2.8C: Power of a Mirror

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Mar 5, 2022
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- 2.8B: Power of a Refracting Interface
- 2.9: Derivation of Magnification

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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.

FIGURE 11.13 .png

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