1. Imaging
ABCD matrix can represent an imaging system, including object distance do and image distance di
optics
ABCDtotal condition for imaging! _____ = 0. Why? B
Because rays of all (small) angles must go to the image!

2. Magnification
Which element of ABCDtotal gives M for an optical system? ______
Choose A B C D A

3. Mirror/thin lens imaging equation
Derive the thin lens equation: …it’s easy
this approx works only for the similar triangles of thin lens imaging!

4. doesn’t work for a thick lens
doesn’t work for a thick lens. Using ABCD we got for a thick lens, sketch out how you would find a “thick” lens imaging equation. a
I tried but got it mostly wrong
I got it mostly right
Sketch out how you would find the magnification M for a thick lens imaging setup in terms of do and di.
I got it mostly right
I tried but got it mostly wrong

5. Principal planes method
For the purposes of finding images, we can* reduce an optical system to a thin lens. Principal plane distances p1 and p2 are “added” to the physical system, and distances do and di are measured from the planes. (*The system must begin and end in the same index).

6. Principal planes method
Since these = 1, then = 0.
Imaging equation:
Magnification
p1 or p2 can be negative

7. For a thick lens
Assume thickness d=2 cm, R­1 = 2 cm, R2 = and n=2
The effective focal length is ___ cm 1 2 3 4 5

8. For a thick lens
Assume thickness d=2 cm, R­1 = 2 cm, R2 = and n=2
The principal planes are ___ cm from the edges 1 and 2
2, 3
0, 2
0, -1
1, 4

9. Where will parallel laser light (object at infinity) be focused if coming from the left?
…if from the right?
If an object is 3 cm to the left of the lens edge, find the position of the image vs the right edge.

10. Two equivalent methods
Today’s:
Add principal planes matrices to find ABCDeffective
Set the diagonal elements to 1 to find p’s
Treat as thin lens, use thin lens imaging equation
Last lecture:
Add do and di matrices to find ABCDtotal
Find imaging equation by setting Btotal = 0.
(only 2. will work for water to air imaging)

11. Laser stability criterion
Stability: q, y remain small after many round trips

12. http://stwww. weizmann. ac. il/Lasers/laserweb/Java/CavityB/Cavstabe2
java rays in cavity…good Choose Confocal Adjust numbers only by arrows!. left click in yellow medium, then right click start a ray.
Stability diagram applet

13. Stable cavities

14. Laser stability criterion
Geometrical interpretation of
A cavity is stable if the segments between the mirrors and their centers of curvature partially overlap. (One cannot lie entirely within the other)

15. Laser stability criterion
For mirrors Ro and 2Ro, the cavity will be stable if L is ____
0 …Ro
Ro …2Ro
Ro …3Ro
2Ro …3Ro
e) two of the above

16. Laser stability criterion
If a diverging mirror (-Ro) is used and a converging one (2Ro) find all allowable L’s
0 …Ro
Ro …2Ro
Ro …3Ro
2Ro …3Ro
e) two of the above

17. Converging thin lens/mirror imaging review

18. Converging thin lens/mirror imaging review

19. Diverging thin lens/mirror imaging review
"The picture shows a spherical mirror, resting on [my] left hand… Such a globe reflection collects almost one's whole surroundings in one disk-shaped image. the whole room, four walls, the floor, and the ceiling, everything, albeit distorted, is compressed into that one small circle. Your own head, or more exactly the point between your eyes, is the absolute center. No matter how you turn or twist yourself, you can't get out of that central point. You are
immovably the focus, the unshakable core, of your world." - M. C. Escher

20. Diverging thin lens/mirror imaging review