Can someone explain the matrix method

[dukebdx12]

Homework Statement

I have the answer completed, but not using the matrix method. That is what I am confused on, I am unsure on how.

Required to use matrix method. In figure, a real inverted image I of an object O is formed by a certain lens (not shown); the object-image separation is d = 45.2 cm, measured along the central axis of the lens. The image is just 1/2 the size of the object. (b) How far from the object must the lens be placed? (c) What is the focal length of the lens? Again, I am required to use matrix method, which I am unsure of.
Figure:
http://i812.photobucket.com/albums/zz41/uofmx12/phy34p58.jpg


2. Homework Equations and solution
The answer for (b) is
i = (d - p) and
i / p = (1 / 2)
p = (2 d / 3) = 30.13

And for C
the focal length will be
i = 45.2-30.13 = 15.07
1/f = 1/p+1/i = 10.04

 

[Delphi51]

Ray transfer matrices are explained here: http://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis

You need to "trace" two rays from object to image. Usually your best bet is to pick
(1) a ray from the top of the object going parallel to the lens, bending to the tip if the image
(2) a ray from the top of the object going through the middle of the lens to the tip of the image.
Just set up your matrix for a ray's distance from the axis and tan of the angle, then multiply it by the free space matrix to take the ray to the lens, then multiply it by the thin lens matrix, then by the free space matrix to the image location. Knowing the answer you want for your image, you should be able to solve for the unknown distance. Give it a shot. Post your work here and someone will help!