Question

The linear magnification of a convex mirror of focal length 15cm is 1/3. what is the distance of the object from the focus of the mirror?

Answer 1

As per the data given in the above question is as follow,

The focal length of a mirror is $15 \:cm$.

The given magnification is $\frac{1}{3}$.

We have to find the distance of the object from the focus of the mirror.

Here we have have to use the formula of magnification of convex mirror,

i.e. $u=(\frac{m-1}{m}) \times f$

Where $u$ is the distance of object from the mirror,

Focal length of a mirror is $f$.

Now substitute the value in the equation of magnification of convex mirror.

$u=(\frac{\frac{1}{3} }{\frac{1}{3} } ) \times 15\\u=(\frac{\frac{1-3}{3} }{3}) \times 3 \times 15\\u=-2\times 15\\u=-30\:cm$

Therefore the distance of the object from the pole of the mirror is $OP= 30\:cm$.

Now the distance of the object from the focus of the mirror is,

$OF=OP+PF$

where $OF$ is distance of object from focus,

$OP$ is distance of object from pole,

While $PF$ is focal length.

substitute the value in above equation we get,

$OF=30+15=45\:cm$

Hence the distance of the object from the focus of the mirror is $45\:cm$.

Answer 2

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