{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture14

# Lecture14 - Matrix formulation of geometric optics We...

This preview shows pages 1–3. Sign up to view the full content.

Lecture 14 10. Analytical ray tracing Matrix formulation of geometric optics We consider only beams close to the optical axis of our system • all angular displacements are small • sin ! ! tan ! ! ! • all beams can be characterized by a vector at z 1 we have r 1 " 1 # r 1 ' \$ % & ( ) z 2 r 2 ! 2 z 1 r 1 ! 1 optical axis after an optical element we get at z 2 r 2 " 2 # r 2 ' \$ % & ( ) This transformation can be expressed by a matrix: ABCD matrix A B C D " # \$ % & The ABCD matrix We can write: r 2 r ' 2 " # \$ % & = A B C D " # \$ % & ( r 1 r ' 1 " # \$ % & or r 2 r ' 2 " # \$ % & = Ar 1 + Br ' 1 Cr 1 + Dr ' 1 " # \$ % & Snell’s Law: n sin " ' = sin r 1 ' n " ' # r 1 ' " r L = # ' = r ' 1 n r 2 = r 1 + L n r ' 1 r 2 ' = r 1 ' r 2 r ' 2 " # \$ % & = 1 L / n 0 1 " # \$ % & ( r 1 r ' 1 " # \$ % & Example 1: r 1 r 2 ! L z 1 z 2 n " r Example: 2 Thin lens r 1 r 2 s o s i r 1 =r 2 lens equation: 1 f = 1 s 0 + 1 s i r 1 s 0 = r 1 ' and r 2 s i = r 1 s i = " r 2 ' r 1 f = r 1 ' " r 2 ' # r 2 ' = " 1 f r 1 + r 1 ' r 2 = r 1 r 2 r 2 ' " # \$ % & = 1 0 ( 1 f 1 " # \$ % & ) r 1 r 1 ' " # \$ % &

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Laser and nonlinear optics Combinations of ABCD matrices As usually for matrix transformation, the result for a combination of optical elements can be obtained by multiplication of the individual ABCD matrices r 2 r 2 ' " # \$ % & = A 12 B 12 C 12 D 12 " # \$ % & (
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Lecture14 - Matrix formulation of geometric optics We...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online