Lecture14 - Lecture 14 10. Analytical ray tracing Matrix...

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Unformatted text preview: 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 " # $ % & Snells 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 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 + 1 s i r 1 s = 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 ( 1 f 1 " # $ % & ) r 1 r 1 ' " # $ % & 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...
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This note was uploaded on 08/06/2008 for the course PHYS 352 taught by Professor Dierolf during the Fall '04 term at Lehigh University .

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Lecture14 - Lecture 14 10. Analytical ray tracing Matrix...

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