1. Rays and imaging http://webphysics.davidson.edu/physlet_resources/da v_optics/examples/optics_bench.html

2. Imaging principle The purpose of a focusing (or imaging) system is to bring many rays to one point, or to create many allowed paths to the same point (we like bright images) Imaging and Fermat’s principle: Hence many paths from object to image must be of the same _______

3. Rays and imaging Describe ray state by Between interfaces: straight lines…____ changes, but ___ does not At interfaces: ____changes, but ____ does not y y  

4. Paraxial approximation: angle vs z axis is small  restriction on  angle of incidence on any surface is small  restriction on y: Rays and imaging y<<R

5. How small is small enough? Rays and imaging

6. ABCD matrices Ray moving a distance d along z, in any material Don’t confuse this with which is for going through a slab of glass of index n, thickness d

7. ABCD matrices Reflection from curved surface Sign of radius R for reflection? Same ABCD for thin lens!

8. ABCD matrices Refraction through curved surface

9. Sign of R for refraction? + if convex when “viewed” by the ray as it encounters it.

10. Thin lens So thin that only  changes, not y or x!

11. Write three matrices in order that when multiplied would give you the ABCD matrix for a thick lens (index n) which has width a at the center, and R 1 and R 2 on the left and right respectively, for light traveling from the left a)I got it mostly right b)I tried but got it mostly wrong a

12. Imaging ABCD matrix can represent an imaging system, including object distance d o and image distance d i ABCD total condition for imaging! _____ = 0. Why? B Because rays of all angles must go to the image!

13. Magnification Which element of ABCD total gives M for an optical system? ______ Choose A B C D C

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

15. 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 a)I tried but got it mostly wrong b)I got it mostly right Sketch out how you would find the magnification M for a thick lens imaging setup in terms of d o and d i. a)I got it mostly right b)I tried but got it mostly wrong

16. ABCD matrices Reflection from curved surface Derive from diagram

17. ABCD matrices Refraction through curved surface Derive from diagram

18. For a thin lens, you can get f from the n’s and R’s by ABCD matrices. Sketch out how you would get this “lensmaker’s formula”: a)I got it mostly right b)I tried but got it mostly wrong