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# 5 interference and diffraction

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### 5 interference and diffraction

1. 1. 15 Interference andDiffraction1
2. 2. IntroductionWhat happens when two waves meet?Two snooker balls would bounce off one another, butlight behaves differently.They show behaviour known as interference.Constructive interference –two waves on left arrive inphase (in step).Resultant wave (bottom left)has twice the amplitude.Destructive interference – twowaves on the right arrive out ofphase (out of step).They cancel each other out.2
3. 3. Interference of soundWalking around in the space beyond two loudspeakers,you can hear point where the sound is loud, and pointwhere 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 theother, there is a path difference of 1 m for the twowaves.They will be in phase; they interfere constructively andyou hear a loud sound.3
4. 4. Interference of soundIf your ear is 4 m from one speaker and 5.5 m from theother, the path difference is 1.5 m.The waves will be out of phase; they will interferedestructively and you will hear no sound (or a very faintsound).• 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 barin a ripple tank.2. Microwaves – direct the microwaves through twogaps in a metal plate3. Light – the ‘Young’s slits’ experiment4
5. 5. Diffraction of ripplesWhen ripples pass through a gap, they spread out intothe space beyond.The effect, which is known as diffraction, is greatestwhen the width of the gap, x is similar to thewavelength of the ripples, λ.5λ = xWidth of gap = xλ << x
6. 6. Explaining diffractionWhen light from lasers is shone through a single slit, adiffraction pattern of light and dark interferencebands (called ‘fringes’) is seen on the screen.6We picture waves spreading out fromall pints in the slitEach point on the screen receives waves from each pointin 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 brightfringe (constructive interference).
7. 7. Coherent sourcesTo observe interference patterns when two sets ofwaves overlap, they must be coherent.This means they must have the same wavelength andfrequency; also the phase difference between themmust be constant.Two loudspeakers are coherent sources.They are connected to the same signal generator, sothey 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 stepwith each other.Laser light is coherent, its photons remain in stepbetween the source and screen.7
8. 8. Questions1. What will be observed if two waves, in phase and onehaving twice the amplitude of the other, interfere?2. Draw a ripple diagram to show ripples of wavelengthλ being diffracted by a gap of width 2λ. Draw asecond diagram to show what happens if ripples oftwice this wavelength pass through this same gap.3. Two dippers are used to produce an interferencepattern in a ripple tank. Are they a pair of coherentsources? Explain your answer.8