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== Introduction ==

The thin lens equation <math>\frac1i + \frac 1o = \frac1f</math> to compound microscope with two lenses. The lens that is closer to the object is called ''objective'' and the the one closer to the eye is called ''ocular''. The distance between the lenses is <math>L</math>.

== Theory ==

We have <math>\frac1{i_1} = \frac1{f_1} - \frac1{o_1} </math>. The distance between the lenses is <math>L</math>, thus <math>i_1 + o_2 = L</math> which gives <math>o_2 = L-i_1</math>. Thus we have for the image distance of the second lens

<math>\begin{align}
\frac1{i_2} &= \frac1{f_2} - \frac1{o_2} \\
&= \frac1{f_2} - \frac1{L-i_1} \\
&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\
&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\
&= \frac1{f_2} - \frac{o_1-f_1}{ \frac{L(o_1-f_1)- f_1 o_1} \\
\end{align}</math>

Magnification (for the thin lens) is <math>m = - \frac io = -  \frac{i_2}{o_1}</math>.