Rays and imaging v_optics/examples/optics_bench.html

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 _______

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

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

How small is small enough? Rays and imaging

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

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

ABCD matrices Refraction through curved surface

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

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

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

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!

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

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

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

ABCD matrices Reflection from curved surface Derive from diagram

ABCD matrices Refraction through curved surface Derive from diagram

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