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Huygen's principle of secondary waves

Huygen's principle states every point on the current wavefront acts as a source of secondary spherical waves. These secondary waves propagate outwards, in the forward direction, and a common tangent (an envelope) to all these waves constitute the new wavefront. Created by Mahesh Shenoy.

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Video transcript

if you shine a parallel rays of light on a cardboard with a tiny hole in between what would you expect to happen to this light after it went through the hole well if you think in terms of newton's idea where light is a bullet then we'll all see that these bullets will get blocked and these bullets will just go straight through and this is the picture that gets painted but careful experiments show that when the light goes through the hole it actually spreads out and forms a bigger spot if there was a screen over here how do you explain that how does light just bend like that well if you think of light as a wave and use heighgan's principle then we'll be able to explain this and that's pretty much what we want to do in this video so you want to introduce this idea of heightens principle but before i do that let's do a quick recap of what we've already seen before hygiene's assumed that light is a wave in the ether medium that exists everywhere in the universe and the ripples that these things are carrying we gave a name to that these ripples are called wavefronts and one of the important things that we saw about the wavefronts is that the angle between the direction on which the light is traveling the rays of light and the wavefronts that is always perpendicular look at this the rays of light and the wavefronts at every point will be perpendicular to each other that's important that's going to be important for this video as well and this will be true even if you go very very very very far away you will now see that the rays of light are pretty much parallel to each other but if you look at the wavefronts notice the rays are perpendicular to the wavefront rays of light always perpendicular to the wavefront okay but how does this wave theory explain our original question for that we need one more piece of information from huygens how do these wavefronts evolve in time here's what i mean let's say we have a light bulb giving us light and let's concentrate on one of its spherical wavefront this is what it looks like right now i want to know what this wavefront is going gonna look like say two minutes later how do i figure that out now at first it might look like a silly question you might think or at least i should think that that's easy right a little later this new wavefront is just gonna be a bigger version of our old wavefront right isn't that the solution well yeah that's true over here it works but that's that this only works provided there are no obstacles over here but what if there is a mirror or there is a lens somewhere over here or if there is a i don't know a cardboard with a small hole in that then what the new wavefront looks like that's not so easy to answer now is it and this is why people went to high guns and say hey higgins tell us if i know what the new current wavefront looks like how do i know what the new wavefront is going to be sometime later in general in any situation and that's basically what heightens principle is all about it it's going to help us reconstruct wavefronts so what does the principle say well according to heightens every single point on this wavefront is an ether particle which is oscillating pretty much with the same frequency as the original wave and it starts producing its own spherical mini waves so here's what it says remember that there is ether particle everywhere and the ether particles on this wavefront they're all oscillating they're all moving back and forth as you saw in the animation and as a result he says that every single one of them is going to produce its own mini ripples on mini waves he calls them secondary waves so this is going to produce its own secondary wave this is going to produce its own secondary waves so all of them are going to produce their own secondary waves now since a little hard to draw i've already drawn it nicely so this is what it would look like and you draw that for all of them and there are infinitely many because every point he asks us to assume it to be a particle oscillating and producing its own secondary wave so these are all our secondary waves and then he says you draw a common tangent to all these secondary waves a common envelope so if i use a different color to do that a common envelope which might look somewhat like this this common envelope according to him a common tangent that represents the new wavefront so he says this oops this is a new wave front again let me show you an animation so you can see it better so here's our current wave front and these are the ether particles which are going to oscillate and act like a point source giving out secondary waves i've not drawn all of them there are infinite as many okay and notice these secondary waves keep expanding keep expanding keep expanding and a common tangent to all of them that now represents a new wavefront so if i draw a common tangent over here that common tangent would be our new wavefront and the same thing would hold true for some other shape as well so if i takes let's say a plane wavefront again these are our ether particles oscillating and they're giving out secondary waves and notice if the waves are going towards the right this now common tangent will represent our new wavefront so this method works for any shape of our waveforms the particles will always give you spherical ripples and the common tangent will give us the new wavefront and if you're now a little bit curious you might have some questions like why are we drawing the common tangent only on one side why not on the other side for example well hygiene would say well because we know the in which direction the waves are traveling we know the waves are not traveling backwards so we'll ignore them but you could ask why and eigen doesn't have an answer for that and that's one of the drawbacks over here but you could have more fundamental questions like why does this method even work i mean why are we drawing a common tangent why does that work these are some great questions which we can try to tackle uh in a separate video all together but remember just like any scientific theory heightens theory is also not a perfect picture or representation of the world then why do we use it because it's simple and it's pretty powerful as we will see it will be able to explain a lot of phenomena including deriving the laws of reflection and refraction in the future anyways let's come back to our original question and see if we can answer that using huigen's principle so we were shining light on a cardboard apparently a blue cardboard and we want to know why does why does the light bend that is our question right so let's use wave theory heightens principle well since there is of a lighter parallel um our our wavefronts are going to be plane wavefronts so it's going to look somewhat like this it's not a line it's supposed to be a plane and if i want to know what the new wavefront looks like after some time i have to use hygien's theory but until here i know the wavefront is going to look just like this because there are no obstacles i don't need eigen theory till here but once i reach here now comes the question what does the new wavefront look like after this is it just going to be like this is going to be this way let's find out for that we need to think of every single point on this as a source for secondary waves we call these hygiene sources and then we have to draw a common tangent to all those secondary waves i want you to pause the video and see if you can give this a shot all right if you've tried let's do this so here are our eigen sources these are the ether particles which are oscillating and they're going to start giving out their own ripples so here's the ripples that i'm drawing here we go and now what does the common tangent look like well just like before let me draw in white just like before over here the common tangent is going to look like this but what's important now is that because this is a because it's a finite wavefront there will be one last eigen source over here which will give you one last circular ripple over here sorry spherical triple over here and as a result the tangent is not going to end here it's not going to go straight like this but it's going to end like this this is what the new tangent looks like and the same thing over here remember we're drawing an envelope to all these secondary sources and this is what the envelope looks like and so notice that the sec the the new wavefront is not completely plain it has this curved edges and as a result after this it's just going to be a larger version of this so the new wavefront after this is going to be let me try and draw it nicely it's going to be like this and again like this this is what the new wavefront is going to look like and now if i try to draw the rays of light over here the rays of light are going to be like this they are always perpendicular remember to the wave front but over here notice the rays of light have to be going this way somewhat like this and over here is going to be somewhat like this and so there you go heightens theory helps us understand why the light spreads out because when the wave exits this slit it is no longer a plane wave it gets curved towards the end and as a result it starts spreading out this and some other phenomena of light can only be explained by thinking of light as waves and not as bullets and this is how a wave theory gained popularity all right so to summarize here are the two questions that you should try and answer yourself now can you explain hygiene's principles to maybe a friend or maybe to someone in your family and explain how you construct new wavefronts from a given wavefront and can you then use heightens principle to explain why when you shine light through a tiny hole it expands the light tends to spread out if you have difficulties no worries you can just go back and re-watch parts of the video