Iin the toolbox of optical elements that you have to build optical systems we want to discuss first prisms. Prisms are, as we've already seen, a way to disperse the light and sometimes that's what you want to do with them. And so I mentioned that here as one of the things you can do with prisms. So we won't talk about that one, because we already have. But they actually have a host of other uses. One of them that I also list here is to divide the light. The canonical example of that would be, let's say, a beam splitter. That's a prism that you've put on one surface, a dielectric thin film coating that might separate the two polarizations, one goes straight through, one reflects. Or separate color, red goes through and blue reflects, or something like that. Those are relatively straightforward to understand. You can look up the specs. So the thing I'm going to talk about today is the use of prisms to fold and I'll call it control the optical path. And this is a very handy when you start making systems that are small. You might not be using those so much on the optical table but when you make portable systems, particularly folding will become very important. So here's some examples of how you can use prisms, primarily you notice as reflective devices. And we're coming in normal incidence through our transmission or refractive paths. And then using typically total internal reflection to bounce the light off of some hypotenuse or subsurface of the prism. Though you could put dielectric or metal coating on that surface if you wanted to. And in this sense these prisms are essentially mirrors but they're very compact, very mechanically robust mirrors. And particularly like this geometry here where I want two mirrors very close together. It would be difficult to have separate mirrors held up by an external metal scaffold with this precise 90 degrees between them. But it's relatively easy to grind a piece of glass and polish it. So that's the core idea here, is that these prisms are nice compact mirrors, particularly for multiple reflections. And the reasons you might want multiple reflections, you can see through this technique we call bouncing pencils. You will have noticed that whenever you look in a bathroom mirror, that left and right seems to have changed from your perspective. And when you bounce off of a mirror, you get a parity switch, you get a change of coordinates. And the easiest way to understand that is to imagine a little element here one arrow with an arrow head and one with a circle and to imagine how they bounce through a system. I actually kind of like to use my thumb and forefinger and imagine how that must bounce as it goes through a system. And you can see as you do this that for example, notice this right angle prism here, with a single reflection. And the light bends 90 degrees. Very similar function of this penta prism, penta because it's got 5 sides. Light comes in and is bent out 90 degrees. But notice that the arrow head, the pointy one, is pointing in a different direction. And the reason here is we're undergone two reflections, and here only one. And that's why there was a penta prism in that single lens reflex camera cutaway we looked at way back in course one. Is this image when presented to the viewfinder, to the person looking through the camera, was correct, was upright. Where if you'd used just a single mirror, the image will have been upside down. So this bouncing pencils technique or your thumb and forefinger are a nice way to trace through and understand whats the orientation of the image. There's a host of prism tricks people have learned to do these kind of foldings. I'll mention one that's useful and typical but it's one of a whole set that if you start looking at optical systems, look at the prisms and figure out what they're doing. A dove prism is basically a right angle prism, we've cut of the top because we're not using it. And here we refract in not at 90 degrees, reflect probably due to total internal reflection off of the hypotenuse of the right angle, and then go back out in a symmetric way. If you do your bouncing pencils, you see that the pointy arrow head here is turned upside down, it's rotated by 180 degrees. But the coordinate through which it's rotated depends on the orientation of the prism. So if I imagine rotating this prism around it's axis it turns out that the image here rotates by twice the angle. So this is a clever little image rotator, you can spin an image this way. Now obviously there are aberration issues. Or not obviously, that's what we're going to talk about more in this whole class. But we are going through a tilted a piece of glass here, and that has some issues. So this generally works only for relatively low numerical apertures for paraxial images. And you might imagine there's some color issues with that refraction right there or could be. But it's an example of how the folding we're doing right here doesn't have to be static, we can change the orientation of this prism. And the fact that all of these surfaces are tightly bound together, because I made it with single piece of glass, is what makes this work. This would be very difficult to make out of a bunch of independent elements. Here's another example of sort of a clever prism idea or shape that's been constructed. It's similar to the penta prism, we want to bend through 90 degrees but we want to change the orientation of our pencils, of our image that comes out. And you notice in the case of the penta prism we put the two reflections in a plane such that when we bent, we got the pointy headed arrow here pointed in the same direction. The roof prism is a similar idea, but instead of adding these two planes sort of as we've shown here, we're going take this hypotenuse and we're going to make a roof out of it. So that we can bounce off of the hypotenuse twice. And so now if you looked at this prism sideways, if you just saw the projection, it would actually look a lot like a right angled prism. But we see we actually come a little off to the side and we bounce off of this roof, what's replaced the hypotenuse single bounce with two. And again if you follow the pencils through, you see we've changed the parity, we've changed the orientation of the output. And this again allows us to get a fold in the beam path, a 90-degree bend, but to manipulate the orientation of the image. This kind of problem, the need to do this occurs a lot in imaging systems. Because you remember that a single lens, let's the objective of a telescope let's say, has a negative magnification if it creates a real image out of the object. And that orientation may not be what you want if you're going to see it with an eyeball. If it's a camera you can just rotate the camera all is good. But if there's a person there, they may not want to stand on their head. So these kind of prisms will often show up, devices that talk to eyeballs, because you need to get the image correct for that eyeball.