1. HW #4, Due Sep. 21
Ch. 2: P28, PH8, PH16
Ch. 3: P3, P5

2. Lecture 9 (chapter 3 continued)
Quick Review:
Reflection from Curved Mirrors (Convex Mirrors)
The ray rules
This Lecture:
Ray rules for concave mirrors
Finding the image
Lenses

3. Chapter 3 Mirrors and Lenses
Read , 3.2, 3.3 (A, B, C* , D), 3.4, 3.5**
* Anamorphic Art
** Aberrations

4. Flat mirror revisited
virtual
image
Read Text about the Kaleidoscope

5. (simply apply the law of reflection)
Spherical Mirrors
Where is the image?
What is the field of view?
Ray Tracing
(simply apply the law of reflection)

6. Reflection in Curved Mirrors
Convex and Concave
Mirrors

7. axis O C F center focal point
Paraxial Rays: Rays that are close to the axis

8. Ray Rules for a Convex Mirror
Ray Rule 1: All rays incident parallel to the axis are reflected so
that they appear to be coming form the the focal point, F.
Ray Rule 2: All rays that (when extended) pass through center C
are reflected back to themselves.
Ray Rule 3: All rays that (when extended) pass through F are
reflected back parallel to the axis.

9. C F O 1 C F O 3 C F O 2

10. Locating the Image Mirrors *Concave Mirrors
*Concave Lens: virtual image
*Convex Mirrors
spherical aberration

12. “Hand with Reflecting Globe”
M. C. Escher,
“Hand with Reflecting Globe”
Fig 3.9

13. Concave Mirror
axis O C F
center
focal point

14. Ray Rules for a Concave Mirror
Ray Rule 1: All rays incident parallel to the axis are reflected so
that they appear to be coming form the the focal point, F.
Ray Rule 2: All rays that (when extended) pass through center C
are reflected back to themselves.
Ray Rule 3: All rays that (when extended) pass through F are
reflected back parallel to the axis.

15. *Concave Mirrors

16. Spherical Lenses

17. Refraction at Curved Surfaces
axis O C
center n2 n1
Simply apply the laws of refraction

18. I R
axis O C
center n2 n1

19. Thin Spherical Lenses
Converging Lens: focal length (f) is positive

20. Thin Spherical Lenses
Converging Lens: focal length (f) is negative

21. Ray Rules for Converging (and Diverging) Lenses
Ray Rule 1: All rays incident parallel to the axis are deflected
through F’ (or as if it came from F’)
Ray Rule 2: All rays passing through the center of the lens
Continue undeviated.
Ray Rule 3: All rays that (when extended, if necessary) pass
through F are deflected parallel to the axis.

22. Example: Ray Rules for a converging lens| F’ F | f
f= focal length F’ F |

23. *Magnification (Magnifying Glass)
* Lens Action (Many Applets)
principle rays
*Thick Lens (Spherical Aberration)

24. Fresnel Lenses

25. Lens Aberrations Chromatic *Thick Lens (Spherical Aberration)
spherical aberration

26. Spherical Aberration

27. *Thick Lens (Spherical Aberration)
spherical aberrationv

28. Curvature, Coma

29. Astigmatism

30. Distortion

31. *Thick Lens (Spherical Aberration)
spherical aberration