# Diffraction, Interference and Superposition

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## Diffraction, Interference and Superposition

#### Diffraction

A wave will diffract (spread out) as it goes through a gap or past an obstacle.

Note: The wavelength remains the same before and after the gap.

Remember this: The nearer the slit size is to the wavelength, the more the wave will diffract.

1. The smaller the gap the greater the diffraction.
2. The longer the wavelength the greater the diffraction.

You should be able to describe experiments such as the ripple tank or microwave kit that will show diffraction.

Interesting Point:

It is not only waves that can be diffracted. In 1923, Davisson and Germer showed that electrons and all sub-atomic particles could also be diffracted. This is supported by De Broglie's theory of wave/particle duality, which shows that electrons have a mass but can behave just like waves with no mass, such as light waves.

#### Single Slit Diffraction Pattern

If a wave goes through a slit a diffraction pattern can be detected on the other side, with regions where the wave is intense and regions where the intensity falls to zero. graph of intensity against distance from the centre of the pattern can be drawn:

The reason for this pattern is explained in 'interference and superposition'

Did you know that X-rays can be diffracted by the gaps between atoms in crystal structures, so by analysing the diffraction patterns we can work out the shape of the crystal structure. This only works because the gaps between the atoms are roughly the same size as the wavelength of X-rays!

Coherence:

Coherent waves are waves with a constant phase difference. (Note: They don't have to be in phase for this to be true.) They will have the same frequency and wavelength (they are normally produced from one source).

#### Interference and Superposition

When two waves meet they will interfere and superpose. After they have passed they return to their original forms. This is true if they are coherent or not.

At the point they meet, the two waves will combine to give a resultant wave whose amplitude (or intensity) may be greater or less than the original two waves.

The resultant displacement can be found by adding the two displacements together:

This is called the Principle of Superposition.

If two waves of the same type and the same frequency combine so that the crest of one coincides with the trough of the other, they will completely cancel each other out. This is called destructive interference. Alternatively, the two waves could combine when their crests coincide; then there would be constructive interference and the resultant amplitude would be equal to the sum of the separate amplitudes:

Superposition will occur whether waves are coherent or not. (However, if the waves are coherent, they will interfere to produce a fixed pattern.)

The same rules apply... the resultant displacement at any point is always the sum of the separate displacements of the wave at that point:

#### Path Difference

You will need to be able to work out whether there will be constructive or destructive interference at a point. We do this by comparing how far the two waves have travelled to reach the point. The difference in the distances will tell us if the waves are in phase or not.

In the diagram above the waves are in phase when they leave each slit.

A bright fringe occurs at P if S2P - S1P = nλ

In other words, for the waves to be in phase and constructively interfere, the difference in the distances travelled by the waves must be a whole number of wavelengths.

A dark fringe occurs if S2P - S1P = nλ + l/2λ

In other words, for the waves to be out of phase and destructively interfere, the difference in the distances travelled by the waves must be exactly half a wavelength, or 1 1/2 , or 2 1/2 , etc.

If you don't have a nice 1/2 or whole number of wavelengths you can find the phase difference using:

Note 1: The wave that has travelled the furthest will have lost more energy, so will have a slightly smaller amplitude than the other. This means that the waves might not completely cancel each other out.

Note 2: If a wave is reflected off a surface it will have a 180 degree phase change which must be taken into consideration!

#### Fringes

So why do we get fringes?

The same principle shown in this diagram produces fringes even when it is only diffraction through a single slit. This is because a wave front can be thought of as being made up of lots of wave sources in a row that will then interfere with each other as you move away from the wave front!

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