Matrix optics; simple lens system

[mathman44]

Homework Statement

Calculate the matrix for the optical system which takes rays from the object plane
to the image plane for a simple lens and show how this leads to 1/v = 1/u + 1/f


Also show that the matrix can be written in the form


$$\left[ \begin{array}{cc} 1/M & b \\ 0 & M \end{array} \right]$$

The Attempt at a Solution

Ok... so the matrix for the system is going to be m3*m2*m1

where m3 is the translation matrix for a distance "v"


$$\left[ \begin{array}{cc} 1 & 0 \\ -v & 1 \end{array} \right]$$

m2 is the thin lens matrix


$$\left[ \begin{array}{cc} 1 & -1/f \\ 0 & 1 \end{array} \right]$$


m1 is the translation matrix for a distance "u"


$$\left[ \begin{array}{cc} 1 & 0 \\ u & 1 \end{array} \right]$$

Multiplying these out, its obvious that it cannot be written in the required form. So far, does this look okay? I can't see anything immediately wrong with what I've done so far.

 

[mathman44]

bump ;)