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# 2.8.3: Power of a Mirror

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.