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Physics33. Geometric OpticsRay Diagrams For Lenses

So when you go get your prescription at the eye doctor. It will say on your prescription for your contacts, or your glasses. It's basically the same idea. You're going to get a prescription that says plus 2.5 or plus 3.0 or plus 3.5 or negative. What does that number mean? What is the lens power? Power, or more specifically refractive power, is 1 over f. Okay, it's just 1 over the focal length of the lens. So this is measured in something called diopters. Diopters is, of course, just 1 over meters. All right, so if you have a plus 1 lens. If your power equals plus 1, then that means the focal length is 1 over that. It's 1 meter. But if you have a power of 2, focal length is one over that which is a half a meter. Okay, so my glasses here. The left eye is a plus 3 and the right eye is a plus 2.5. And that means that the focal length here is about a third of a meter on this side. Okay, 30 centimeters. If you have negative numbers for your prescription, then you have diverging lenses. So if your power equals negative 2, then your focal length is negative 0.5 meters. Okay, and so when you look at your prescription, you can tell right away. Do I have eyes that need a big converging lens? A lot of power. Or something that's a little more relaxed, a little more loose. Okay, so let's think about power in terms of your eyeball. Okay, what we said was the power is going to be 1 over the focal length. And now we're worried about the focal length of your eye. And we talked about the focal length of your eye last time. It has to be basically the size of your eye. Which is about 25 millimeters. Okay? So this is 1 over 25 times 10 to the minus 3 meters. Which is 40 diopters. Okay, that cornea is very curved. It's a very powerful lens. These are sort of typical numbers for your glasses, right? So when I think about the glasses that I put on to read and I'm gonna add a power of 2.5, That's going on top of 40 diopters already. So it's a small fractional change And the way you can tell this is if I just look at the glasses, edge-on, they're not very curved. Okay, they're a little bit curved, but not very. And if I look at my eyeball, edge-on, it is really very curved, right? It looks like a marble. The more it's curved, the shorter the focal length, the bigger the lens power.