Clutch Prep is now a part of Pearson
Ch 34: Geometric OpticsWorksheetSee all chapters

# Thin Lens And Lens Maker Equations

See all sections
Sections
Ray Nature Of Light
Reflection Of Light
Refraction Of Light
Total Internal Reflection
Ray Diagrams For Mirrors
Mirror Equation
Refraction At Spherical Surfaces
Ray Diagrams For Lenses
Thin Lens And Lens Maker Equations

Concept #1: Thin Lens Equation

Transcript

Hey guys, in this video we're going to cover something called the thin lens equation. Just like for mirrors, we used ray diagrams to find qualitative information about the images but when it came down to actual numbers, we relied on the mirror equation. The thin lens equation is going to replace ray diagrams for lenses and allow us to find numeric answers to where the image is located, the height of the image, etc. Alright let's get to it. For images produced by lenses really all we're going to consider are thin lenses. What a thin lens is is it's a lens composed of two pieces of glass that are spherical and all that it means to be spherical is that it's part of some imaginary sphere with some radius of curvature. And to be thin, the radius of curvature has to be a lot larger than the thickness of the lens. For instance, maybe the radius of curvature is 10 centimeters for a particular piece of glass, but when you put 2 of them together the lens is actually only a couple millimeters thick, so it's very very thin. Thin lenses come in five basic types. We have our biconvex. We have our convex concave, convex from one side, concave from the other. We have our plano-convex. It's flat or plane from one side and it's convex from the other.We have our biconcave lenses which are concave from both sides and lastly we have our plano-concave lenses. Concave from one side, plane from the other. Now the rule of thumb for deciding which of the lenses are converging and which of the lenses are diverging are the lenses that are the thickest in the middle are converging lenses, and lenses that are the thinnest in the middle are diverging lenses. So you can look at this lens right here, it's thick in the middle, thin at the edges. That's a converging lens. This lens, thin in the middle, thick in the middle sorry, thin at the edges that's a converging lens. For the biconcave, thin in the middle, thick at the edges. That is a diverging lens. For the plano-concave, thin in the middle, thick at the edges. That is a diverging lens the only one of for grabs is the convex concave lens. That one could be either converging or diverging. It just depends on the radius or the radii of curvature for the two pieces of glass that make it up. For a lens with some focal length F, the image location is given by the thin lens equation and if you notice, this is the exact equation as the mirror equation because this is all based on geometry and it actually doesn't matter whether you have a spherical mirror or a spherical lens. That was why our rules for drawing rate diagrams were almost identical for lenses and for mirrors the equation too is identical. Now, the sign conventions that are important are if the lens is converging, remember the rule of thumb for a converging lens is it's thick in the middle, thick at the edges, the focal length is positive. If the lens is diverging, the focal length is negative. And just like always, if the image distance is positive it is a real image and it is an inverted image. You guys should have this memorized down packed by now. There have been so many videos that cover this exact concept and if the image distance is negative, it's virtual and it's upright. We also have a magnification equation for thin lenses that is identical to that of mirrors. So luckily you don't have to memorize a new set of equations. The thin lens equation is identical to the mirror equation and magnification for images produced by thin lenses is identical to the magnification for images produced by mirrors. Let's do a quick example. A biconcave lens has a focal length of 2 centimeters, if an object is placed 7 centimeters in front of it, where is the image located? Is this image real or virtual? Is it upright or inverted? Now this biconcave lens looks like this. Actually, I'm going to minimize myself I'm going to draw off the side where we don't really need it except to illustrate this point. Biconvex, sorry, biconcave means that the image is concave on sorry the lens is concave on both sides. So this is thin in the middle and thick at the edges, so this is a diverging lens. If it has a focal length of 2 centimeters, since it's diverging, that focal length has to be negative so the focal length is going to be -2 centimeters. Besides that now we can use the thin lens equation. The object is placed 7 centimeters in front of the lens so the object distance is 7 centimeters. So one over S I plus 1 over S O equals one over F. We're going to isolate the 1 over S I which is 1 over F minus 1 over S O. This is 1 over -2 right that's the sign for sorry yeah that's the sign for the focal length minus 1 over 7. This whole thing is going to be -0.64 but we still have to reciprocate our answer. This is only the solution for 1 over S I, it's not the solution for S I. So if I reciprocate the answer, we get -1.6 centimeters. So is this image real or is it virtual? Well the image distance is negative so you should know automatically that this is a virtual image. And since it's virtual automatically, it's upright. Alright guys that wraps up our discussion on the thin lens equation. Thanks for watching.

Practice: A biconvex lens has a focal length of 12 cm. If an object is placed 5 cm from the lens, where is the image formed? Is it real or virtual? Is it upright or inverted? What’s the height of the image if the object is 2 cm tall?

Concept #2: Lens Maker Equation

Transcript