How Do You Calculate the System Matrix for a Lens After a Beam Waist?

[girlinphysics]

Homework Statement

A thin lens is placed 2m after the beam waist. The lens has f = 200mm. Find the appropriate system matrix.

This is a past exam question I want to check I got right.

Homework Equations

For some straight section [[1 , d],[0 , 1]] and for a thin lens [[1 , 0],[-1/f , 1]]

The Attempt at a Solution

[[r2],[r2']] = [[1 , d],[0 , 1]] [[1 , 0],[-1/f , 1]] [[r1],[r1']]

I multiplied the two matrices and found [[1-d/f, d] , [-1/f , 1]]

Is this correct? Or am I meant to add an additional straight section after the lens? I get confused as to when to use the straight section matrix. Thanks.

 

[blue_leaf77]

[[1 , d],[0 , 1]] [[1 , 0],[-1/f , 1]] [[r1],[r1']]

You made a mistake here. The free propagation should come first, then followed by the lens.

 

[girlinphysics]

You made a mistake here. The free propagation should come first, then followed by the lens.

Oh okay, thank you very much for your help!