Waves and optics
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Introduction to Waves
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Amplitude, Period, Frequency and Wavelength of Periodic Waves
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Introduction to the Doppler Effect
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Doppler effect formula when source is moving away
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When the source and the wave move at the same velocity
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Mach Numbers
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Specular and Diffuse Reflection
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Specular and Diffuse Reflection 2
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Refraction and Snell's Law
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Refraction in Water
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Snell's Law Example 1
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Snell's Law Example 2
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Total Internal Reflection
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Virtual Image
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Parabolic Mirrors and Real Images
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Parabolic Mirrors 2
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Convex Parabolic Mirrors
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Convex Lenses
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Convex Lens Examples
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Doppler effect formula for observed frequency
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Concave Lenses
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Object Image and Focal Distance Relationship (Proof of Formula)
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Object Image Height and Distance Relationship
Parabolic Mirrors 2 Parabolic Mirrors 2
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- Let's draw a bunch of parabolic mirrors
- In this video, I want to do a bunch of examples of objects in front of parabolic mirrors
- and think about what the images of those objects will be
- based on how far those objects are
- Besides just giving us a better understanding of parabolic mirrors
- this will hopefully also gives us a sense of how to conceptualize this light rays
- which will be pretty useful tool when we tackle other types of reflective or refractive devices
- like lenses
- So that's a parabolic mirror. I've drawn its principal axis right over here
- Let me just copy and paste this. Let me draw the focal point too
- So this is the focus right over here
- And this is the center of curvature, twice the distance from this point as the focus
- So that is the center of curvature right over there
- Let me copy and paste it so we can reuse it later on in the video
- Alright, so I have copied that
- Now let's put an object. I think we did this in the last video
- Let's put an object beyond the center of curvature
- So let's put an object here
- The convention is to use upward pointing arrow
- This isn't a light ray. It's used to show an object
- And we use the tip of the arrow to really show the top of the object
- and that's usually where we trace our light rays from
- but it doesn't have to be there. You can do the middle; you can do the bottom
- and you can figure out what the image of the object's going to be. So let me do that
- We're dealing with parabolic mirrors
- It's easiest to have just 2 light rays
- one that goes parallel to the principal axis
- and one that goes through the focus
- because you know what's going to happen at each of those when they reflect
- You don't have to do any math there
- Let's have the parallel ray
- That's the parallel incident ray. When it reflects, it'll go through the focus
- And Let's have an incident ray that goes through the focus
- And when it reflects, it will be parallel
- This is the example we actually saw in the last video
- And so whatever light is being emitted from this point over here in that direction
- it will come back and converge again at this point
- We could actually do it at every point along the--we could do it halfway
- This halfway point of the arrow, just to make it clear. It's the same thing
- You have a parallel incident ray. It will reflect through the focus
- And I'll just do it for this one right over here. It will reflect through the focus
- And if you have an incident ray that goes through the focus, it will reflect parallel
- So this point will correspond to this point over here
- I think that makes it clearer that
- the image of this object was reflected by this parabolic mirror will look just like that
- So it'll actually form a real image that is smaller than this original one
- It's not so clear the way I did it over here but you can further back out
- and it will be clear that this is going to be a smaller real image than that right over there
- Now let's do a couple of more examples. So let me just paste my drawing
- So I don't have to redraw it
- Let's see what happens. So let me write it just so we can keep track of things
- So here the image is real and smaller than the actual object
- when the actual object is beyond the center of curvature
- Let me make it a little bit clear by drawing another example like that
- I'll do something big and way out here just to make it clear
- So once again, we go parallel
- reflect through the focus
- and then we can go through the focus and then reflect out like that
- And there you see. Now it's much clearer that the image is going to be much smaller
- and of course inverted relative to the actual object
- Now let's do this again
- But this time, let's place the object at the center of curvature right over here
- So right at that distance that's twice the distance from the vertex of the parabola to focus
- So we'll do a parallel line, parallel incident ray, parallel to the principal axis
- This is the principal axis right here
- That's what this line is right over here. Kind of the line of symmetry of the parabola
- When it reflects, it will reflect through the focus
- and then let's take another incident ray that goes through the focus
- and when it reflects, it will reflect parallel
- My drawing isn't the neatest drawing on the planet. Actually let me draw it a little bit better
- than that. Well that's pretty good. Let me just--
- That's the incident ray that's parallel
- and then an incident ray that goes through the focus
- will then come out and reflect right over there
- And they'll converge. My drawing isn't ideal
- but the reality is that they'll converge so that the image will just be a
- inverted same size version of this thing up here because it's symmetric
- Let me see if I can redraw this whole thing so it comes out neater
- So far, that looks good
- Then you want to reflect like that, coming through the focus
- Then you have another ray that goes through the focus
- and this whole thing should be symmetric and then it would reflect
- It comes back out like that. So that makes it a little bit clear
- So this is the object. And its image is just an inverted version of this object
- The ray converge at the same distance from the actual mirror as the actual object
- And it's going to be the same size, just inverted
- So here the image is real and the same size as the object
- Let's just do a couple more of this
- I think you've got the hang of it
- You might want to try them out. You might want to pause the video and try them out on paper
- Really nothing deep practice
- So let's stick our object between the center of curvature and the focus, or the focal point
- So if we put our object there, we could
- have a light ray that goes parallel to the principal axis
- And then it will reflect out through the focus
- And then you could have another ray that goes through the focus
- And then it will reflect out
- Let me do it better than that. I should probably have used a more precise tool when I did all this
- So let me draw it right over here
- So I have the parallel one
- Then it goes through the focus just like that when it gets reflected
- Maybe I should have had a line tool for this to have neater drawings
- And then a ray that goes through the focus will be reflected out parallel
- At least for the light that comes from that tip, they will reconverge at that tip
- And if you did it for every point on this arrow
- the image would have been inverted arrow that is bigger than the original
- And it is beyond--it's almost the opposite of the first example that we showed
- So now the image is bigger than the original
- So the image is real and it is bigger
- And the image will converge beyond the center of curvature
- And you can imagine if this was the object right here
- then this would be the image of it, if you just trace the lines backwards
- So there's some symmetry here between this example and the first one we did up here
- Let's just do a couple more. Let's imagine that the object is actually at the focal point
- Is actually at the focus
- Let's draw an object there. Think about what would happen
- So if we're at the focus
- a ray that comes out parallel will go through the focal point, just like that
- And then here we can't have a ray that just goes into the object
- So here I'll do a slightly different ray that intersects the parabolic mirror right over there
- The reason why I want to do it there is because
- there the parabolic mirror is essentially flat and essentially vertical
- So you can kind of imagine that the incident ray is gonna be the same thing as a reflected ray
- Let me draw a ray that comes in like that. This is a departure from what we did before
- The reflected ray will come out like that
- So what happens when the object is at the focal point
- is that all of the light that's coming off of this object in any direction
- will all be made parallel. So it won't converge
- So it won't converge. So it won't be able to form a real image
- And it does not look like it is diverging from some point in the mirror
- So it even won't form a virtual image
- So here, there will actually be no image
- No image when the object is actually at the focal point
- And then the last case as you can imagine is if an object is closer than the focal point
- Let's draw that
- Let's put the object at the focal point
- So right over here
- And here just for the sake of argument, I can always draw a parallel
- Anything that's parallel will then look
- to come out in a direction that would go through the focal point
- Although the object itself is blocking, it will look to go in that direction
- it will be reflected in that direction
- And then you can imagine a ray of light that would have been coming from the focal point
- or would've been coming from the same direction as a focal point
- would be reflected in a parallel direction to that principal axis
- Now these two light rays are not converging
- but they look like they're diverging from some point behind the mirror
- So in this case, we're forming a virtual image
- And the virtual image will actually look something like this
- And so it will be larger than the original
- Virtual image
- So it's kind of a magnifying. If you were to go to a fun house or amusement park, whatever
- if you were to get close enough to a parabolic mirror
- it would show a magnified version of you
- Actually, let me draw that a little bit bigger just because it might not be clear
- This is the mirror
- That is the focal point
- This right here is the principal axis
- This is maybe you, maybe whatever object
- You could draw a ray that goes parallel
- It will reflect in the direction of the focal point; it will reflect out like that
- It'll be blocked by the object though
- And then something that looks like it would've come from the focal point
- from the same direction as a focal point
- would then be reflected parallel to the principal axis
- So these two rays once again they're diverging, but they look like
- to the human brain, to the human eye, they look like they came from that point over there
- And so this would correspond to that point on the virtual image
- that point on the virtual image
- So hopefully, that gives you some practice
- But the most important thing, it gives you some practice dealing with these
- arbitrary ray we're showing emanating from the tip of the arrow
- For the whole arrow, the reason we're picking these rays and these directions
- is they're easy to work with. If they go through the focus, they'll come out parallel
- If the incident ray's parallel, it'll come out through the focus
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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