1. J.M. Gabrielse Concave (just a part of a sphere)

2. J.M. Gabrielse Spherical Mirrors (concave & convex)

3. J.M. Gabrielse Concave & Convex (just a part of a sphere) C: the center point of the sphere r: radius of curvature (just the radius of the sphere) F: the focal point of the mirror (halfway between C and the mirror) f: the focal distance, f = r/2 r f C F

4. J.M. Gabrielse Concave Mirrors (caved in) Examples include: Shaving and makeup mirrors Inside of a metal spoon

5. J.M. Gabrielse optical axis Concave Mirrors (caved in) F Light rays that come in parallel to the optical axis reflect through the focal point.

6. J.M. Gabrielse Concave Mirrors Because concave mirrors are curved inward they reflect light rays in special way: reflected light rays travel toward each other, or converge.

7. J.M. Gabrielse principal axis Concave Mirror (when object is between focal point and mirror) F

8. J.M. Gabrielse principal axis Concave Mirror (when object is between focal point and mirror) F The first ray comes in parallel to the principal axis and reflects through the focal point.

9. J.M. Gabrielse principal axis Concave Mirror (when object is between focal point and mirror) F The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis.

10. J.M. Gabrielse principal axis Concave Mirror (when object is between focal point and mirror) F The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. A third ray travels to the vertex and reflects at the same angle.

11. J.M. Gabrielse principal axis Concave Mirror (when object is between focal point and mirror) The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. A third ray travels to the vertex and reflects at the same angle. A virtual image forms where the sight rays converge. F

12. J.M. Gabrielse principal axis Your Turn Concave Mirror (when object is between focal point and mirror) F concave mirror Note: mirrors are thin enough that you just draw a line to represent the mirror Locate the image of the arrow object

13. J.M. Gabrielse principal axis Your Turn-Answer Concave Mirror (when object is between focal point and mirror) F concave mirror Note: mirrors are thin enough that you just draw a line to represent the mirror Locate the image of the arrow object

14. J.M. Gabrielse Characteristics of images in Concave Mirrors (when an object is between the focal point and the mirror) S The image is larger than the object. P The image distance is larger than the object distance. O The image is upright. T The image is virtual ( object's image lies behind the mirror).

15. J.M. Gabrielse Concave Mirror (when object is between the focal point and 2 times the focal point) F 2F principal axis The first ray comes in parallel to the principal axis and reflects through the focal point.

16. J.M. Gabrielse Concave Mirror (when object is between the focal point and 2 times the focal point) F 2F principal axis The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis.

17. J.M. Gabrielse Concave Mirror (when object is between the focal point and 2 times the focal point) F 2F principal axis The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. A ray travels to the vertex. A real image forms where the light rays converge.

18. J.M. Gabrielse principal axis Your Turn Concave Mirror (when object is between the focal point and 2 times the focal point) F object concave mirror Note: mirrors are thin enough that you just draw a line to represent the mirror Locate the image of the arrow 2F

19. J.M. Gabrielse principal axis Your Turn-Answer Concave Mirror (when object is between the focal point and 2 times the focal point) F object concave mirror Note: mirrors are thin enough that you just draw a line to represent the mirror Locate the image of the arrow 2F

20. J.M. Gabrielse

21. Characteristics of Images in Concave Mirrors (when object is between the focal point and 2 times the focal point) S The image is larger than the object. P The image distance is larger than the object distance. O The image is inverted. T The image is real (located in front of mirror)

22. J.M. Gabrielse principal axis Concave Mirror (when object is beyond 2 times the focal point) F

23. J.M. Gabrielse principal axis Concave Mirror (when object is beyond 2 times the focal point) F The first ray comes in parallel to the principal axis and reflects through the focal point.

24. J.M. Gabrielse principal axis Concave Mirror (when object is beyond 2 times the focal point) F The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis.

25. J.M. Gabrielse principal axis Concave Mirror (when object is beyond 2 times the focal point) F The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. A real image forms where the light rays converge.

26. J.M. Gabrielse principal axis Your Turn Concave Mirror (when object is beyond 2 times the focal point) F object concave mirror Note: mirrors are thin enough that you just draw a line to represent the mirror Locate the image of the arrow

27. J.M. Gabrielse principal axis Your Turn-Answer (Concave Mirror) (when object is beyond 2 times the focal point) F object concave mirror Note: mirrors are thin enough that you just draw a line to represent the mirror Locate the image of the arrow

28. J.M. Gabrielse Characteristics of Images in Concave Mirrors (when object is beyond 2 times the focal point) S The image is smaller than the object. P The image distance is smaller than the object distance. O The image is inverted. T The image is real (located in front of mirror).

29. J.M. Gabrielse Interactive Activity See the effects of moving the object closer to the mirror, first between the center of curvature and the focal point, and then between the focal point and the mirror surface (to form a virtual image): http://micro.magnet.fsu.edu/primer/java/mirrors/concave mirrors/index.htmlhttp://micro.magnet.fsu.edu/primer/java/mirrors/concave mirrors/index.html See how moving the object farther away from the center of curvature affects the size of the real image formed by the mirror: http://micro.magnet.fsu.edu/primer/java/mirrors/concave mirrors3d/index.htmlhttp://micro.magnet.fsu.edu/primer/java/mirrors/concave mirrors3d/index.html

30. J.M. Gabrielse Can You Name Some Other Examples of Concave Mirrors? Other examples of concave mirrors include: spotlights, flashlights, overhead projectors, car headlights, and lighthouses.

31. J.M. Gabrielse More Examples The largest telescopes all use concave mirrors to collect light because the mirror concentrates the light so effectively. Satellite dishes that receive television signals are curved dishes that reflect the microwaves coming from satellites.