all waves transfer energy without transferring matter longitudinal waves are those in which the direction of the oscillations is parallel to the direction of energy transfer that is the direction the wave is going in these ways particles Bunch up we call those compressions and when they're spread out we call those rare refractions transverse waves are those in which the direction of oscillations is perpendicular to the direction of energy transfer we can represent any wave including longitudinal waves like this we call this a waveform displacement is up the y- AIS basically just how far the particles have oscillated is from their original position and it can be either distance or time on the x-axis the peak of a wave is called the amplitude it's the maximum displacement from equilibrium if it's distance on the x-axis one complete wave here gives you the wavelength we give this the symbol Lambda for short but it's measured in meters if it's time on the x-axis instead one complete wave gives you the time period this is the time it takes for one complete wave to pass frequency on the other hand is how many waves pass a point every second and the unit is HT frequency is equal to 1 over time period f = 1/ t you can often be asked to find frequency from a waveform like this measure the time period Then do one divided by that easy the wave equation is this V equal F Lambda that's wave speed equals frequency time wavelength it's worth remembering that visible light wavelengths vary from around 400 to 750 nanm or 4 to 7.5 * 10- 7 m with red light having the longest wavel length and blue the shortest the intensity of a wave is proportional to the amplitude squared that means that if the amplitude doubles the intensity quad rupes when light waves move from one medium to another say from Air to Glass they change speed in this case the wave slows down and the wavelength also decreases a change in medium also results in a change in Direction This is called refraction that is if it's at an angle to the normal the line we draw perpendicular to the surface if light slows down it moves closer to the normal so that means that the angle of refraction is smaller than the angle of incidence now all of these angles are measured from the normal how much a medium refract light is determined by its refractive index symbol n it's just a ratio that's equal to the speed of light in a vacuum basically the same for air divided by the speed of light in the medium so it will be a number that's always greater than one if you calculate sin I over sinr for a light Ray entering a medium from Air this happens to also give us the refractive index the full equation for refraction is Snell's law N1 sin Theta 1 = N2 sin Theta 2 you can see that we've just replaced i and r with thetas bear in mind that in reality the refractive index of material varies with wavelength blue light's refractive index will always be higher than red lights for the same medium that means that it refracts more than red that's why white light undergoes dispersion when it passes through a prism let's say the light rate is coming out of the glass block and into air now if we keep increasing this angle of in incidence eventually we'll end up with an angle of refraction of 90° that light Ray will be going along that boundary along the surface the angle of incidence is now equal to what we call the critical angle and that's going to be different for every medium if we make the angle of incidence even bigger than the critical angle that means that no light is going to be refracted out of the block instead all light is reflected back inside by the way we always get some reflection but now we have total internal reflection want to calculate the critical angle well you can start with Snow's law you call Theta 1 Theta C instead make N2 90° and we end up with sin Theta Cal N2 over N1 this incidentally is how optic fibers or fiber optics work basic optic fiber is a glass core surrounded by a protective sheath the issue is that this will have a higher refractive index than the core so TI would not happen if it were not for the extra layer called the cladding that is in between them it has a lower refractive index than the core so TI can occur one of the issues with optic fibers is the fact that light will diverge spread out as it travels down a fiber this means Rays can take different paths and therefore different times to reach the other end this is called modal or multipath dispersion and it results in pulse broadening if pulses are stretched too much they start to overlap as the next one has started to arrive before the first one has completed its Journey your data are goner to mitigate this we can do a few things number one make the fiber really thin the thinner it is the less light will diverge number two put repeaters in every so often to retransmit the slightly broadened pulses as brand new ones the final clever idea is to use graded index fibers lenses use refraction to make rays of light converge or diverge a convex lens can make Rays converge if Rays enter parallel to what we call the principal axis for example the light from an object very far away the lens will make the Rays converge at this point here here this is called the principal Focus the distance from the center of the lens is called the focal length this doesn't change for a lens and we can draw it on both sides and you'll see why in a bit however light doesn't usually come from objects infinitely far away but from objects a little bit nearer the object could be anything but we often represent it with just an arrow convex lens can then project an image using the light that comes from the object but we only consider the light coming from the top of the object and we can do that by drawing two rays one always goes straight through the center of the lens and one goes parallel into the lens then through the principal Focus where these two rays meet is where the image is formed that's where you want your projector screen or retina or camera sensor to be in order to get a clear image formed you'll also notice that the image is smaller than the object so we say it's diminished it's also upside down so we say it's inverted things get a bit trickier when the object is very close to the lens now the Rays don't meet the image can't be projected however if we extrapolate the two rays back behind the lens they do meet we can draw the image here and we can say that it's magnified it's upright but it's virtual that means that it can't be projected this would be what a magnifying glass does for example your eye can deal with this diverging light accordingly to make it focus on your retina but that means that you see this magnified virtual image so things appear bigger concave lenses always diverge like Rays they always produce a virtual image with these our line parallel in goes back through the other principal Focus behind the lens where it meets the other Ray is where the virtual image is a couple more equations for lenses the power of a lens is just the reciprocal of focal length we give it the unit diopter for lenses we should probably say thin lenses used together total power is equal to the sum of individual Powers the full lens equation is this 1 / f = 1 / U + 1/ V light emitted from the Sun oscillates in all orientations however if you have a polarizing filter made of very small lines it only lets half of the light through only half is transmitted the other half is absorbed this is because it only lets waves of certain orientations through we say that if the lines are vertical waves oscillating vertically are absorbed while horizontally orientated waves are transmitted p through and vice versa waves between vertical and horizontal are transmitted or absorbed according to their angle it's very complicated in reality but but simply the light is is now polarized and the intensity of the light is halfed put another polarizing filter at 90° behind the first and all of the light is absorbed a normal wave is what we call a progressive wave the wave moves while the medium or particles just oscillate around a point say up and down two points one wave apart are said to be in Phase they're doing the same thing at any time we say their phase difference is 0 or 360° as we can represent wave Cycles as circles we can also split circles and therefore Cycles into radians instead of degrees there are two Pi radians in a circle so again the phase difference of these two points is 2 pi radians like we said that's the same thing as zero points on opposite sides of a wave are completely out of phase or we might say in anti-phase they're half a wave out of phase so their phase difference is 180° or Pi radians these two points are a quarter of a wave out of phase so that's a phase difference of 9 ° or Pi / 2 radians we generally don't give phase differences above 180° Pi radians as we can just give the opposite phase difference so 270° is just given as 90° Etc any phase difference can be calculated as a fraction times the total inner cycle so we can do the distance between two points divided by the wavelength or time difference between two points divided by the time period depending on what graph we're given then we just multiply by 360 or 2 pi depending on whether we we want the phase difference in degrees or radians when two Progressive waves traveling in opposite directions meet they undergo super positioning they are superposed when these waves have identical frequency in wavelength a stationary wave is formed the points at which the resulting wave doesn't move is called a node that's because the displacements are always summing to zero at these points we call this destructive interference so the amplitude is zero at a node no energy is transferred at all other points the resulting wave will oscillate due to constructive interference where the amplitude is a maximum these are called anti noes we can see this if we attach a string under tension to a vibration generator the wave is sent down the string and it reflects at the pulley and these two waves interfere the simplest stationary wave looks like this we call this the first harmonic or the fundamental one Loop one anti- Noe and a node at both ends we have half a wave on the string so that means L equal Lambda / 2 the frequency of this is given by the the equation 1/ 2 L length of the string time < TK t/ mu T being the tension in Newtons which is usually the weight of the masses hanging on the end and mu being the mass per unit length of the string so that's in kilogram per meter incidentally root T over mu actually gives you the wave speed double this fundamental frequency and we get the second harmonic L equal Lambda in this case third harmonic L equal 1 and a half Lambda and so on stationary waves can also be formed in tubes of air at a closed end a node must be formed at an open end an antinode we can represent the stationary wave much like we do for a string just bear in mind that the first harmonic is likely to be different than that of the string because one or two of the ends are probably going to be open unlike Progressive waves points on stationary waves can only ever be completely in Phase or completely out of phase it just depends on if they're the same side of equilibrium or not that's because two points above equilibrium will reach their own different amplitude at the same time and they'll both reach equilibrium at the same time too even if waves aren't traveling in opposite directions they still interfere when they meet Thomas Young put a thin slit next to a candle to First ensure that the light used for the experiment was coherent all of the light was in Phase but the definition of coherent is this actually all waves have a constant phase difference this light then passed through a double slit the result was bright and dark fringes appearing on the screen called these Maxima and Minima we have a central maximum because those two rays me have traveled the same distance so therefore they interfere constructively the dark fringes or Minima are due to the light from the two slits traveling slightly different distances to each other we say their path difference is half Lambda that means that they arrived 180° completely out of phase and interfered destructively canceling each other out the first bright Fringe from the central Fringe is a result of the path difference being the same as the wavelength Lander that means that these arrive in phase two interfering Construction ively resulting in a bright Fringe the next dark Fringe was a result of the path difference being 1 and a half Lambda and so on youngest double slit equation is this W equal Lambda D / s where W is The Fringe spacing that's the distance between the center of two bright fringes or two dark fringes for example D is the slit to screen distance and S is the slit separation note that isn't slit width changing the actual width of the slit doesn't change the Fringe width at all however this equation is an approximation and it can only be used when the screen distance is much much larger than the slit separation that's why the equation is likely to break down when we use sound instead if you have two speakers producing the same waves in Phase if you walk at right angles to them you'll hear the volume fluctuate as you go through Maxima and Minima we can represent the pattern by drawing a graph of intensity against distance from the central Max the intensity Falls away gradually and they all have the same spacing but light can also defract when you just use a single slit as defraction occurs at both edges of the slit it gives this defraction pattern instead the two differences being that the intensity Falls away quicker and the central Maxes double the width of the subsequent fringes don't forget that if you do this in reality it's always more accurate to measure 10 fringes than divide by 10 to get W when we do the experiment we're probably going to use a laser as it provides coherent light that's also monochromatic just one wavelength is emitted resulting in clearly defined fringes however using a candle that emits a spectrum of wavelengths young saw the white light splitting into the different colors as red light has the longest wavelength it defract the most so it could be seen on the outside edge of the fringes blue light has the shortest wavelength so it defract the least so it could be seen on the Inside Edge of the fringes if you replace Young's double slit with a grating of very small lines separated by line spacing Little D you only get constructive interference at a few points very far away from the central Max we call these orders instead of fringes the central Max is the zeroth order as we're dealing with large angles we can't use Young's double slit equations so we use the more accurate equation n Lambda equal D sin Theta often you'll be given the line or grating spacing in lines per millimeter which you need to turn into meters essentially meters per line is the reciprocal before it can go into the equation you can also be asked to find the maximum visible order in this case we want to find out what order is made at 90° sin 90 = 1 so n = d/ Lambda let's say this ends up being 3.8 there's no such order so only orders up to three are visible also they might try to catch you out by asking hey how many orders will be visible rather than what is the highest order in this case you have to count the orders on both sides including the zeroth order so that will be seven in this case very cheeky just be careful with some multiple choice questions involved in this equation you might get asked what will happen to the orders if the wavelength is halfed say in this case you don't look at Theta at all as it's not proportional to anything in the equation instead we say n is inversely proportional to Lambda if Lambda halves n doubles that means that what was the first order is now the second order and a new first order is created between it and the zeroth order if D is changed we say n is proportional to D leave a like if you found this helpful I've also put together these into videos that cover whole papers to help you revise for your exams more effectively click on the card for your board if it's there or go to my channel for more including International boards