ABCD matrix for an optical system of two thick lenses

[Michael Sullivan]

Homework Statement

I have an object at distance x1 from the first thick lens(convex) then air at distance x2 to the next thick lens(concave) then air of distance x3 to a mirror. I need to build an ABCD matrix representing this.

Homework Equations

thick lens equation: [ A B ] = [ 1-d/R1 (1-1/n) dn ]
[ C D ] [ -(n-1)(1/R1 -1/R2)+d/R1R2(2-n-1/n) 1+d/R2(1-1/n)]
The above is supposed to be 2x2 matrices.

I think I need the principal planes equation:

[ 1 p2 ] [ A B ] [ 1 p1 ] = [ 1 0 ]
[ 0 0 ] [ C D] [ 0 1 ] [ -1/f_eff 1 ]

The Attempt at a Solution

I think I can figure it out once I get going, but I can't figure out how to reduce the two thick lenses into one effective lens considering the air gap between the two lenses. Also do I need to work the mirror into it from the start?

I am not asking for anyone to do my homework for me, just help to start it.

The end goal will be to determine an image location given the image starting location and position of the lenses and mirror.

 

[Asim Riaz]

A:You have to think of the two lenses as one effective lens. To do this, you need to determine a focal length for the system. This is done by first determining the focal length of each lens separately, and then using the thin lens equation to calculate the effective focal length. The thin lens equation is $1/f=(1/f_1)+(1/f_2)-(n_1-1)(1/R_1)-(n_2-1)(1/R_2)+d/(n_1n_2R_1R_2)$Where $f$ is the effective focal length, $f_1$ and $f_2$ are the focal lengths of the two lenses, $R_1$ and $R_2$ are the radii of curvature of the lenses, $n_1$ and $n_2$ are the refractive indices of the lenses, and d is the distance between the lenses. Once you have the focal length of the system, you can work out the ABCD matrix using the principal plane equation you provided.