Main content

### Course: Class 12 Physics (India) > Unit 10

Lesson 1: Huygen's principle# Angle between wavefront & rays of light

Wavefronts are always perpendicular to the rays of light, always! Let's explore why. Created by Mahesh Shenoy.

## Want to join the conversation?

- I had a question from the previous video. The ether theory has been disproven. So what is considered the "particles" of light now? Photons?(3 votes)

## Video transcript

in this video let's explore the angle between wavefronts and rays of light the angle between these two and why should we do that well we will see in future videos it will be really important for us to be able to reconstruct wavefronts given the rays of light or given the wavefronts draw the rays of light it'll be really easy to do that if we understand the relationship between that you know the angle between them and that's why we're exploring that now before we start let's quickly remind ourselves what what wave fronts are well i always like to go back and look at the animation representing heightens picture wavefronts are basically set of particles which are oscillating in sync with each other which are in phase with each other over here if you look at these ripples these ripples are what represent the wavefronts since these ripples are spherical this is in three dimension we say the wavefronts over here are spherical in nature and why do we say that well that's because if you look at a particular sphere notice every single particle on that sphere will be oscillating in sync with each other look at that they'll be oscillating in sync and that's why we say that this sphere represents a wavefront and so over here every single sphere which is centered at the source will represent a wavefront and what we want to do now is find the angle between the wavefronts and the rays of light okay so if i were to draw those wavefronts those spherical waveforms here they are what would be the angle between these wave fronts and the rays of light if i were to draw them that's what we want to explore now before i do that can you pause the video and think about this from this image if it would draw rays of light what would the angle be all right let's see if you were to draw the rays those rays of light would be emanating outwards from here right let's draw them all right there that's how it would look like and notice that means these rays of light would represent radii to these spheres because these spheres have a center at the at the source and these rays of light are also starting from the source and therefore they are radius they form the radius to the sphere and what's the angle between the radius and the surface of a sphere that's always 90 degrees so the angle between wave fronts and the rays of light over here turns out to be 90 degrees the question is would it always be true well let's see let's consider another wavefront let's consider plane wavefronts to get plane wavefronts we'll have to go far away so let's do that let's go far away from this source that's when we get plane wavefronts now notice we have plane wavefronts look at the direction of the rays of light now the rays of light are parallel to each other if this was like very far away they would be perfectly parallel but more important look at the angle between these it's still 90 degrees in fact it turns out that this is a general case let me close this it turns out that if you take any wavefront wavefront of any shape and the ray of light at any point on that wavefront they will always be 90 degrees always 90 degrees now i could have said that and just close the video but what's really interesting is why should this be true it's really interesting okay so let me let me clarify with an example what i mean so let's say i were to draw some you know some random random wavefront okay let me let me make it okay random wavefront that looks like this okay so now if i have to ask you to draw the rays of light uh due to this wavefront on this wavefront the way we would draw this if this wavefront was traveling to the right i would say that over here the direction should be like this this is how it should be perpendicular over here it should be traveling this way the ray of light should be this way over here the ray of light should be this way always perpendicular you get the point right it has to be and my question to you is why should this be true in general i mean for the sphere and the plane we saw it made sense to us by but why is this in general again can you pause the video and think a little bit about why should this be true and i'll give you a clue think about what would have happened if the rays were not perpendicular something would break so okay something in physics would break and i want you to think a little bit about this all right hopefully you're tried so here's how i like to think about it i know that every single particle on this wavefront is oscillating in sync with each other right that's the definition of wavefront another way to say that which is going to be helpful to understand this is that every single particle must have finished exactly the same number of oscillations if this particle has finished three and a half oscillation all particles must have finished the same number of oscillations because they're always oscillating in sync so now let's think about what would have happened if the rays were not perpendicular so let's say that this ray over here this ray over here was not perpendicular maybe it was i don't know maybe it was somewhat like this what would happen in this case well let me zoom in then the way i like to do this is i would say that this ray can now be divided into two components okay so you know bear with me it will make sense why i'm doing this it'll be two components one component which is parallel to the wavefront so let me use yellow to represent that there'll be one component of array parallel to the wavefront and there'll be another component which will be perpendicular to the wavefront okay now let's concentrate on the ray of light that is parallel to the wavefront we agree that the ray represents the direction in which the wave is traveling right the direction in which the light is traveling so since there is a parallel component we are saying that there is some light traveling along the wavefront and that poses a problem why because if there are two particles if i consider two particles very close to each other consider these two particles very close to each other we are saying there's a wave traveling from here to here if there was a wave traveling from here to here then these particles could not be in sync this particle would have started oscillating first and then this particle would have started oscillating that's what happens along the direction of a wave i mean if you look at a string for example if this wave is traveling this way can these two particles ever be in sync with each other no because this would always have finished this this got hit by the wave first so it would have finished oscillation some oscillations more than this one and similarly because the wave is traveling parallel this particle would have finished more oscillations compared to this one there would be some particle over here which would have finished more oscillations compared to this one and that breaks our idea of wavefronts because we said in wavefronts all particles must have finished exactly the same number of oscillations and therefore there can never ever they can never ever be a component of the direction which is parallel to the wavefront and so the only component of the direction that can be allowed is perpendicular and that's the reason why that's the reason why the rays of light must always be perpendicular and this is super super useful because if if i if someone tells me that there are rays of light going this way and they ask me what would the wavefront look like i can tell now if it's in three dimensions and you have parallel rays of light i know the wavefronts need to be this way because i know this will always be perpendicular if someone tells me that the rays of light are like this and ask me what does the wavefront look like i can try drawing that wavefront i will i'll try drawing the wavefront in such a way that will always be perpendicular to the direction of the wave the rays of light