A15.0 cm object is 12.0 cm from a convex mirror that has a focal length of -6.0 cm. what is the height of the image produced by the mirror?

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:

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