Transfer matrices - drift distances I have a question regarding transfer matrices in optics. For thin lenses, the thickness of the lense is not taken into the calculation because it is very small compared to the dimensions of the rest of the system.
Now let's say I have a lens like this one (just a thicker lens):

The thickness of the lens does now play a bigger role, but the length of the drift cannot be determined, because it depends on the beam. It might be close to 0, or could even be equal to the full thickness of the lens. This makes a difference of course. But how do I treat such a lens? Do I ignore the drift distance, and just calculate it as a thin lense?
 A: I would say that it depends on your application. If the beam is small compared to the clear aperture of the lens, then you can probably treat it as a thin lens without any trouble.
If the beam is large, you will probably have to treat the rays differently depending on their distance from the optical axis. IIRC you won't be able to use a transfer matrix for that.
In the end, it all depends on why you need to calculate it, and how much accuracy you need.
A: Assuming the two surfaces are still spherical, you can still use transfer matrices to treat a thick lens.  Citing the Wikipedia article on transfer matrices, the transfer matrix for a curved interface is 
$$
I_C(n_i,n_f,R) = \begin{pmatrix}1&0\\\frac{n_i-n_f}{n_f R}&\frac{n_i}{n_f}\end{pmatrix}.
$$
The ray matrix for translation is, as usual, 
$$
T(d) = \begin{pmatrix}1&d\\0&1\end{pmatrix}.
$$
So, if your initial medium is vacuum ($n_i=1$), the index of refraction of your lens material is $n$, the thickness of your lens is $t$, and the curvature of both sides is the same and is given by $R$, then the combined transfer matrix is 
$$
I_C(n,1,-R)T(t)I_c(1,n,R)=\begin{pmatrix}\frac{(1-n)t}{nR}+1&\frac{t}{n}\\
  -\frac{(1-n)(2nR+t(1-n))}{nR^2}&\frac{(1-n)t}{nR}+1\end{pmatrix}
$$
Notice that if you take the thin lens limit of this transfer matrix ($t\rightarrow0$) and apply the lensmaker's equation, then you recover the thin lens transfer matrix.
