Skip to main content
Physics LibreTexts

2.9: Derivation of Magnification

  • Page ID
    8302
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    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 \(p\).

    FIGURE II.14 .png

    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

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


    This page titled 2.9: Derivation of Magnification is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.