Superposition of Interference

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Superposition Principle of Waves

When two or more wave motions traveling through a medium superimpose one another, a new wave is formed whose resultant displacement at any instant is equal to the vector sum of the displacement due to individual waves at that instant

The two short lined waves traveling in opposite direction first add up (center) to form a resultant wave and then move off as if nothing happened to them.

(It is important to note that each wave preserves its individual characteristic of wave motion)

This shows that when an up-wave (crest) meets a down-wave and are identical, then the resultant is a straight line.

When two down waves superimpose one another, a new wave is formed but in a downward direction (the amplitude of the resultant wave is the sum of the amplitudes of two waves).

The above picture shows what happens when a wave meets another. It is even more surprising to know that such things happen with light. Two light waves produce brightness as well as darkness! This phenomenon where there is redistribution of light intensity, when two or more light waves superimpose, is called interference. The experiment to observe such a phenomenon was first done by a doctor, Thomas young.

Thomas YoungThe above phenomenon was difficult to observe as the two waves had to be coherent i.e., the two waves should have a constant phase difference with respect to time at a particular place where they meet. This is clear from the following diagram.

Notice that a, d, e, f, the phase (if on meeting) relation between the two sets of waves is constant. Such waves can be produced by a single light source and then made to pass through two slits as described later. Two separate light sources can never produce waves whose phase relation is constant at a particular place where they meet i.e., their phase relation keeps changing and as a result, a uniform illumination is obtained on the screen.

Notice a, b, c, the phase relation between wave trains from the two lamps keeps changing randomly.