1. Thin Lenses If the thickness of the lens is small compared to the object and image distances we can neglect the thickness (t) of the lens. All thin lenses have two refracting surfaces, therefore we can combine the two expressions for each of the refracting surfaces. Refracting Surface 1 Refracting Surface 2 Combining the three equations above into a single expression for a thin lens: Note that dues to the sign convention we are using we must introduce a negative sign with f in this expression. Lensmaker’s Equation To avoid confusion we will remove the subscripts and recognize that this expression is for a single lens.

2. Thin Lenses: Thin lenses are constructed from two surfaces, which can be either concave, convex or flat. From geometry we can obtain an expression relating the object distance, image distance and focal point. We can also obtain an expression for magnification. These are the same relationships that were obtained for mirrors! Thin Lens Equation (valid only for thin lenses) Magnification The sign convention is different for lenses! Sign Convention - Lenses Object: Positive location – in front of lens (Real) Negative location – behind lens (Virtual) Image: Positive location – behind lens (Real) Negative location – in front of lens (Virtual) Positive height – upright (Same) Negative height – inverted Positive focal length – concave Negative focal length – convex

3. f2f2 f1f1 f1f1 f2f2 i i o o Lens Ray Diagrams 1) The incident ray is drawn parallel to the principle axis. The refracted ray passes through f 2. Convex: 2) The incident ray is drawn so it passes through f 1. The refracted ray is parallel to the principle axis. 3) The incident ray is drawn through the center of the lens. The ray is not refracted an continues along a straight line path. Concave: 1) The incident ray is drawn parallel to the principle axis. The refracted ray passes through f 1. 2) The incident ray is drawn so it passes through f 2. The refracted ray is parallel to the principle axis. 3) The incident ray is drawn through the center of the lens. The ray is not refracted an continues along a straight line path.

4. Biconvex   From the diagram above we can determine the magnification for a thin lens. This can also be accomplished using the diagram for the Biconvex lens. This is identical to what was done for mirrors. The negative sign is from the sign conventions we are using. Biconcave 

5. Example: A system of two lenses is setup, where f 1 = f 2 = 15 cm, and the two lenses are separated by 60 cm. The object is located 25 cm in front of the first lens. The first lens in convex (biconvex) and the second is concave (biconcave). a)Describe the image formed by the first lens. b)Describe the image formed by the second lens. a) Real Image s 1 = 25 cm f 1 = -15 cm