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Wave phenomena

AQA AS Physics A Unit 2. Also covers this topic for Edexcel Unit 2, OCR B Unit 1 and OCR B Unit 2 but in extra detail. If you're doing OCR A, you need a bit extra on how to measure the speed of sound using stationary waves which isn't in here.
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J SF

on 2 June 2011

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Transcript of Wave phenomena

Wave Phenomena 1. Refractive index The refractive index between two substances is the RATIO between the SPEED of LIGHT in the first substance and the speed of light in the second substance. Water travels slower in denser materials like water. The refrative index of a substance can be calculated from Snell's law:

n1 sin(α) = n2 sine(β) The refractive index between two substances is equal to

speed of light in first substance (v1) / speed in second substance (v2)

or n2/n1 Total Internal Reflection At an angle of incidence above the critical angle, light is reflected by the material it hits, instead of being refracted. (at the critical angle, the angle of refraction is 90 degrees) This is what happens in optical fibres: sin (90) = 1 and refractive index of air = 1, so:

n2 sin (i) = n(air) sin (r)

becomes

n2 sin (C) = 1

sin (C) = 1/n2 2. Superposition and Coherence Superposition happens when two or more waves pass over each other. If a crest and a trough meet, they cancel each other out; this is DESTRUCTIVE interference. If two crests or two troughs meet, a bigger crest or trough is formed; this is CONSTRUCTIVE interference. Constructive and Destructive Interference Phase Difference Two points on a wave are in phase if they are at the same point in the wave cycle. In the diagram, the points A and B are in phase, but the points A and C are out of phase. *If the two waves don't have a similar amplitude, the destructive interference isn't total and is less noticeable. One complete cycle is shown as 360 degrees. Two points with a phase difference of 0 or any multiple of 360 degrees are in phase. Any two points with a phase difference of an odd number of multiples of 180 degrees are exactly out of phase. Coherence To get interference patterns, the two sources of the waves must be coherent. This means they must have the SAME WAVELENGTH, the SAME FREQUENCY and a FIXED PHASE DIFFERENCE between them. Did you know?
It's an urban myth that Marilyn Monroe had an extra toe. Path Difference Whether interference is constructive or destructive depends on how much further one wave has travelled than the other. The difference in how far the two waves have travelled is the path difference Constructive interference occurs when

path difference = nλ (where n is an integer) Destructive interference occurs when

path difference = (n+½)λ 3. Stationary (standing) waves A stationary wave is the superposition of two progressive waves moving in opposite directions. This can be a wave and its reflection after it hits a boundary, or the vibrations on a string which is fixed at one end. NO ENERGY is transmitted by a stationary wave. The points marked 'N' are the nodes. These are points of no displacement. Where the amplitude is zero. Antinodes are the points where the amplitude is a maximum. The first wave in the diagram is vibrating at its fundamental frequency (the lowest possible frequency). It has one antinode and two nodes. It shows half a wavelength. The next wave is the second harmonic (or first overtone). This is a whole wavelength. The notes played by stringed and wind instruments are stationary waves. 4. Diffraction The smaller the gap, the wider the diffraction pattern. For the widest diffraction pattern, the gap should be the same size as one wavelength. When waves go round corners or through gaps they spread out. Diffraction Patterns If the gap is about the same size as the wavelength of a light wave, a diffraction pattern with light and dark fringes is formed. The pattern has a central bright fringe with alternating bright and dark fringes either side. The central fringe is the widest. pretty Electron Diffraction Electrons diffract too, creating a pattern like this: 5. Two-Source Interference This is diffraction too really ... so's the next topic ... sorry To create two-source interference, you need 2 coherent sources. This is pretty easy with sound and water - you can use one vibrator driving two dippers for water or one oscillator connected to two speakers for sound. For light, you could use one light souce shone at a double slit. A laser is a good light source to use. By the way, AQA say you need to know about how to use lasers safely. Laser light damages your retina, so don't shine it in anyone's eyes - not even after it has been reflected. In fact - don't shine it on reflective surfaces at all if you can avoid it. You get a pretty, stripey fringe pattern like this: And this is why: Remember interference? Back here ... ... as the light from the two slits overlaps, the waves interfere with each other. Wherever there is constructive interference, a bright fringe is formed. Wherever there is destructive interference, a dark fringe is formed. Young's Double-Slit Formula OK ... this is the boring bit. But, it is really important. Right, listen up. In this formula, X is the fringe spacing (meaning the distance from the centre of one minimum to the centre of the next minimum), λ is the wavelength, d is the spacing between the slits and D is the distance from the slits to the screen. And finally... 6. Diffraction Gratings A diffraction grating is basically lots of lines, creating lots of slits to diffract light. Using a diffraction grating does the same thing as double slits do, but the bright fringes are brighter and narrower and the dark fringes are darker. When monochromatic light (light of one wavelength) is shone through a diffraction grating with hundreds of lines per millimetre, you get a really sharp interference pattern because there are so many beams reinforcing the pattern. On the pattern from a diffraction grating:

1) There is a line of maximum brightness in the centre called the zero order line.

2) The lines either side if this are called the first order lines. The next pair out are called the second order lines etc. For a grating with slits a distance, d, apart, the angle between the incident beam and the nth order maximum is given by: By the way, if the grating has N slits per metre, the slit spacing, d, is 1/N metres. Deriving The Equation (sorry!) 1) At the first order maximum, the waves from one slit line up exactly with the waves from the next slit which are exactly one wavelength behind. 2) All the symbols in the diagram are the same as those used earlier, to make it easier. 3) Look at the triangle in the diagram. using basic geometry, we know that the angle is equal to θ. The path difference (the top bit of the triangle) is equal to λ. 4) So, for the first order maximum, using trig:
d sin θ = λ 5) At the other maxima, the path differences are 2λ, 3λ, 4λ etc. So, to make the equation more general, for any maximum, replace λ with nλ. You need to understand: If λ is bigger, so is sin θ, which means that θ is bigger. Hence, the bigger the wavelength, the more the light will spread out.
If d is bigger, sin θ is smaller. Hence, the coarser the grating, the less the pattern will spread out.
Values of sin θ greater than one are impossible. That's a bit of maths for you. Hence, if sin θ is greater than 1 for a value of n, that order cannot exist. You can use this idea to work out the highest order maximum possible, which is handy. White Light Shone Through a Diffraction Grating is Fun White light is made up of a mixture of colours. I hope you already knew that. This means it obviously isn't monochromatic. As different wavelengths of light spread out by different amounts, the diffraction pattern from white light shone through a grating is made up of lots of pretty colours. Each order in the pattern becomes a spectrum. It has red on the outside and violet on the inside. The zero order maximum stays white because it's stubborn like that (and because all the wavelengths just pass straight through). Like this: This is a pretty picture of this, if you're interested: And that's about it, for this topic. If you got all that, congratulations! You might want to look over it again if you didn't!
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