Answer: 5 cm
In convex mirrors the focus is virtual and the focal distance is negative. This is how the reflected rays diverge and only their extensions are cut at a point on the main axis, resulting in a virtual image of the real object .
The Mirror equation is:
(1)
Where:
is the focal distance
is the distance between the object and the mirror
is the distance between the image and the mirror
We already know the values of
and
, let's find
from (1):
(2)
(3)
On the other hand, the magnification
of the image is given by the following equations:
(4)
(5)
Where:
is the image height
is the object height
Now, if we want to find the image height, we firstlu have to find
from (4), substitute it on (5) and find
:
Substituting (3) in (4):
(6)
Substituting (6) in (5):
Finally we obtain the value of the height of the image produced by the mirror:
