# a convex mirror has a focal length of 18 cm . the image of an object kept in front of the mirror is half the height of the object . what isthe distance of the object from the mirror?

By sign convention magnification m = image size / object size

So m = 1/2 * object size / object size = 1/2

Recall m = f /(f - u)

So 1/2 = 18 / (18 - u)

==> 18 - u = 36

OR - u = 18

Negative sign indicates that we measure object distance right from pole and opposite to the incident ray

So Distance of object in front of the mirror = 18 cm

Let us find the image distance too

Plug in 1/u + 1/v = 1/f

Here u = - 18 cm (by sign convention)

f = + 18 cm

Plugging - 1/18 + 1/v = 1/18

==> 1/v = 2/18

OR v = 9 cm

Here is the related diagram