The use of prisms to fold the beam treats the prisms as compact multi-surface mirrors that are convenient to mount because they bring all of those surfaces into a single part that then you'll only have to hold one part up instead of a bunch of separate mirrors in free space. What I'm going to talk about now is a different use, a different thought of way of thinking about prisms. Where we're primarily going to be thinking about not reflected but refracted or transmitted beams through the prisms. There are books written about this but the main way you learn these sort of things is is looking at optical system. So, whenever you see a prism, go see what someone's doing with it because it's often a clever little trick that you can pick up as a designer. I learned a lot of these things working in industry, where I would use them in building brass board, the first prototype of an instrument that had to get off of an optical table. An optimal table, you may have lots and lots of very fine micrometer knobs to steer the light around and control and align the system. But as you begin to make the optical systems small, moving it towards a product let's say, you lose the dollars to spend or you lose the space that those mounts take up but you may still have very difficult alignment problems. I'm going to show you three examples of how prisms can help you do that. My favorite example is important enough it's got a name, it's called a Risley prism originally. Let's imagine we make a prism but we keep the apex angle very small. It actually might look like an optical window with a fraction of a degree tilt between one surface and the other. We know now that the deviation angle of the light that refracts out that prism will be like the apex angle times about a half, given typical refractive indices. So, this is also very small. Imagine now that you inserted this into an optical beam, it would deviate by this angle, small angle, but now you rotate the prism around the optical axis. Well, you can see that the deviated beam is going to spin in a cone with a fixed apex angle given by this. Doesn't seem very exciting, why do you care? Well, the point is is that as I rotate this thin-wedged prism by 180 degrees, that's a lot of rotation, my beam coming out also rotates by 180 degrees but it's a small amount of total angular deviation because this cone angle is also small. So, with my thumb and I have done this, you can rotate a very close to parallel plate here with a very small angle alpha and you can do micro radiance of angular adjustment on the beam coming out. Now, with a single prism, the beam is going to spin in a cone, but if I put two prisms here, I can actually address any angle within a circle given by twice this total angle. So, I used these in systems where I had to make a system small but a very tight pointing tolerance on the beam going farther down an optical system. So, I would drop these Risley prisms in and we had just a little thumb mounts and you could sit there with your thumbs and rotate the Risley prisms and then finally, lock them down and adjust pointing angle of the beam coming out, by basically making this very small angle scanner with your fingers, which was amazing. We can do the same trick but now instead of adjusting the angle of the beam, let's adjust the position of the beam. We take one of these same prisms and instead of rotating it, let's slide it transversely along the optical axis and you see that the beam deviates in position, the angle doesn't change. Again, if this wedge angle is sufficiently small, I could cause a micron or two of total physical displacement here, transverse displacement and I can make the distance when I slide this sliding prism a centimeter. So, I can push this back and forth with my finger by centimeters and I can adjust this position here but microns. That again can be a trick to get very fine mechanical control in some space where you can't afford a micrometer to maybe move this camera or whatever it is by microns. Let's do it again. What if you have a system where you need to adjust the focus? So, maybe the lenses are big or for some reason, you just can't do a traditional motion of an optical element, maybe it's going onto a camera or something. Again, maybe it's big or you just don't have the room or the mechanics to move the camera back and forth, so you want to lock the lenses down, you want to lock the camera down but you can only get the focus due to other tolerances to within some range that's not quite good enough. Well we could take a pair of these prisms, put them back to back. If we really are concerned about reflections, we could put an oil film maker perhaps. Whether that's reasonable for your application depends on the application itself. Now, we could slide this prism instead of longitudinally, we can slide it transversely. And you can see here that the light is going to see just a plain parallel plate but the with variable thickness. Again, that variable thickness can be changed with a great big optical lever based on simply the prism angle. So, there are tons of ideas and tricks like this, I've shown you three. But once you see the basic idea, you realize that these prisms can give you this optical lever, I like to think of it this way to have a large mechanical change. Introduce a small optical change on your system.
