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Lens Maker's Formula

Question

How can $\frac{1}{\infty} + \frac{1}{f} = \frac{2}{R} b e w r i t t e n a s f = \frac{R}{2}$ ?

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Solution

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$\frac{1}{\infty} + \frac{1}{f} = \frac{2}{R} \Rightarrow 0 + \frac{1}{f} = \frac{2}{R} \Rightarrow \frac{1}{f} = \frac{2}{R} \Rightarrow \frac{R}{f} = 2 \Rightarrow R = 2 f \Rightarrow f = \frac{R}{2}$

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