# OPTICS: finding image position using matrix methods

1. Mar 23, 2014

### user_

1. The problem statement, all variables and given/known data

Hello! The question I'm looking to solve is asking me to "analytically evaluate the image" produced by a concave mirror (which I'm assuming is telling me to use matrix methods to find image position, though I'm not sure). I've come across matrix methods which give me the distance from the optical axis to where an incident ray crosses the input plane of the system, but I'm wondering what steps to take in order to find image position.

I haven't been to class is a few days and so I'm really quite lost, and not being able to find any resources which are consistent with this course is really frustrating. Hopefully someone can steer me in the right direction...

Thank you!

2. Mar 23, 2014

### Simon Bridge

Welcome to PF;
That's not what the term "analytically" means - no.
It just means the answer should be an analytical solution rather than a numerical one.
Related to "closed form expression".

Thus you should find a closed-form expression for the position.

OTOH: it sounds like your coursework is covering matrix optics right now.

Sketch the situation for ray diagrams - what is special about the image position?
Can you describe the special quality as something you can find from the matrix formalism.

I haven't been to class is a few days and so I'm really quite lost, and not being able to find any resources which are consistent with this course is really frustrating. Hopefully someone can steer me in the right direction...[/QUOTE]
Google for "matrix optics" or "ray transfer matrix".

If the light ray is represented by vector (y,y'), then it goes from the object position o to the mirror, gets reflected, and comes back to the viewer position. At some point the rays appear to diverge from a position other than the object.

So why not start with the transfer matrixes for translation and reflection?

Last edited: Mar 23, 2014