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2.8C: Power of a Mirror

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  • In Figure II.13 shows a reflecting surface of radius of curvature \(r\) submerged in a medium of index \(n\). I show a real object at O, a virtual image at I and the centre of curvature at C. We see that \(h = \alpha p = \beta q = \gamma r\). By Euclid, \(\theta = \alpha + \gamma\) and \(2\theta = \alpha + \beta\). Remember again that all angles are supposed to be small (even \(\beta\)!), in spite of the drawing. From these we obtain

    \[ \frac{1}{q} = \frac{1}{p} + \frac{2}{r}. \label{eq:2.8.4} \]

    On multiplying this by −n, we find that the power is −2n/r. Again the reader should try this for other situations, such a concave mirror, or a real image, and so on. The same result will always be obtained.