1. Geometric Optics This chapter covers how images form when light bounces off mirrors and refracts through lenses. There are two different kinds of images: –A real image is formed when light rays pass through and diverge from the image point. –A virtual image is formed when the light rays do not pass through the image point but appear to diverge from that point.

2. Geometric Optics We will define: –p as the object distance –q as the image distance –M as the magnification –h as the object height –h’ as the image height –f as the focal length

3. Flat Mirror The image is as far behind the mirror as the object is in front of the mirror (p = q) The image is unmagnified (h = h’), virtual, and upright The image has front-back reversal

4. Flat Mirrors Both the object (O) and the images (I 1 and I 2 ) create images in this two-mirror configuration.

5. Magnification There is a relationship between the object height and the image height which we call the Lateral Magnification, or just the Magnification.

6. Spherical Mirrors – Concave

7. Spherical Mirror - Concave Here we see light rays from a very distant object reflect on a concave mirror. They meet at the focal point (F). The distance from the mirror to F is defined as the focal length (f). For spherical mirrors,

8. Spherical Mirrors – Convex

9. Spherical Mirror Equations Mirror Equation And since,

11. These are examples of ray diagrams for spherical mirrors. Compare the three rays in each diagram to the rules on your handout. –Ray 1 is drawn from the top of the object parallel to the principal axis and is reflected through the focal point F –Ray 2 is drawn from the top of the object through the focal point and is reflected parallel to the principal axis –Ray 3 is drawn from the top of the object through the center of curvature C and is reflected back on itself

12. Boundary Refraction - curved surface

13. Boundary Refraction – flat surface

16. Thin Lenses These are examples of thin lenses. We will refer to the “biconvex” as a converging lens and the “biconcave” as a diverging lens in practice

17. If the radius is different on each side of the lens, a special equation is used. This is called the Lens Maker Equation. The ‘n’ in the equation represents the index of refraction of the lens glass.

18. Lens Equations (for any type of thin lens) Thin Lens Equation Magnification

20. Ray Diagrams for Lenses

22. Combinations of Thin Lenses If two lenses are used to form an image, the system can be treated in the following manner: –The position of the image from the first lens can be calculated while ignoring the presence of the second lens. –Then that image can be used as the object for the second lens. –The image from the second lens is the final image position for the system. It is very important to remember the Sign Conventions for Thin Lenses when solving this type of problem.

23. Example 26.8