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Mirror Formula Formal Proof

Question

The relation between u, v and r is:
$r = \frac{2 u v}{u + v}$
$r = \frac{2}{u + v}$
$r = \frac{2 (u + v)}{(u v)}$
None of these

A

r = \frac{2 u v}{u + v}

B

r = \frac{2}{u + v}

C

r = \frac{2 (u + v)}{(u v)}

D

None of these

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Solution

Verified by Toppr

We know,
$1 / f = 1 / u + 1 / v$
Or $2 / r = 1 / u + 1 / v$
Since radius of curvature is double the focal length. This leads to option A.

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