Choose the correct relation between u, v and r for a spherical mirror:

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

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

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

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

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Solution

The correct option is A $r = \frac{2 u v}{u + v}$
For a spherical mirror,
$u$ is distance of object from pole,
$v$ is distance of image from pole.
$f$ is focal length of mirror.
From mirror formula
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\frac{u + v}{u v} = \frac{1}{f}$
So, $f = \frac{u v}{u + v}$
and since $r = 2 f = \frac{2 u v}{u + v}$

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Choose the correct relation between u, v and r for a spherical mirror:

The correct option is A r=2uvu+vFor a spherical mirror,u is distance of object from pole,v is distance of image from pole.f is focal length of mirror.From mirror formula1v+1u=1fu+vuv=1fSo, f=uvu+vand since r=2f=2uvu+v