Operator algebraic derivation of the impulse response of a lens system

We apply the operator algebraic method to give a simple derivation of the impulse response for a paraxial lens system. The expression that we give contains the elements of the system's ray matrix that is seen to arise in a waveoptical context. In addition to providing a useful computational technique, the approach used here illuminates the relationship between physical and geometric optics in a Hamiltonian context.