The previous examples we showed of using prisms primarily treated them as compact solid mirrors. That's a useful and very common technique to use for prisms. Now, we're going to talk about primarily refracting through prism surfaces rather than reflecting off of them. The functions you can implement here are, of course, quite different than those that you get via refraction through the surface of the lens because that lens surface is curved. There's a lot of these. There's books written about the use of prisms. So, I'm just going to give you two extremes that consist of either very strong change of right angles, so you pay significant deflection, or the opposite, very, very weak, and those give you very different functions that will give you a flavor of the kind of things you can do. The example I have here for controlling the light is in this case controlling the shape of a beam of probably monochromatic light. Hopefully, it's obvious to you now why if you're doing strong refraction through a prism surface, monochromatic or laser light would be probably the thing to use. You'll find these often in front of laser diodes. Laser diodes have a typically elliptical beam that, of course, we'd like to circularize because most of our applications for users would like a round beam. So we need something that's telescope-like, but just in one dimension. We could implement that literally with cylindrical lenses and a standard telescope, but this is actually more commonly used because it's more compact. So, what we're going to do here is we're going to bring in the beam, which I've shown just two rays of, but we imagine that we have a bunch of parallel rays here, and simply refract at large angle out of this present face. I've shown the easy case to compute, which was where were coming in normal incidence to one of the person faces. Just a little bit of geometry here will show you that you get an effective magnification of a change of scale of this collimated beam that depends only on the fact that the two protected areas here have to be equal and that gives you something that relates to the cosine of the refraction angles. You can then use Snell's law to discover a function only of one of the incidence angles. Pretty darn convenient. Good is that you can make this with just a single prism. That's a pretty cheap element. If you want to not deviate the beam, you can use two prisms in a symmetric arrangement. Now you get two factors of that magnification at inexpensive. If you got nice flat surfaces, which are a relatively easy thing to fabricate, tends to be very low aberration cylinders. You got to make sure that you've made a truest cylindrical surface. It is a little bit tricky as you go to make very large magnification here or small magnification in the sense of one over a large number. You're going to be coming off at increasingly large angles. That's going to start to get interesting in terms of tolerances and of course, polarization dependence for no losses so that surface are going to be quite different from the two polarizations. Because the tolerances are going to go up, you approach, of course, zero magnification or infinite compression of the beam when you get right close to total internal reflection. That means if you have angular deviation or bandwidth in this beam, if it's got some content, then it's going to see a very different magnification depending on the angles that are coming in here. So, this really is most appropriate for very collimated beams, things like laser beams. However, it gives you an example of something that you could do with cylindrical lenses that would be something traditional, what we've learned in this course, but here's a function that you can implement instead with these prisms and strong refraction through the surfaces.