2. Mirrors

3. Law of Reflection The angle of incidence with respect to the normal is equal to the angle of reflection. www.sol.sci.uop.edu

4. Specular & Diffuse Reflection Light incident upon an object with a smooth surface will create specular reflection. Light incident upon an object with a rough surface will create diffuse reflection.

5. Images Produced by Plane Mirrors  dodo didi hoho hihi  P P’ An object placed at point P in front of the mirror will form an image at point P’ behind the mirror. d o = distance from object to mirror. d i = distance from image to mirror. h o = height of object. h i = height of image. For a plane mirror: d o = d i h o = h i

6. Images Produced by Plane Mirrors Images in plane mirrors are always upright. Images in plane mirrors are the same size as the object creating the image. Images in plane mirrors are the same distance behind the mirror as is the object making the image is in front of the mirror. Images in plane mirrors are considered virtual images.

7. Spherical Mirrors Concave Mirror: A spherical mirror where the inside surface is polished. Convex Mirror: A spherical mirror where the outside surface is polished.

8. Spherical Mirrors Principle Axis C F R C = Center of Curvature C = Radius (R) F = Focal Length F = ½ R or -½ R Light ray will pass through the focal point if it lies close enough to the principle axis. Normal  

9. Concave Mirror Ray Diagrams Principle Axis C F 1 2 3 Object Real Image Object placed between the focal point and the center of curvature C produces a real and inverted larger image. Mirror Surface

10. Concave Mirror Ray Diagrams Principle Axis C F 1 2 3 Real Image Object Object placed beyond the center of curvature C produces a real and inverted smaller image. Mirror Surface

11. Concave Mirror Ray Diagrams Principle Axis C F 1 2 3 Object Virtual Image Object placed between the focal point and the surface of the mirror produces a virtual image. Mirror Surface

12. Spherical Aberration Principle Axis C F Light rays will only pass through the focal point if they lie close enough to the principle axis. What happens if the rays are not close to the principle axis?

13. Convex Mirror Ray Diagram C F 1 2 3 Object Virtual Image Object placed in front of a convex mirror always produces a virtual image that is smaller and upright. Mirror Surface

14. Images for Concave and Convex Mirrors Images for Concave Mirrors Images for Convex Mirrors

15. The Mirror and Magnification Equations 1 1 1 f d o d i Where: d o and d i are the distances of the object and image from the mirror, respectively. f = focal length = ½ R. Image height, h i d i Object height, h o d o = + m = = - Use this mnemonic: If I d o I d i

16. Examples: Mirrors 1. The radius of curvature of a concave mirror is 40 cm. The focal length of the mirror is: a. 5 cm b. 10 cm c. 20 cm d. 40 cm e. 80 cm 2. An object is placed at a distance of 20 cm from a convex mirror. The focus of the mirror is 100 cm. The image is located at: a. 25 cm b. -25 cm c. 16.7 cm d. -16.7 cm e. 12.0 cm

17. Sign Conventions for Spherical Mirrors Focal Length f is positive for a concave mirror (½R). f is negative for a convex mirror (-½R). Object Distance d o is + if the object is in front of the mirror (real object). d o is - if the object is behind the mirror (virtual object). Image Distance d i is + if the image is in front of the mirror (real image). d i is – if the image is behind the mirror (virtual image). Magnification m is + for an image that is upright with respect to the object. m is – for an image that is inverted with respect to the object.

18. Key Ideas Light reflecting off a smooth surface obeys the law of reflection. The angle of reflection relative to the normal equals the angle of incidence. A virtual image is one where the rays of light do not come from the image but appear to do so, and they appear behind the mirror. A real image from which all of the rays of light actually come from, and they are in front of the mirror. Concave and convex mirrors are spherical mirrors where the mirror surface is on the inside for the former and the outside for the latter.

19. Key Ideas The center of curvature and radius of curvature R are the same for concave and convex mirrors. The focal point for concave and convex mirrors is +½ R and -½ R, respectively. The magnification of the image is determined by the relationship between the height of the image divided by the height of the object. The magnification is also equal to the negative of the quotient between the distance of the image from the mirror and the distance of the object from the mirror.