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The convergence and power method has great advantages when you have a complex systems of many lenses, mirrors and interfaces in succession. You just add the powers one after the other. But I expect there are some readers who don’t want to be bothered with all of that, and just want to do simple single-lens calculations with a simple formula that they are accustomed to, in particular the well-known $$\frac{1}{p}+ \frac{1}{q}=\frac{1}{f},$$, which is appropriate for the “real is positive” sign convention – and they want to get the calculation over with as soon as possible and with as little effort as possible. This section is for them! I have drawn a simple diagram in Figure II.23. It is not extremely accurate – it is the best I can do with this infernal machine that I am sitting in front of. All you need in order to draw a really good version of it is a sheet of graph paper. There are three axes, labelled $$p$$, $$q$$ and $$f$$. For any particular problem, to solve the above equation, all you do is to lay the edge of a ruler across the figure. For example: $$p$$ = 40 cm, $$f$$ = 26 cm. What is $$q$$? The dashed line gives the answer: $$q = 75$$cm. Another example: $$p = 33$$ cm, $$q = −60$$ cm. What is $$f$$? The dotted line gives the answer: $$f = 73$$ cm.