$6\mathrm{.}19*$ Show that Eq$.(6\mathrm{.}36),$ relating the object and image distances measured from the vertices of a lens, reduces to Gauss's Formula $[$Eq$.(5\mathrm{.}17)]$ for thin lenses. Remember that when $s_o>0,d_{1O}<mn>0</mn>$ and when $s_i>0,d_{I2}>0.$

Figure $6\mathrm{.}9$ Image geometry. Note that $d_0$ is negative here, whereas $d_l$ is positive.

And so the image distance measured from the last vertex on the right, $d_{\text{I}},$ is related to the object distance measured from the first vertex on the left, $d_O,$ by

$d_{\text{I}}=\frac{-a_{21}+a_{22}{d}_O}{a_{11}-a_{12}{d}_O}$