# Homework Help: Matrix methods for optics

1. Mar 10, 2009

### jaejoon89

For my optics class we are trying to use matrices to "simplify" problems. The notes we are using can be found at: http://www.fen.bilkent.edu.tr/~ilday/courses/2006/415/geometric_optics.pdf

We learned that:
[x_out theta_out] = ...[first surface][medium][x_in theta_in]

In the notes, the thin lens matrix is calculated from the multiplication of the two matrices for the curved interfaces? How does that fit the formula above? I am trying to learn how to do this so I can modify it for a thick lens.

Also, how is the matrix for each interface calculated? (see work below or link)

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The medium is given by
x_out = x_in + z*theta_in
theta_out = theta_in

Thus,

[1 z
0 1]..............(1)

At the interface,
x_out = x_in
theta_1 = theta_in + theta_s
theta_2 = theta_out + theta_s

z = R - sqrt(R^2 - x_in^2) = 1/2 (x_in^2 / R)
theta_s ~ x_in / R

How on earth is the matrix for a curved interface calculated:
M =
[1 0
(n1/n2 - 1)/R n1/n2]????? ....... (2)