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15 Interference and Diffraction

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Introduction What happens when two waves meet?Two snooker balls would bounce off one another, but light behaves differently.They show behaviour known as interference.

Constructive interference – two waves on left arrive in phase (in step).Resultant wave (bottom left) has twice the amplitude.

Destructive interference – two waves on the right arrive out of phase (out of step).They cancel each other out.

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Interference of sound

Walking around in the space beyond two loudspeakers, you can hear point where the sound is loud, and point where it is much softer.These loud and soft points have a regular pattern.Your ear receives waves from both speakers.Suppose the wavelength of the sound waves is 1 m.If your ear is 4 m from one speaker and 5 m from the other, there is a path difference of 1 m for the two waves.They will be in phase; they interfere constructively and you hear a loud sound.

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Interference of soundIf your ear is 4 m from one speaker and 5.5 m from the other, the path difference is 1.5 m.The waves will be out of phase; they will interfere destructively and you will hear no sound (or a very faint sound).• For constructive interference, path difference = nλ• For destructive interference, path difference =

(n + ½)λInterference of other wavesThe same effect can be shown for:1. Ripples – use two dippers attached to a vibrating

bar in a ripple tank.2. Microwaves – direct the microwaves through two

gaps in a metal plate3. Light – the ‘Young’s slits’ experiment

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Diffraction of ripplesWhen ripples pass through a gap, they spread out into the space beyond.The effect, which is known as diffraction, is greatest when the width of the gap, x is similar to the wavelength of the ripples, λ.

λ = x

Width of gap = x

λ << x

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Explaining diffractionWhen light from lasers is shone through a single slit, a diffraction pattern of light and dark interference bands (called ‘fringes’) is seen on the screen.

We picture waves spreading out from all pints in the slit

Each point on the screen receives waves from each point in the slit. These waves interfere.

Where all the interfering waves cancel each other out, we see a dark fringe (destructive interference)

Where all the interfering waves add up, we see a bright fringe (constructive interference).

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Coherent sourcesTo observe interference patterns when two sets of waves overlap, they must be coherent.This means they must have the same wavelength and frequency; also the phase difference between them must be constant.Two loudspeakers are coherent sources.They are connected to the same signal generator, so they vibrate back and forth in step with each other.Light from a lamp is not usually coherent.It is emitted as photons, and they do not keep in step with each other.Laser light is coherent, its photons remain in step between the source and screen.

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Questions 1. What will be observed if two waves, in phase and

one having twice the amplitude of the other, interfere?

2. Draw a ripple diagram to show ripples of wavelength λ being diffracted by a gap of width 2λ. Draw a second diagram to show what happens if ripples of twice this wavelength pass through this same gap.

3. Two dippers are used to produce an interference pattern in a ripple tank. Are they a pair of coherent sources? Explain your answer.