# If Shlok stands 3 feet in front of a plane mirror how far from the person will her image be located.?

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Feb 9, 2018

The mirror formula is $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
where, $f$ is the focal length of the mirror, $u$ is object distance and $v$ is the image distance.

Here, since a plane mirror is mentioned, $f = \infty$
so $\frac{1}{f} = 0$

$\frac{1}{v} = - \frac{1}{u}$

$v = - u$

It's given that $\textcolor{m a \ge n t a}{u = - 3}$ feet ("-" comes from the sign convention)

so applying the formula, $\textcolor{red}{v = 3}$ feet (on the other side of the mirror.)

The total distance of the person from the image = object distance + image distance
$= \textcolor{m a \ge n t a}{u} + \textcolor{red}{v}$
$= \textcolor{m a \ge n t a}{3} + \textcolor{red}{3}$ (here we're considering just the numerical value.)
$= 6$ feets.

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Jane Share
Feb 9, 2018

In case of a plane mirror,image is formed at a same distance ($v$) from the mirror to that of the object's distance($v$) from the mirror.(i.e $u = v$)

So,total distance between the image and the object is $\left(u + v\right) = 2 u$

Here, $u = 3 f t$

So, $\left(u + v\right) = 6 f t$

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