1. Today 2/10  Multiple Lens Systems 26.9  Curved Mirrors 25.5-6  Lab: Mirrors and Thin Lenses  HW:“2/10 Two Lenses” Due Thursday 2/12  Exam IThursday, Feb 13

2. Reflection (Mirrors) When a ray of light reflects from a mirror the angle of incidence equals the angle of reflection. ii rr

3. An object is placed off to the side of a plane mirror. Where is the image? Ray Tracing This is a “virtual” image. The image is the same size as the object, same orientation, and the same distance behind the mirror.

4. Flat (Plane) Mirrors How much mirror do I need to see my entire image? Find the image with a ray diagram. Only the top half!

5. Finding images for a concave (converging) mirror. Focal point = R/2 Center of curvature R R stands for the “radius of curvature” of the mirror

6. Finding images for a concave (converging) mirror. Any ray parallel to the axis will be reflected through the focal point. Cf Bend the rays at the dotted line to be consistent with the mirror equations. (We did the same thing when we when we bent the ray at the middle of the lens.)

7. Finding images for a concave (converging) mirror. Any ray through the focal point will be reflected parallel to the axis. Light is “reversible.” Cf Any ray passing through the focal point will be reflected parallel by the mirror.

8. Finding images for a concave (converging) mirror. Where would an image be for a far away object? Cf Object Image Image is smaller than the object, inverted, and near f. This is a “real” image. If the object were at infinity, the image would be at the focal point but would have zero size. Note this is also true for converging lenses.

9. Finding images for a concave (converging) mirror. Bring the object closer. Cf Object Image is still smaller than the object (larger than before), inverted, and farther from f. Still a “real” image. Image

10. Finding images for a concave (converging) mirror. Bring the object closer yet. Cf Object Image is now larger than the object, inverted, and farther yet from f. Still a “real” image. Caution: You must bend the ray at the dotted line to match the math. Note the difference in image position when the rays bend at the mirror.

11. Finding images for a concave (converging) mirror. What if we place the object at the focus? Cf Object Image is now at infinity, infinitely large, and really doesn’t make much sense. This is the inverse of the situation when the object was at infinity.

12. Finding images for a concave (converging) mirror. What if we place the object inside the focus? Cf Object But these rays do not intersect, similar to the flat mirror case. Now the image is larger than the object, upright, and well behind the mirror. This is a virtual image. Image Ray drawn as if it came from f.

13. Finding images for a concave (converging) mirror. Last time, very close to the mirror. Cf Object This is getting very much like the flat mirror case. Now the image is slightly larger than the object, upright, and nearly the same distance behind the mirror. This is a virtual image. Image

14. Mirror Equations: (look familiar?!)  Image location  Magnification Minus signs are important!

15. Example: d o = 23, f = 4 d i = ? Cf Object Image +4.8 m = ?m = -d i /d o = -0.2 meaning inverted and smaller

16. Example: f = + 6 cm and - 18 cm lenses are 1 cm apart d o = + 12 cm dodo Find the image due to the first lens, ignore the second for now. Now ask what happens to these rays at the second lens. dodo Need another ray-- from the center of the diverging lens along the first image.

17. dodo Math First lens d o = 12, f = 6 d i = ?d i = 12 Second lens d o = -11, f = -18 d i = ? dodo d i = 28.3 didi didi What about Magnification? First image m 1 = -12/12 = -1 Second image m 2 = -28.3/-11 = 2.6 Total m = -1(2.6) = -2.6 Inverted and real Example: f = + 6 cm and - 18 cm lenses are 1 cm apart d o = + 12 cm

18. dodo Math First lens d o = 9, f = 6 d i = ?d i = 18 Second lens d o = -9, f = -18 d i = ? dodo d i = 18 didi didi First image m 1 = -18/9 = -2 Second image m 2 = -18/-9 = +2 Total m = -2(2) = -4 Inverted and real Example: f = + 6 cm and - 18 cm lenses are 1 cm apart d o = + 12 cm