2. Chapter 34: Mirrors 1 We will consider three varieties of mirrors Spherical Concave Mirror Plane Mirror Spherical Convex Mirror Photos from Fishbane, et al.

3. Chapter 34: Mirrors 2 Four Incident Rays Four Reflected Rays Photo from Fishbane, et al. The Spherical Concave Mirror Reflected rays focus at one point.

4. Chapter 34: Mirrors 3 Find the center of this spherical mirror. The white lines are all normal to the surface of the mirror. The Spherical Concave Mirror Photo from Fishbane, et al. Center of curvature

5. Chapter 34: Mirrors 4 radius of curvature, r Focal Point: The place where the reflections of parallel rays converge. focal length, f “optic axis” The Spherical Concave Mirror True for concave & convex mirrors. Center of curvature

6. Chapter 34: Mirrors 5 Optical Ray Diagram: a line drawing depicting a small number of key light rays. For a mirror, an optical ray diagram should include: 1.Parallel Ray. A ray parallel to the optic axis which passes through an object. 2.Focal Ray. A ray that passes through both the focal point and an object. 3.Chief Ray. A ray that passes through both the center of curvature and an object.

7. Chapter 34: Mirrors 6 “optic axis” object 1. Parallel ray. All rays parallel to the optic axis pass through the focal point. f The Spherical Concave Mirror

8. Chapter 34: Mirrors 7 “optic axis” object 2. Focal ray. A ray that passes through the focal point is also parallel to the optic axis after reflection. f The Spherical Concave Mirror

9. Chapter 34: Mirrors 8 “optic axis” object f 3. Chief ray. A ray that passes through the center of curvature hits the mirror normal to its surface and reflects directly back center of curvature The Spherical Concave Mirror

10. Chapter 34: Mirrors 9 object f The Spherical Concave Mirror Image. The result of converging reflected rays. Draw all three key rays. The reflections converge at the image. image (notice it’s small) inverted image: an image which is seen below the optic axis.

11. Chapter 34: Mirrors 10 The Spherical Concave Mirror f Example 1: Locate the image in this mirror. In this example the reflected rays don’t converge. Does that mean there is no image? reflected rays

12. Chapter 34: Mirrors 11 The Spherical Concave Mirror In this case, the image is behind the mirror. Extend the reflected rays behind the mirror. They converge on the image. f Notice the image is (1) above the optic axis, (2) behind the mirror, and (3) larger than the object.

13. Chapter 34: Mirrors 12 Virtual Image: Behind the mirror. Light doesn’t pass through it. Real Image: In front of the mirror. Light passes through it. Inverted Image: Below the optic axis. Upside down. m<0 Upright Image: Above the optic axis. Right-side-up. m>0

14. Chapter 34: Mirrors 13 f hihi hoho Where is the image? f soso sisi The mirror equation: Caution: distances behind the mirror are negative.

15. Chapter 34: Mirrors 14 The Convex Mirror The Spherical Convex Mirror

16. Chapter 34: Mirrors 15 The Convex Mirror Focal Point =r/2 Extrapolate the reflected rays back to find the focal point. The Spherical Convex Mirror

17. Chapter 34: Mirrors 16 The Convex Mirror  f=r/2 r chief ray parallel ray The Spherical Convex Mirror focal ray

18. Chapter 34: Mirrors 17 Example 2: You are standing s o =3.0 m in front of a convex mirror. The height of your image is half your actual height and is upright (m=+0.5). What is the radius of curvature, r, of the mirror? r=2f  f=r/2 s o =3.0 m The Spherical Convex Mirror sisi

19. Chapter 34: Mirrors 18 radius of curvature: r=2f How can we find f? First, we need d i : Example 2: You are standing s o =3.0 m in front of a convex mirror. The height of your image is half your actual height and is upright (m=+0.5). What is the radius of curvature, r, of the mirror? The Spherical Convex Mirror

20. Chapter 34: Mirrors 19 r=2f=-6m  f=r/2 Example 2: You are standing s o =3.0 m in front of a convex mirror. The height of your image is half your actual height and is upright (m=+0.5). What is the radius of curvature, r, of the mirror? The Spherical Convex Mirror A negative radius of curvature indicates convex.