Ray Nature Of Light - Video Tutorials & Practice Problems
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Ray Nature of Light
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Hey guys in this video, we're gonna talk about something referred to as the ray nature of light describing light as a ray instead of a wave. OK. Let's get to it. Now, light as we know is composed of electromagnetic waves. OK. All waves have things called wave fronts which is a point of maximum oscillation for that wave. In the case of light, it's a point of maximum electric field because of this, it's often convenient to describe these moving electromagnetic waves as just rays which are individual lines that point perpendicular to those wave fronts. OK. Consider the image above me, I've drawn a moving light wave of propagating electromagnetic wave as a series of green wave fronts. Those wavefront which are points of maximum electric fields, right? Their peaks have to be separated by the wavelength, right? The peak to peak distance is just the wavelength and the rays that are gonna be drawn have to be drawn so that they're always perpendicular, no matter where they are to those wave fronts. OK. Now, light is always gonna travel in a straight line when in a single medium. OK? Whether it's air or water, I wrote a vacuum. But vacuum is technically the absence of a medium light being the only wave that can propagate in the absence of a medium. However, when light's disturbed, when it crosses a boundary between media, then interesting things happen. OK. They may not be interesting to you, but they're interesting to physicists. And so you're forced to learn them. These are in particular refraction and diffraction, which are gonna be two things that we talk about while discussing light and optics. OK. In order to understand these two phenomena, we have to understand something called Hagen's principle. All right, now, Hagen's principle makes two points. The first point is that all points on a wavefront act as point sources for spherical wavelets. OK. So if I were to draw a wavefront, then every single point on that wavefront is gonna be producing these smaller waves which are called wavelets. OK. And the second point is that new wave fronts. So new in time, where is the wave gonna be after some amount of time, new wavefront are formed by the tangent line across the apex of the wavelets that were produced by the last wavefront. OK. This is a lot of information, but Hagen's principle is fairly simple in application. OK. Let's do um just a little bit of application so we can see what exactly it's saying. So on the left, I have a wavefront produced by light that is moving in a single direction. OK. This light is what would be called collated light. OK. Coated because if I were to draw rays for this light, right, all the rays have to be perpendicular to the front, those rays are all parallel to one another. So Collum light is light whose rays are all parallel to one another. So if I were to choose a point on this wavefront, you'll see that these little wavelets right are being produced and they travel some distance in some amount of time, the distance I chose is just the wavelength because that's where the next wavefront is gonna be. So that's one point they can, I can choose another point on the wavefront and it will also produce these spherical wavelengths. OK. And a third point on the wavefront and also these spherical wavelets are gonna be produced. Now, what Hagen's principle says is that the next wavefront, right, located one wavelength away is gonna be produced perpendicular sorry tangent to the apex of each of these wavelets. OK. So here's the apex for the red wavelet, here's the apex for the green wavelet, here's the apex for the black wavelet and our new wavefront is just going to be tangent to those apexes. This is the new front. And as you can see the light doesn't change direction light that was moving to the right is still moving to the right, right, all of those rays are still pointing in the same direction as they should because in a single medium light shouldn't change direction. All right, let me minimize myself. For the next thing according to the old wavefront, we have a light that's moving in all manner of different directions. OK. It's actually moving in all possible directions, it's moving spherical and this kind of light we would call isotropic the same in all directions. All right. Now, if I choose a point on this wavefront, you can see that these spherical waves are emitted and they're emitted for a distance of the wavelength, right, the next wavefront is gonna appear one wavelength away, right? I choose another point, spherical wavelets come out travel a distance of the wavelength, choose a third point spherical wavelets come out traveling a distance of one wavelength. OK. Now, I wanna mark the apexes on all of these waves because those apexes are gonna determine where the next wavefront appears and that wavefront has to be tangent. Sorry, my hand got a little sweetly there tangent to all of those apexes. OK. So it's going to be another spherical wavefront and you'll see that once again, the light continues traveling in a straight direction because it's still perpendicular at all those points on the new wavefront. And that is to be expected, light should continue to travel in a straight direction unless it moves into a new medium. OK. So let's do an example. We wanna explain light reflecting off of a mirror using Hagen's principle. OK. For this, I'm gonna draw wave fronts. OK? I have the light ray, I wanna draw wave fronts. Each new wavefront I draw is going to be at a new point in time, right? This wave is traveling. So at one point in time, the wavefront is here, then it travels a wavelength and now it's here, then it travels some more and it's here and then it's here and then it's here and then it's here and then it's here. OK. So where did the wave front or where did the electromagnetic wave first contact the mirror? It first contacted the mirror here? OK. Where did it contact the mirror? It's all right. First, where did it contact the mirror? Second, it contacted the mirror. Second right here. And where did it contact the mirror? Last? It contacted the mirror last right here. OK. That means that that third point of contact is gonna have the least amount of time for the wavelet to propagate, right? Because it occurred last. So its wavelet is gonna be the smallest. The second point is gonna have an intermediate wavelength because it occurred second. So it has the second largest amount of time to propagate. So I'll draw the wavelet like this. Now, the first point of contact occurred the earliest it occurred the longest amount of time ago. So its wavelet is gonna be the largest because it had the most time to propagate. So its wavelet is gonna look something like this. OK? And Now I'm gonna redraw this scenario because that picture is already getting complicated and I wanna see what the new wavefront look like. So my blue point is here, my green point is here. My red point is here. My red wavelet is small. My green wavelet is intermediate. My blue wavelet is large. OK? And now where are the apexes? Remember that the apexes tell us where that new wavefront is gonna be. There's an apex, there's an apex, there's an apex and I'm just gonna draw a line like this. OK? If this had been done properly with computers and everything, that line would be perfectly tangent to all of the wavefront, sorry, all the wavelets, but I'm a person so I can't draw things perfectly. But the line looks something like that, which means that my new ray should look like this and because it moves in a straight line, the new wavefront propagate like this and this is what my new light ray looks like. OK. And that is how you explain reflection using Hagen's principle. All right guys, that wraps up our discussion on the rain nature of light. Thanks for watching.
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