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2.9: Derivation of Magnification

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  • Figure II.14 shows an optical element separating media of indices \(n_1\) and \(n_2\). I have drawn the element as an interface, though it could equally well be a lens (or, if I were to fold the drawing, a mirror). An image of height \(h'\) is formed at a distance \(q\) of an object of height \(h\) at a distance \(p\).

    Assuming, as ever, that angles are small, we have

    \[\text{magnification} = \dfrac{\theta_2q}{\theta_1p}.\]

    But Snell’s law, for small angles, is \(n_1\theta_1 = n_2\theta_2\), and therefore

    \[ \text{magnification} = \dfrac{n_1q}{n_2p} = \frac{C_1}{C_2}. \label{eq:2.9.1} \]

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