is not strict. Then the two waves could give the constructive or the destructive interference.
If one drops two stones into the water of a lake, constructive interference occurs where the crests of the two waves coincide. As a result a new wave is formed. This wave has amplitude equal to the the sum of the individual amplitudes of the original waves. Destructive interference occurs when the intersecting waves of the same frequency are completely out of phase - that is, when the crest of one wave coincides with the trough of the other and finally the two waves cancel each other out. The produced diagrams of the previous cases are quite simple and at the same time very proctorial.
Of course the previous cases do not cover the phenomenon of interference. Two waves -or light waves- can interfere with each other even they do not have the same frequency or wavelength. These occasions produce much more complicated diagrams.
We used before the soap bubble. Let us see how the colors are produced. The light waves that reflect off the inner surface of the bubble interfere with light waves of the same wavelength that reflect off the outer surface of the bubble. Some of the wavelengths interfere constructively, and other wavelengths interfere destructively. Since different wavelengths of light correspond to different colors, the light reflecting off the soap bubble appears colored.