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!

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

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!

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

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).

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

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

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

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.

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)

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

http://stwww. weizmann. ac. il/Lasers/laserweb/Java/CavityB/Cavstabe2 http://stwww.weizmann.ac.il/Lasers/laserweb/Java/CavityB/Cavstabe2.htm java rays in cavity…good Choose Confocal 25 25 25. Adjust numbers only by arrows!. left click in yellow medium, then right click start a ray. http://stwww.weizmann.ac.il/Lasers/laserweb/Java/Cavity/Cavstabe.htm Stability diagram applet

Stable cavities

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)

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

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

Converging thin lens/mirror imaging review

Converging thin lens/mirror imaging review

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

Diverging thin lens/mirror imaging review