33. Geometric Optics

Thin Lens And Lens Maker Equations

# Lens Maker Equation

Patrick Ford

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Hey, guys, in this video, we're going to talk about something called the lens maker equation, which is the equation that will tell us the focal length of a thin lens based on the shape off the two pieces of glass that make it up. All right, let's get to it. The focal length of the Thin Lin's depends upon three things. It depends on the radius of curvature of the near glass. What I mean by near is if I have an object over here, this face is the near glass, so it depends upon that radius of curvature. It depends upon the radius of curvature of the far glass, the glass on the opposite side. So that radius of curvature. And it depends on the index of refraction off the glass itself, whatever that index is. Okay, the lens maker equation is going to tell us what the focal length off this thin lens is going to be. And it is in minus one times one over R one. Where are one? Is the radius of the near glass minus one over R two. Where are two is the radius of the far glass. Now, remember that this equation is one over the focal length. It's not the focal length. So don't forget to reciprocate your answer. There is an important sign convention that we need to know in order to apply this equation. If the center of curvature is in front of the lens like this guy right here the near sorry. The far glass has a center of curvature on the front side of the lens. Then the radius is negative. Okay, If the center of curvature is behind the Linz like this guy, the near glass, then the radius is positive. Okay, so this radius is positive. This radius is negative. All right, let's do a quick example to illustrate this point. The following lenses for my glass with a refractive index of 1. What is the focal length of the following lens within objects placed in front of the convex side? What if in object, is placed in front of the con cave side. So first I'll apply the lens maker equation to find it. If in object is placed here in front of the convex side, so it's gonna be in minus one one over R one minus one over R two. The index of refraction of the glasses 15 to minus one. What is the radius of the near glass? That's 10 centimeters. Is it positive or negative? It's positive because the center of curvature is behind the lens. So this is one over positive. 10 minus one over positive seven. Right. That radius of curvature is also behind the lens. Plugging this into a calculator. We're gonna get negative 0.22 But don't forget, we have to reciprocate our answer. So F one is negative. 45 centimeters. That's what the focal length is if you place an object in front of the convex side, all right. Now, for the second part, I'm gonna minimize myself so that I don't get in the way. And what would happen if we were to place an object here? What would the focal length B. Well, we're gonna use the same lens maker Equation one over F two in minus one one, over R one minus one over R two. Okay, the end is the same. 15 to minus one. What about our one now? What's the near glass? The near glasses. The seven centimeters is the center of curvature in front of the lens or behind the lens. Now it's in front of the lens, and if it's in front of the Linz, its negative. So this is negative seven minus one over negative for that 10 centimeter piece of glass. The center of curvature is also in front, off the lens, plugging this into a calculator. We get negative. 0022 We'll look at that. We got the same answer regardless of which side of the lens we put our object on. And this is actually a fundamental result of the lens maker equation that no matter what side of the lens you put the object on, you're gonna have the same focal length. Okay, When we were drawing Ray diagrams for lenses, we assumed that the focus was at the same distance on either side of the lens. OK, this is a fundamental result off the lens maker equation. All right, guys, that wraps up this talk on the lens maker equation. Thanks for watching

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