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How does a concave mirror give images of same linear magnification for two different object distance?

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I assume that you mean $|m|$ can be the same for two images generated by a concave mirror.

In that case, the object can be placed in two places, one which is outside of the focal length, which will produce a negative value for $m$, and another that is inside of the focal length that will produce a positive value for $m$.

A way to see this is to get into the mirror equation and equation for linear magnification.

The mirror equation reads $$ \frac{1}{o} + \frac{1}{i} = \frac{2}{R} $$ With $o$ representing the object's distance from the mirror, $i$ representing the image's distance from the mirror, and $R$ representing the radius of curvature for the concave mirror

The equation for linear magnification $m$ is $$ m = \frac{-i}{o} $$

Solving for $i$ in terms of $o$, $$ i = -om $$

Then substitute this into the mirror equation $$ \frac{1}{o} - \frac{1}{om} = \frac{2}{R} $$ Then solve for $o$. This will give you one value of the object distance.

In the other case, you will use $m = i/o$ which will give you a different value for $o$.

You can try using the simulation at http://www.edumedia-sciences.com/en/media/362-concave-mirror and move the object around to see how this works.

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