In a concave mirror experiment, an object is placed at a distance $x_{1}$ from the focus and the image is formed at a distance $x_{2}$ from the focus. The focal length of the mirror would be

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$\sqrt{\frac{x_{1}}{x_{2}}}$

$\sqrt{x_{1} x_{2}}$

$x_{1} x_{2}$

$\frac{x_{1} + x_{2}}{2}$

answer is B.

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Detailed Solution

$Given u = (f + x_{1}) and v = (f + x_{2}) The focal length f = \frac{uv}{u + v} = \frac{(f + x_{1}) (f + x_{2})}{(f + x_{1}) + (f + x_{2})} on solving, we get f^{2} = x_{1} x_{2} or f = \sqrt{x_{1} x_{2}}$

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