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.

$Diagram illustrating the concept of refraction, with light rays bending through a curved surface.$

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