The Science of Everything Podcast - Episode 52: Applications of Optics

Episode Date: November 28, 2013

We begin by discussing some of the basic principles of image formation in lenses and mirrors, including reflection in flat mirrors and curved mirrors, use of ray diagrams, real and virtual images, and the different ways in which images can be formed. These basic principles are then applied to gain an understanding of a number of interesting optical phenomena, including mirages, rainbows, and thin-film interference. I conclude the episode with a discussion of optical magnification, and how this is used in telescopes and microscopes.

You're listening to The Science of Everything podcast, episode 52. Applications of Optics. And I'm your host, James Fodor. This episode, we continue on from the discussion of light and optics way back in episode 32, so very strongly I recommend you listen to that first. And in this episode, we'll look at mirrors and lenses and how they work, and then apply that knowledge to examining how optical instruments, like simple cameras, telescopes and microscopes work, and how they magnify images.

And we'll also talk about a few other interesting optical instruments. phenomena, including mirages, rainbows, and thin film interference. So we've got a lot to talk about, so let's jump straight into it. Okay, so let's start with the discussion of mirrors and lenses, and before we get into the details of that, there's an important concept that we need to know about, which is that of the ray diagram. So the ray model of light is a simplified model of the behaviour of light that is useful when we're talking about the production of images through lenses and mirrors and so forth.

the ray model of light abstracts away from all the details of photons and the wave behavior of light and quantum mechanical properties and so forth. So it's not especially realistic in that sense, but it's very useful for when we have a large amount of light in sort of more usual everyday settings, particularly in cameras and so forth. And also where we have relatively long distances that we're concerned with, you know, much longer than the length of a photon or a proton or something like that. So the basic rule of how ray diagrams work is that when a ray of light hits a smooth surface, the angle of incidence is always equal to the angle of reflection, regardless of whatever other qualities there are of the media in question. So the angle of incidence is just the angle between at which the light ray is hitting the surface and the surface itself. So if it's perpendicular, it'll be a 90 degree angle of incidence.

And the angle of reflection is just the angle. between the reflected ray and the surface. So that should be fairly intuitive. It's just sort of like if you bounce a ball. Like if you're playing pool and you hit a ball at an angle onto the side of the table, the ball will reflect off and proceed away in sort of continuing the same path,

but with the angle of incidence roughly equal to the angle of reflection, you can sort of imagine what happens when you hit a ball against the side of a pool table. It goes off at the same angle, in the sort of different direction. Hopefully you know what I mean there. It's a bit hard to describe without a diagram,

but that's basically what's happening with the ray model of light. The angle of incidence is equal to the angle of reflection and that doesn't depend on any particular properties of the medium. That is the material

through which the light is travelling. It just, that'll always happen whenever the light moves from the boundary of one medium to another. So that's when light moves from water to air or air to water or glass to air or anything like that. You'll always have this reflection occur.

We talked a bit about that in episode 32, so go back there if you're a bit confused about what I'm talking about there. But we just need to have that ray model of light in mind when we're talking about mirrors and lenses. Okay, so let's first talk about flat mirrors or regular plane mirrors. How do they work? Images are produced in mirrors, not because of a fundamental property of the mirror itself, but really because of the way our brains work. So this is probably the single most important thing to understand about applications of objects. Our brains always interpret light as having originated in a straight line from the direction in which it, you know,

in the opposite direction to that in which it enters our eyes. So if we see light coming in a particular direction, our brains automatically assume or interpret or build an image on the assumption that the light came from the direction in which it is now entering your eye. And so it projects back the direction of light. And usually that's a pretty good assumption because usually light does come from the direction in which it enters our eyes. But if there are reflective surfaces, which can change the direction of which light is travelling, then that assumption will not be true. And that's exactly what happens in the case of a plain mirror.

Plain mirrors, or flat mirrors, are simply reflective surfaces that bounce light off. That basically light is incident on the surface of the mirror, and it reflects off according to the rule. Remember the angle of reflecting, reflectance equals the angle of incidence. And then the reflected light then enters our eyes, and we see an image there. Our eyes project back the light, assuming that it is always travelled on that path, which it enters our eyes, even though, in fact, it didn't.

It was reflected by the mirror, but our brain doesn't incorporate that information, obviously, it doesn't know about that. And so that's why we see objects as lying behind the mirror. There's nothing really behind the mirror. The light that we see as coming, that we perceive as coming from the mirror, is actually coming from somewhere behind us, or maybe from our face, or wherever the object is. It just looks to us like it's coming from behind the mirror, because that's where our eyes project, the light. back to. That's where our brain assumes the light was coming from, because it ended our eye, as if it was coming from that direction. But to get a nice, crisp image in a mirror, you have to have a sufficiently flat reflective surface, because if you have a really bumpy surface,

basically the different parts of the image are going to be all jumbled up. You know, part of the light that, let's say I'm looking at my face in the mirror, part of the light that, if the mirror is not flat and really smooth, then part of the light that came from my nose will be mixed up with the light, part of the light that came from my forehead or my ear or wherever else. They'll all be reflected at slightly different angles and the relative relationship won't be preserved because you think about looking at the surface of the mirror, the surface of the mirror is bumpy and irregular, so some light will be reflected, some light will be reflected a bit too much this way and some light will be reflected a bit too much that way. Relative relationships between the

position of the parts of my face won't be preserved and so I won't see a nice clear mirror, I'll just see a jumble of colours. Generally this is what happens when you look at most dopaic objects. You look at the white wall, you see it as white because it's not, it's still reflecting light from your face, so why don't you see an image there? The reason you don't see an image is because it doesn't, the reflection is not smooth. It's not regular because the surface of the wall is bumpy, and therefore you don't get a nice, neat, clear image of your face. You just get a jumble of colours, which we see as white. So in order for a nice clear image to be preserved, we have to have a very flat, smooth surface, and so that's why mirrors are made

generally out of metal. You often think of mirrors as being made of glass. I mean, glass can reflect like this as well, which is why when you're looking at a window, you can sometimes see a faint reflection as well as seeing whatever object lies behind the glass. But for ordinary mirrors, there's glass covering the metal, but it's the metal itself that does the reflection. The metal itself is what provides the smooth surface that reflects the light, and therefore allows us to perceive a nice clear image. So, what happens if we were to put two flat mirrors parallel to one another so that they were directly in front one of the other and facing each other and facing each other. What would we see? Well, basically, if the angle was just right between them so that they were exactly parallel,

you would see, if you could somehow look in between them without blocking the light, an infinite number of images reflected, you know, further and further deeper into the mirror, because essentially what you've got is that one mirror is reflecting the other mirror, reflecting the other mirror, and so on and so on infinitely. as you then tilted the mirrors so that the angle was no longer perfect, you would get a sort of a curve in the image, or in the images, and you would no longer have an infinite number of images going into the mirror. You'd have a large number, but they would sort of peter off. So in order to get a truly infinite number of images in parallel mirrors,

you would have to have them perfectly parallel, which is, or perfectly in front of each other, which is not really possible in the real world, but it's pretty cool when you have two mirrors in front of each other. If you haven't seen that, it should look it up on Google, because it's a pretty cool phenomenon. And it's just, you know, the result of the combination of two mirrors interacting with each other. One mirror reflects the second, which in turn reflects the first reflecting itself and then so on.

Okay, so that's a bit on flat mirrors. Now, what about curved mirrors? How do they work? Well, unlike flat mirrors, curved mirrors do not preserve all of the angles and relationships of the light rays. So that means they distort the size and shape of images. There's two basic types of curved mirrors. A concave mirrors and convex mirrors. A concave mirror is sort of like a depression.

It curves inwards. And you can think of it as being both sides of a concave mirror are like the insides of a sphere, so it bends inwards. A convex mirror is the opposite. It bulges out in the middle. And so it's like the outside of a sphere or the outside edges of a sphere. So a concave... Sorry, a convex mirror is like the type of...

Well, a convex lens is the type of lens you have in a microscope. So that's why it bulges in the middle. The difference between a lens and a mirror, by the way, is that a lens allows the light to pass through, so it's transparent, whereas a mirror reflects the light. But other than that, they're quite similar in how they work. Well, in the broad principles anyway, we can use the ray model of light to understand how their birth function. But anyway, coming back to curved mirror. So we've got concave, which is like bulging out at the sides and poking and pressing inwards in the middle. Sort of like a red blood cell, you push it in the middle, and it splays out of the air.

around the sides. That's a concave mirror. Convex is the opposite where it bulges in the middle and then peters out to the edges. So concave mirrors can be used to focus light to a point because essentially what happens as the light shines onto the mirror and then as the light's reflected off, it's being, it's all directed to a central convergent point. The concave mirrors converge light. They take light from a large area and focus it down to a single point and that's that it because of the way that the mirror is curved inwards. So, you know, light falling on the very center of the mirror is simply reflected back straight through, but light that falls around the edges is also directed inwards towards a central point.

Just like if you move inwards from any point on the inside of a sphere, you always move towards the center of the sphere. That's just how a sphere works. That's basically what a concave mirror is doing. It converges all of the light that it takes up into a single point, which is called a focal point in the very center of the sphere, of which the concave mirror forms a part. I mean, concave mirrors aren't usually an entire sphere, then the light wouldn't be able to get in. But you can imagine it as cutting off a bit of the sphere, and so you only have a partial curve there.

All of the light that's picked up in that part of the sphere, in that external surface of the part of the sphere, is then concentrated to a single point, the focal point. So that's why concave mirrors can be used to focus light to a single point. So if concave mirrors focus, take in light from a large area and focus it to a single point, you can hopefully see how convex mirrors do the exact opposite.

Convex mirrors take in light from a large area, sorry, convex mirrors take in light from a narrow area and disperse it to a large area. And again, think about the shape of a convex mirror. A convex mirror pokes out in the middle, so if you shine a beam of light on the

convex mirror, that's going to bounce off and then spread out in all sorts of different directions. It's going to move out away from the surface of the outward poking surface of the mirror in all the different directions. And so that includes, you know, directly towards us and also a bit off to the side and to that side. It's kind of similar to the way in which the wavefront of a wave spreads out. It moves, it sort of pushes out in a circular pattern. And so it spreads out. It doesn't just go in one direction.

So concave mirrors, focus light to a point. Conve mirrors spread light out. So, in a moment I'm going to talk a little bit more about the different kinds of images that curved mirrors can make. I've already said that they can produce distorted images, but they can also, one property of curved mirrors is that they can magnify or diminish images, and they can change their size and orientation. We'll talk about that in a moment. First of all, I need to introduce the concept of what an image is in optics, and also explain the difference between real and virtual images. So in optics an image is just, well, it's something that we see, but let's try and make that concept a bit more explicit. An image is formed when all of the light from a given object or a given point on an object in the real world, in the environment,

converges at a single point in an image. And so this is what I was talking about before when I was talking about the need to have a flat, smooth surface for a mirror to work, because only that will ensure that all of the light from my nose, that all of the light that comes from my nose converges to a single point on an image so I can see my nose clearly. Otherwise, if that doesn't happen, the light from my nose is mixed up with the light from my forehead and the light from my ear and so on.

And so you don't have an image, it's just a mush of colours, which we might perceive as white or black or something. So in order for an image to occur, any type of image, you have to have sort of a one-to-one mapping. Light from one part of an object goes to one part of the image. Light from the top of the tree goes to the place on the image or in the image, where you see the top of the tree.

Same thing with light from the bottom of the tree. There's no mixing up of light from the top and the bottom of the tree. Otherwise, again, you would not have an image. You would just have colors. So that's what an image is. We have to have that convergence of light. But what's the difference between a real and a virtual image? Well, a real image is when the light really does converge like that.

In other words, if you put a piece of paper there, you could see the light shining on the paper. So that's sort of the most basic form of an image. That kind of image is the kind that you could put your eyeball there and see it. So the light really is at the location where the image appears to be. Well, what other type of image could there possibly be, you might be wondering? Well, the other type of image is a virtual image, and that occurs where the light is not really at the location, where the image appears to be. And this is, virtual images are the result of how our brain

works, as I mentioned before. Our brain always assumes that the light has come from the direction in which it enters our eyes. So if it looks like, if the light enters our eyes from the direction of the mirror, then we project, our eyes project back, well, our brains project back, and interpret the light as having come from behind the mirror. And that's why we see an image in the mirror. But if you want to actually go there, you know, the image isn't really there. There's no light actually inside the mirror or behind the wall or behind the glass or anything like that. So that's why it's a virtual image. The image does not actually exist there. It just looks to us like it does. So images that occur in mirrors are always virtual images. There's no real

light there, whereas images of things that we see in the real world are generally real images, or at least they produce real images in our eyes. It can be complicated, because often there's some mixture of real and virtual, because there's often some kind of mixture of real and virtual where one lens or mirror will produce a real image, which then another one produces a virtual image of it, and so on. So we didn't get into complexities of that, but the important thing is to understand the difference between real and virtual images. Real, the light is actually there, virtual, the light is not actually there. Okay, so now that we understand the different real and virtual images. I want to come back to our curved mirrors, concave and convex,

and explain the different types of images they can make. The way you work this out is to use ray diagrams. Ray diagrams, you just draw a sort of an outline sketch of the shape of the lens, whether it's convex or concave or flat or whatever, and then you draw some light rays coming in, as straight lines, and make sure they reflect at the proper angle. Remember, angle of incidence should equal angle of reflection. And then you see where all those different lines that you've drawn in converge, because where they converge, that will be the point where the image occurs. because remember the image occurs where light from different, from the same point on the object, also converges to the same point in the image.

So if I draw three different light rays coming from the top of a tree, and they hit the lens and reflect at the correct angles, and then eventually meet up again, those same three light rays meet up again at some other point in space, then an image of the tree will occur at that point. It's a little bit hard to imagine this if you haven't seen a ray diagram before, so I'll post some of those up on the Facebook page, or you can just Google them, and you'll see what I mean, but that's how we work out, sort of it's a simple way where images will be formed.

And depending upon the angles of the lines and the shape of the mirror and whether it's concave or convex, and also depending on where the object is placed relative to the focal point of the mirror, all of those factors will affect the type of image that is formed. So we can have virtual images or real images. Convex mirrors, for instance, always produce virtual images because think about a convex mirror. it spreads out the light.

So there's no way that the light, like, think of our three light rays coming from the top of the tree, they hit the mirror, they'll hit the mirror at different spots on the mirror because they're travelling in different directions. They come from the same point on the tree, but they travel in slightly different paths.

And so therefore the three light rays hit the mirror at different points on the mirror. If it's a concave mirror, and then the concave mirror may be able to converge those three light rays to a single point again, at which point we'll observe an image. But a convex mirror can never do that,

because it always spreads out the light rays that hit it. And so a convex mirror can never form a real image. The light rays can never converge again. However, our brains can trace back the light that we see coming from a convex mirror and interpret it as if the light ray came from a single point somewhere behind the mirror. So that's a virtual image that exists behind the mirror. So to us, it looks like the light came from the top of the tree, which is located somewhere behind the mirror.

In fact, of course, that's not where the light really came from. The light came from the real tree, which is located somewhere else. But our brain traces the lines back to where they would intersect, sort of. And again, if you're having trouble picturing this, look at a ray tracing diagram and it becomes much clearer. So to form an image, the real light rays don't actually have to intersect. That can be the case, in which case you get a real image, or it can be the case that our brains just sort of trace lines back to where it looks like they came from.

and then find where they intersect. And that is a virtual image when that happens. So convex mirrors always form virtual images because they can't actually converge the real light rays together. Concave mirrors can do that, and so they can produce real images. So different types of mirrors produce different types of images, but also the location of the object relative to the mirror will also affect the image.

Depending on whether it's placed inside or outside the focal point, for example, you can get images that are larger than the real object or smaller than the real object. You can also sometimes get inverted or erect images. Inverted just means it's flipped upside down. And by the way, that's not the same thing as the fact that an image appears back to front in a mirror. That's not actually an inverted image.

That's a different phenomenon, so don't get that confused. Inverted, yeah, it just means the image is flipped upside down, and that can happen because of the way the light is reflected. I won't go into too much more detail about exactly where you have to put objects in order to get exactly how much magnification, because it's just too hard to explain that without diagrams. But the real important thing is just to understand that depending on where we place the object and depending on what type of lens we're using,

sorry, what type of mirror we're using, you can get different types of images. And convex mirrors can never produce real images because they diverge light rather than converge them. So that's enough on mirrors. Let's talk a little bit about lenses. So if you remember before, I mentioned lenses briefly. The difference between a lens and a mirror is that a lens is a piece of transparent material, so glass or plastic that allows light to pass through it, whereas a mirror reflects light. So a lens, you may have some small amount of reflection at the very, at the interface of the two media.

So as the light passes from the air into the glass or plastic, say, you might have a little bit of reflection at the boundary there, but not too much. Most of it just goes through. So that's what makes a lens different from a mirror. But you can also have, just like we can with mirrors, we can have converging lenses and diverging lenses, or concave and convex lenses. And again, they will either converge light or diverge light. So if you have a concave lens, that means that the lens is pushed inwards in the middle. So that's the same thing with our mirror. A concave lens will spread light out.

Because if you think about it, imagine that we've got our concave lens, which pushes inwards on both sides. So it kind of looks like letter X and you just draw a line from the top of the... So a lower case X, imagine a lower case X, and draw a line from the top left. to the top right of the X, and then same thing at the bottom, so you've got the two top bits and the bottom bits of the X joined up. That's kind of what a convex lens looks like. Hopefully you can imagine that. If you shine some rays of light into the left side of that convex lens,

then hopefully it's immediately obvious that on the other side, those light rays will converge on the other side, because the surface of the inner surface of the sphere on the other side of the lens causes the light to bend inwards towards the central focal point. So convex lenses, sorry, I think I've muddled my words here, concave lenses

converge light. So concave converges, because the concave lenses will bend the light so that it goes through a central focal point. Convex lenses are the opposite. They're the lenses that bulge out at the middle. Those type of lenses will diverge light. So it's the same thing with

mirrors, in terms of concave mirror, mirrors and lenses converging light, whereas convex mirrors and lenses diverge the light. But lenses are different, of course, because the light passes through the lens rather than reflects off it. So images will be formed in different locations. Depending on exactly where you place the object and exactly the type of lens you're using, the image can be formed on either side of the lens. And it can be diminished or it can be magnified or it can be the same size as the real object.

It can also be erect or inverted, depending on, again, where you place the image. place the image and the type of lens. Lenses also have a focal length, which is the distance between the center of the lens and the focal point. Mirrors also have, a curved mirrors also have focal lengths. So that's the same concept as when we talk about glasses or cameras. You might have heard the concept of focal length. That just means the distance between the center of the mirror or lens and the focal point where the light is converged. The shorter or smaller the focal length is the stronger the lens, which means it converges the light more quickly. So strong lenses are more curved and therefore bend the light more and therefore have a short focal length.

And the process of image formation in lenses is fundamentally similar to that in which it occurs in mirrors whereby you have to get the convergence of points of light from a given point on the object, you have to get convergence of rays of light from a given point on the object to a single point on the image, be it a virtual or a real image. And the exact paths of the light rays will differ, of course, with a lens to compare to a mirror, but the fundamental process is the same. So, that's enough on lenses and mirrors. There's one final concept I want to talk about now, which is relevant to this, called aberration.

So an aberration in optics is any deviation from the ideal or the normal result that we would want or expect in an optical system. Basically, this occurs when that nice story I told about, light from a single point in the object converging to a single point on the image. Aberration generally occurs, or different types of aberration occur when that breaks down, when there's some mismatching between light in this source and light in the image. And there's many different ways that can happen. So one way is chromatic aberration, which is a type of distortion by which different

colours are converged to slightly different points. So you've got basically a sequence of sharp images. It's just that you've got one that's for all the blue light and one for all the red light and one for all the yellow light, etc. And they're not perfectly aligned. So naturally that would be quite annoying and difficult to use, particularly if you're doing precision work. And the reason why you would have different focal lengths or different convergent points for different colours is because the refractive index for a given material can differ between different wavelengths of light.

So that is a given piece of glass or plastic or whatever can be such that it slows down, say, blue light more than it slows down red light and therefore it bends red light more or less than it bends blue light. and I mean this is responsible for the dispersion of light when you pass it through a prism. It's the differential refraction of different wavelengths of light. They're slowed down by different amounts and therefore they're bent different amounts and therefore they spread out. Well, if that happens in a curved mirror or lens, you get chromatic aberration. Another type of aberration is called spherical aberration. This one's a little bit harder to understand, but basically, remember before that I spoke

about mirrors and also you can think of lenses as being like, sections of a sphere that you've cut out, so that it's either the inner curve surface or the outer curve surface of a sphere. Well, it turns out that spheres, that portions of a sphere like that don't actually focus light to a single point perfectly well. They do a pretty good job, but not a perfect point. Just the way a sphere is shaped, it doesn't do it quite perfectly. And again, there's no way of showing that other than our diagram. It just doesn't work. A sphere is not quite the right shape to focus all of the light that comes into a single point. Well, what shape do you need? It turns out a Parabola does the job perfectly.

If you've got it correctly shaped parabola, it'll focus the light onto a single point. And so if you have spheres, sorry, if you have lenses or mirrors that are sections of a sphere, you'll get spherical collaboration, which is some distortion in the image caused by the fact that it is a sphere. And so that's why really sensitive mirrors or lenses are made as parabolic shapes. But the trouble with that is that they can be harder to make and also potentially more difficult to maintain and support and so on. Another possibility is that you can use a combination of lenses to correct for that. Another interesting aberration is called astigmatism. A stigmatism occurs where the light rays in two different dimensions

or in two different planes have different focal lengths. So in other words, the best way to understand this is imagining that an optical system with an astigmatism is used to form an image of a cross. If you do that, what you'll see is that when the horizontal bar is in focus, the vertical bar will be out of focus. But then if you try and focus the vertical bar, the horizontal bar will be out of focus. And this is occurring because basically,

the vertical light focuses at a different focal length than the horizontal light does. Different planes of light have different focal lengths. And so you can't get a single sharp image. You can get sharp images for different portions of the image, but not the whole thing. And there are many, many other different types of aberration as well,

which cause problems in particularly in sensitive optics. Coma, image distortion. There's a whole bunch of other ones as well that I haven't talked about, and some of them can get quite complicated. So this is why, well, this is one of the reasons why it's difficult to build telescopes and microscopes that have very high resolution, especially telescopes, I think, because as you start getting, having larger and larger lenses or mirrors, they tend to use mirrors for the larger telescopes. As you have larger and larger mirrors, these problems of chromatic aberration, spherical

aberration, comat, astigmatism, and so on, and many others, become more and more prevalent, and it becomes very complicated and costly to deal with them and fix them. So at that point, the resolving power of the telescope and how much it can magnify an image is not predominantly determined by the size of the telescope, or like how curved it is, how bent it is. Because remember, I said the more curved it is, the more it can magnify it, or the more it can bend light, and that can translate into high magnifying power, as we'll see in a moment. But the resolving power of sort of real telescopes is not limited by that, because it's pretty easy to make a telescope that magnifies a lot. What's hard is to make a telescope that magnifies a lot and also doesn't have problems with lots of aberration. But we'll come back to that in a little bit when I talk about optical instruments and we go through a bit about telescopes and magnification. Now I want to take a bit of a detour and talk a little bit about some optical phenomena that are interesting.

So we'll talk about mirages, rainbows, colours, and film interference, each briefly in turn. So what are mirages? Well, a mirage is just an image that we think we see, but we in fact don't see. I mean, the image is real. We really see it, but it's misleading what we're actually seeing. So, I mean, a classic example is the person wandering in the desert who sees an oasis, and as they walk towards it, it disappears, and it turns out that they were just seeing the sky reflected on the, well, not reflected, but the sky appeared to be on the ground, and it looked like a puddle of water.

You will probably also see this if you've been driving along the road, and you see this, what looks like water on the road, but as you drive, if you get closer, it sort of disappears, and there was no water on the road. Again, that's a mirage. You're seeing the sky on the ground. There's two many different types of mirages. Inferior mirages where the image is formed under the real object. So that's like your water in the desert, water on the road example,

because what you're seeing is the sky on the ground. And so the image is under the real object. So that's an inferior mirage. The other type is, of course, a superior mirage where the image is formed above the real object. So an example of this is if you see, sometimes in the ocean, you can see superior mirages of where it looks like there's a ship floating in the sky or floating just above the real ship on the ocean. So the image of the ship is above the real ship,

and so therefore it's a superior mirage. Mirages are caused predominantly, at least these two types that I'm talking about, are caused mostly by air temperature differences near the ground. Air has different refractive indexes at different temperatures, so hot air and cold air reflect light by different amounts. And therefore, light passing through these different temperature bands can be bent.

It can be bent either upwards, sort of towards the sky or downwards towards the ground, depending on the temperature gradient, whether it gets hot or going up or colder going up. Again, seeing exactly how this works in terms of ray diagrams is so much easier with a diagram, so I'll put some up on the Facebook post. But for the moment, we'll just take the broad concept that air temperature radiance near the ground, if they're sufficiently compressed so that the light can be bent enough in small enough space, can cause the light to change direction.

And therefore, when we see it, when the light enters our eyes, it looks like that the light has come from the ground, wherein, in fact, it's come from the sky. it's just been bent around so that it looks like it's come from the ground. Remember, that's our brains working again. To fool us, our brains assumed that the light came from a straight line in the direction in which it enters our eyes. And so it looks like the sky is on the ground or the ship. But in fact, the light that we're seeing really came from the sky or the ship, and the sky and the ship are where they should be.

It's just that the light was bent in the meantime because of the temperature difference. So that's how mirages are caused, just by temperature differences, or temperature gradients in the air near the ground. This is why you tend to find them on like on the top of hot roads and deserts and so on. Rainbows. Now everyone knows what a rainbow is, so I need to describe that, but what causes rainbows? Well, rainbows are caused by refraction and total internal reflection of light inside of raindrops, raindrops that are just in the air or in the clouds.

So total internal reflection just means that light is sort of bounced around inside the raindrops until it's reflected back in the direction in which it came. So that's what we're seeing. the light coming, literally what we're seeing when we see the rainbow is light that's been reflected back towards us in the raindrop. But refraction is also important. Refraction is the change in direction of light as a result of the change in speed as it passes from one medium to the other. Remember dispersion, which I talked about just before? Different wavelengths of light, that is different colours of light, have different refractive indexes in many media, including, say,

water or the air surrounding the raindrops. And so when you have this total internal reflection, when the water, when the light is bouncing around inside the water drop, the colours are being separated out because of refraction, because the different colours are reflecting different amounts, and so they go

from being joined to being separated. And so when we see the rainbow, the colours that we see are spread out because they're not joined anymore. The refraction has separated them. Each raindrop produces all the different colours, because if white light shines into the raindrop, well, all the different colours, that comprise white are going to come out of the raindrop again,

but the thing is they'll come out at different angles because they've been spread out by the dispersion of effective refraction. And so only one of the colours is going to actually reach our eye. The person standing next to us might get the red, whereas we get the blue and someone else standing on our other side gets the yellow from a given droplet of water, because the light it admits is spread out at different angles. So that means whenever you move,

you actually see a different rainbow. The light that's entering your eyes is coming from different raindrops. And so the rainbow is not exactly the same. I mean, it looks basically the same because there are so many raindrops. It's effectively, you know, symmetric. But it's technically, they're coming from different raindrops, and so you're seeing a slightly different rainbow. And the other point to understand with rainbows is that although from a given

raindrop you only ever see one color, there are many, many different raindrops, and they're located at different relative positions to you at slightly different angles. And so when you add them all together, you will see all of the different colors of the rainbow. It's just that each color is coming from a different raindrop located at a slightly different angle to you. And someone else standing some distance away is going to be seeing the same rainbow in some sense, because the water droplets are in the same location, but also a different rainbow because the light that's entering their eyes is completely different to the light that's entering your eyes, and it's coming from different raindrops and so on. So rainbows are an interesting

phenomenon. There's certainly not an actual object. It doesn't make any sense to say that there's a pot of gold at the end of a rainbow, because there's no end of a rainbow. It just doesn't make sense. The rainbow ends where, at the point where you can't see it any more. It's, you can't see it because there's something in the way or the light is just not reaching your eyes. In fact, rainbows sort of, if you were to see somehow able to see the whole thing, which you can do, for example, if you're flying in a plane, rainbows are perfectly circular, which hopefully makes sense because, well, so each colour reflects at a certain angle all around you.

And so at a given distance all around you, you'll have that light coming to your eyes. And so, again, very hard to describe this without a diagram, but basically there's a certain pattern of distances and angles that need to be maintained in order for you to see the rainbow. that will be fulfilled at all points in a circle around your position if you're able to see all those points. Of course, when we're standing on the ground, we can't see the points that are in the ground.

Obviously, there's no light coming at us from our feet from the raindrop. So we can't see the rainbow there. But so if you're up in the sky and you're able to see all around you, you can see the light coming in all the directions that sort of match the pattern of the rainbow, and so therefore you see a circular rainbow. And you can look this up on Google. It's pretty cool.

Okay, moving on to complementary and primary colors. So colors are an interesting phenomenon. Colors, as I've said before, are just the result of different wavelengths of light, which our brain interprets differently as per the different types of rhodopsin that is found in the eye and see our episodes on vision for that. But there's such a thing called primary colors or complementary colors. Slightly different, but basically the same thing. Complementary colors are two colors that add up together to produce white.

Two colors are complementary to each other. primary colours are three colors that add up together and can be used to produce any of the other colors. Now, this is a big confusing, so let me try to explain this. There are two sets of primary colors. So within each given set of primary colors, you can produce all of the other colors by mixing them in various combinations. But why are there two sets? You might ask, well, it depends on whether you're talking about subtractive colors or additive colors. What does that mean?

Well, if you're talking about paint, for example, the way paint works is a subtractive process because the paint of a certain colour, so say you have yellow paint. Yellow paint absorbs all colours except yellow and maybe, you know, colours really close to yellow. But what we see is the yellow light that's reflected. Now say I have blue paint. Blue paint absorbs all colours except for blue, which it reflects, and so we see blue. If you combine blue and yellow paint, the result will be a paint that absorbs all colours except for that sort of small sliver of the spectrum that is not absorbed by either the yellow or the blue paint. So in other words, it's the bit that overlaps between the blue and the yellow, whatever that is. And so as you add more and more paints,

more and more colors are going to be absorbed. And therefore, if you add enough paints together, you'll eventually get a, you'll get black. It will look black. And indeed, everyone knows this. When you add lots of paint colors together, it goes a black, brown sort of color. Because by that time, all of the different colors are being absorbed by some paint or other, different pigments and the different paints absorbing the different colors. And so nothing much much. just being reflected, and so you don't see any particular colour. So that's a subtractive colours. These are like mixing paints. So the three primary colours in paint are cyan, magenta, and yellow. These three colours, as paints, are enough to produce any of the other colours that we know when mixed in the right quantities.

And those three primary colours, the subtractive colours, when you add them together, they produce black. Now, what about the additive colours? Well, these colours are produced from beams of light. or rays of light. So spotlights is one way of thinking about this. If I shine a blue spotlight on a white background, I see blue, just like I do when I look at blue paint, but something very different is happening. In the blue spotlight, it only produces

blue light. It's not like the blue paint which subtracts out all the other colours, except for blue, the blue light, the blue light only produces blue light, so it adds in blue light. Same with the yellow spotlight, it adds in the yellow light. So that means if I add all the different colour spotlights together, what will I get? Will it be black? No, it won't be,

because remember the reason it's black when you mix all the paints together is because all of the paints absorb different colors of light. And so when you add all the paints, all of the colors are absorbed. And so you just see black. But when you add all the lights together, it's not like all the light's not getting absorbed. The light's being added. And so if you've got all of the different colors of light added together, what does that look like? It looks white. And so when you add all of the different additive colors together, you get white. So if you combine all your spotlights into one, put them all in the same location to converge them, it looks white. And the primary additive

colors are red, blue, and green. So you'll notice that green is a primary color for additive colors, that is light, spotlights, whereas yellow is a primary color for the subtractive colors, the paints. Cyan and magenta are kind of like red and blue, so those are sort of the same in both cases, but the green and the yellow are different. So if you've heard two different lists of primary colors, this confused me for a long time, they're both correct. It depends on whether you're talking about additive colors, that is spotlights or subtractive colors like paints. Television screens and projections are examples of additive color formation because they produce light by shining lights, whereas paints and pigments are examples of subtractive color.

But in both cases, the sets of three primary colors can be used to form any of the other colors that we know about. And basically, the reason there are three is essentially because we have three different types of rods, excuse me, three different types of cones in our retina, so they can detect sort of three different colors. That's a bit of a simplification. Look at the vision episode for that, but that's where the number three comes from, basically. Okay, that's enough on colours. Now, a final optical phenomena that I want to talk about is thin film interference. So this is an interesting phenomenon.

Thin film interference is basically the colourful fringes and patterns that you see on like oil slicks or oil that's sitting on the surface of water and things like that. Thin films of oil is a common example where you'll see this sort of thing. It's called thin film interference because it occurs when you have thin films of liquid, like, for example, oil. And the reason it happens, the reason we see this, is because as the lightwave passes through the film of oil. Some of it's reflected back off at the bit... some of the light is reflected back in the direction it came at the very first boundary

and some of it continues on, but then some of it's reflected off at the second boundary, because there's going to be two boundaries. It's going to be the first entrance, and then you'll have the oil, and then there's sort of the exit from the oil. So you can have reflection occurring at both of these, both sides of the sort of thin layer of oil, basically. But the light reflected at these two different boundaries will be at a somewhat of a difference apart from each other. There'll be a gap between that reflection of light. If that gap is exactly one wavelength thick, or some multiple of one wavelength,

then there will be constructive interference between the two reflected rays of light. Remember, constructive interferences is when peaks on both waves add up to form a megapique. That will, of course, happen if there's exactly one wavelength of difference between the distances from which the light is reflected, and which in turn will occur, if the thickness of the thin film is exactly equal to one wavelength of the light, or a multiple thereof. There'll be other locations along the thin film where there is exactly one half of a wavelength of a difference between the point of reflection, sorry, the point of reflection of the two different light rays, and therefore you will have destructive interferences where peaks on one wave correspond to troughs on the other,

and they cancel each other out, and you don't see anything. So in these parts of the thin film, we'll see black. On the other parts, we see nice bright colours. The colour, by the way, comes from, again, our old friend, dispersion of light. Different colours of light refract different amounts at different parts on the film, and therefore constructive interference might only occur at a given point on the film for a single colour, maybe red or blue.

It doesn't occur for all of the colours at the same point. So we only observe one colour at that little point where that colour is interfering with itself, and then at a point nearby a different colour interferes with itself, because the thickness of the film is different by just enough so that instead of the red light being constructively interfering, it's the blue light that constructively interferes and so forth. This is where the colourful patterns come from,

and this is where the fringes of light and dark splodges and lines come from on the thin of films. It's because the thickness of the oil's sort of layer varies. It's not all constant. And so at places where it happens to be just one wavelength and thickness, you get this constructive interference and you see a certain colour being reflected there. At other places there's destructive interference, and you don't see anything, and then at a different place, again, there's a different color that constructively interferes, and so you see that color.

So that's how thin film interference occurs. That's why you get that sort of nice, shiny and colorful effect on oil slicks and soap bubbles and things like that. Okay, so to round out the episode, we're now going to move back a little bit and talk about optical instruments, picking up on our discussion earlier of mirrors and lenses, and basically we're going to talk about cameras, telescopes, and microscopes. and they're all sort of fairly similar in broad aspects of it. But first of all, I want to talk about sort of the broad concept of optical magnification and how it works.

So what is optical magnification? Well, optical magnification is simply a change in the apparent size of an object relative to the real size of an object. So this is what occurs when you use microscopes and telescopes and magnifying glasses, camera, zoom lenses, everything like that. That's optical magnification. The apparent size of an object, that is the size it looks to us, doesn't really have anything directly to do with the actual size. of the object. I mean, that might sound counterintuitive, but just look at the moon. Think

about how big that actually is and how big it looks compared to your thumb. So the apparent size of an object is determined by the angular size of the object on our retina, which basically means the angle between a line from our eyes to one side of the object and an identical line drawn to the other side of the object. So if you did that with the moon, you draw a line to one side of the moon and then a line to the other side of the moon and sort of trace both those lines back to the center of your eye. And then if you had a way of measuring the angle to those lines, it would be a very, very small angle. That's simply just saying the moon doesn't look very big. If you do the same thing for your thumb, well, your thumb will look different sizes depending on

how far away you put it from your face. The closer it is to your face, the bigger it looks to you, because the angular size of it is increasing. The image of it is taking up more space on your retina. So, all we have to do in order to magnify an image using optical magnification is increase its apparent size. That is, increase the angular size or the spread out of so to speak of the image. So how do we do that exactly? Well, basically we use lenses or mirrors or both. We often use combinations of mirrors and lenses,

but the basic idea is that we change how spread out the light is by using a curved mirror or curved lens. And then we look at that image using our eye, and because the apparent size of the object has changed as a result of the image being spread out or stretched, we're able to see details that previously we were able to see details that previously we weren't able to make out. The important point is, and this confused me for a long time,

maybe it was just me, but perhaps it's something you've wondered about as well. Telescopes and microscopes don't do anything magical. I mean, well, that's obviously true, but all of the light, sorry, all of the information that we see when we use a light microscope to look at a cell or when we use a telescope to look at the planet Venus or something, all of that light, all of the detail, was present in the light that entered our naked eye. It's not like the telescope or the microscope or the microscope adds any new, light or any new information. It was all there. The only reason we didn't see it before was because

the light was sort of condensed too much and so the image only occupied a small space on our retina so we couldn't make out all those details. If we were just able to scale that size of the image up, we would be able to make out those same extra details that we can see using the microscope or the telescope. So that information is already there. It's just that by spreading the light out, we're able to see the information that was already there. Of course, a telescope microscope can never put extra information in. So if the information was lost to begin with, then you won't be able to see it in the image.

And there's various reasons that can happen. Like if there's a dust cloud in front of the planet that you're trying to observe, the dust might have scattered the light and fuzzied it up such that even with a really high-quality, large telescope, the information just isn't there. We're just not able to make out the details of the planet we're trying to observe, for example.

So that's not a fault of the telescope. That's just the information was never there in the first place. Okay, so that's essentially how optical magnification works. It's tricking our brains into extracting more information from the image than we were able to before by scaling the size of the image up. Okay, so let me now apply that knowledge to telescopes and then microscopes in turn and we'll understand how they work. They're very similar. There's not really much difference actually between a telescope and a microscope. So telescopes and microscopes have more than one lens. Basically, you need that to get the large magnification power. The first lens of a telescope is called the objective lens, while the second is called the eyepiece lens. And these days, especially for larger telescopes, I tend to use mirrors rather than lenses,

but the principle is roughly the same, so I'll just talk about lenses. So the reason we need two lenses in a telescope or microscope is because each lens serves a distinctly different purpose. The purpose of the objective lens is to gather light from a large area, because basically the more light you gather in, the better the image can be, the more information you've got. So that's why telescopes need to be really big, if they're to be really good. The big of the telescope, the more light it takes in, and therefore the more information you get, so the better the image can be. So the objective lens needs to be nice and big to gather lots of light from a large area, and the objective lens will be a convex lens, so bulging out in the middle,

which means that it converges light into a single point near the focal point of the objective lens, sort of behind it. So if we're imagining our object on the left, light comes in, passes through the objective lens, and an image is formed to the right-hand side of the objective lens. That, though, doesn't help us very much, because the image that is, it forms, well, depending on exactly where, depending on various factors, it might be diminished or it might be magnified, but it's not going to be magnified very much, even in the best case. If the object is distant, then generally it'll be a diminished image, in fact, although if the object is close and you put it inside the focal length, then you can get an enlarged dimension.

That's how magnifying glasses work. But anyway, basically, that first image that you form isn't especially helpful, because it's not, it's either not enlarged at all or not enlarged very much. what we need is a second lens which takes the first image that we formed by the way, that first image, it was formed by the convergence of light, so it's a real image.

There's real light actually there, and this is important. So this first real image that we formed, we then put, we use that as the source of light for the second lens, and this is what the eyepiece lens is for. The eyepiece lens takes the first image

that was formed by the objective lens and magnifies that, or in other words, uses that to produce, an enlarged virtual image of the first image, which in turn was created by the objective lens. So let me try and put that another way. The basic idea behind microscopes and telescopes is that if you put an object really close to a convex lens that is inside the focal length, you get an enlarged virtual image.

That's just how the light rays work. You do the ray tracing diagrams. If you put the object really close to the lens, you get an enlarged virtual. virtual image. And that's how, as I said before, that's how a magnifying glass works. You have to put the object close to the lens in order to see anything. And when you do, you get an enlarged virtual image. The trouble with that, though, is it's often very difficult to put a real object really close to the lens, especially if the lens is very large. And if you're looking at a planet that's light years away, you can't put that right in front of the lens. Or, indeed, if you're looking at something that's very small, it might be hard to put that right in front of the lens as well. Or, yeah, there's various other difficulties that prevent that. And so, we use a trick. Instead of putting the real object right in front of the convex lens, we form an image of the real object that's at that same place, that's, you know, at the place where we wanted to put the real object, that is right in front of the convex lens, right in front of the eyepiece lens, we form an image there, a real image, and how do we form that image? Well, we form it using the objective lens. That's how the image,

that's how we get the image to be formed exactly where we want it. So it's important that the objective lens and the eyepiece lens are placed it exactly the right distance apart. And the distance that you, that they need to be placed apart, of course, depends on exactly where the object is relative to the objective lens. And so that's why you need to focus a microscope in particular, or a telescope. You're changing the distance between the objective and eyepiece lenses so as to adjust for the fact that the object that you're looking at is at, you know, various different distances away. And so therefore the image is going to be formed at a slightly different place, and therefore your eyepiece lens needs to move accordingly. Because the I piece lens has always got to

be right near the real image that you formed using the objective lens. But of course, if the objective lens is forming the image at a different place, then you've got to move the eyepiece lens to compensate. So that's why focusing telescopes and microscopes is important. Now, the type of telescope slash microscope that I've described is very simple. It only uses two lenses. I haven't described about versions that use mirrors. Real microscopes can often, and telescopes can often use many more mirrors because they're reflecting the light more times for various reasons and they're compensating optics to deal with aberration and all sorts of other problems. We're not going to get into that, but the simple one that I've described is, you know,

pretty much exactly how the original telescopes used, say, by Galileo, work. And we're it was pretty much just those two lenses, the objective and the eyepiece, pretty much constructed just as I described it. And we've just taken, with modern telescopes, we've taken that core concept and built on it in terms of complexity, but it's still that fundamental insight that if you put an object right in front of a convex lens, you get an enlarged virtual image, and that you can use a second objective lens to form a real image in front of that first, in front of the eyepiece lens, in order to sort of cheat and view enlarged images of objects, even when you can't place the actual object right in front of the eyepiece lens. itself. So hopefully that was moderately clear. I'll post some diagrams up onto the Facebook so that you

can see this because it helps a lot to have a diagram. Just a couple of other points that I want to make. One important difference between a microscope and a telescope is that usually we use telescopes to observe fairly large, bright objects in the sky like stars and planets. Microscopes we use to observe very small objects and that's problematic because the small objects often don't emit any light of their own, or if they do, it's not very much light because they're so small. So that's why for microscopes, generally illuminate the substance that you're viewing. You have to reflect light off it, or reflect light through it, which is often why we use slides for microscopes. Microscopes slides, you cut a very thin strip of the material and project light or pass light through it, and that's just

so you can see the thing. Otherwise, there wouldn't be enough light coming from it from you to be able to see it. Another very interesting fact about telescopes, well, it works for microscopes too, but it's more relevant for telescopes, is that you can actually build telescopes where you have parts of the telescope, say lenses or machinery or other things, located inside the telescope itself. So, like, you could go and sit inside a telescope without blocking the image. Obviously, we're not talking about sitting in front of the objective lens. We're talking about sitting inside the telescope itself,

behind the objective lens, but in front of the eyepiece lens or mirror. How on earth does that work? Well, the reason it's possible is because, remember, each point, and this is the key point, each part of the objective lens of a telescope captures information or captures light from every point on the object. Think about that light coming from the top of the tree.

That light spreads out through lots of different angles and therefore passes through the top of the lens, the middle of the lens and the bottom of the lens, and ever in between. Each point on the lens captures information from all of the different points on the image. And then when that light is then converged again and brought down to a new, to form a real image on the, you know, inside the telescope, the light from all of those three places from the top

of the lens from the middle and from the bottom is brought back together at a single point that corresponds to the top of the tree on the image. Now this is important because if I block some of those rays, say I block the middle ray, the ray that's passing from the top of the tree through the middle of the lens and then to the top of the tree on the image, if I block that ray and maybe some rays surrounding it, that doesn't actually affect the image because light is still getting through from the sides, from both sides of the lens, and then converging again to reach the top of the tree. So if you stand in the middle of a telescope like that, you don't make a big hole in the image. All you'll do is block some of the light, but every point on the lens is getting light from all parts of the image,

and therefore reflecting light back onto the image at all points on the image. So you haven't blocked any single portion of the image, all you've done is blocked some portion of the whole light, and so the image will get a bit dimmer because there's not as much light coming from the object. you've blocked some of it, but no particular parts of the image will just disappear completely. It's very kind of intuitive. When I first heard about this, it just made no sense at all. Again, diagrams are helpful. But the key point is that every part of the lens receives light or receives information from every part of the object that you're viewing.

And so blocking just part of the lens doesn't block all of the information from any single point on the image. It's not like you can block all of the information from the top of the image just by blocking the top of the... the lens. That doesn't work because the light from the top of the tree is also passing through the bottom of the lens. The only way you could block all of the light about the top of the tree is if you blocks the entire lens, but then of course you wouldn't see anything. So you can't block out just a particular part of the image of an object, unless of course you cover it at the source. If you cover it the top of the tree at the source, that's a completely different matter because then no light at all is coming from the top part of the tree, but you can't block it at the

lens. It doesn't work that way. And that's really handy for building telescopes because it means we can put secondary mirrors and all sorts of other things inside the telescope itself without creating holes in our image. I was going to say a little bit about cameras. We're running over time, so I won't say too much. Just the basic idea of a camera is simply that it uses lenses to form a real image on some photographic plate or photographic film, or nowadays, you know, CCDs charged coupled devices which are used in digital cameras.

And it has focal length, and, you know, you can focus it to focus on objects at different distances and all that sort of thing. But fundamentally, it's just the same principle as a camera, as a telescope or a microscope. It's just using multiple lenses to create a real image, which is then captured on photographic plate or on CCDs. And I'll probably talk about the chemistry and some of the interesting details of how those, how photography and CCDs work in some future episode, if I get to that, because that's interesting in and of itself. But that's fundamentally all that's happening with cameras or with basic cameras. It's just the lights being, you form a real image, which then the image is incident on some type of medium, which can maintain the image, even when the original light source is removed. so that could be chemicals which form a photographic image or CCDs which create electrical charges

which are stored in a computer and preserve thereby preserving the image. That's all the camera is doing fundamentally. Okay, so that's all for this episode. Hope you enjoyed it. If you did, jump onto iTunes and give the podcast a favorable review. I'd really appreciate it. Also, our Facebook page, if you jump onto Facebook and search for the Science of Everything podcast and give our page a like, that would also be appreciated us to help spread the word about the podcast.

If you have any suggestions or questions or feedback of any type, you can send me an email. My address is Fods12 at gmail.com. That's F-O-D-S-1-2 at gmail.com. Thank you for listening, and I'll talk to you next time.