a 15.0 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?
–5.0 cm
7.5 cm
-7.5 cm
5.0 cm

5.0 cm

Explanation:

Recall that the formula for finding the magnification (M) of the image of a lens is given by:  , where is the distance from the lens at which we place the object (actually given as 12.0 cm), and is the distance from the lens at which the image appears (not given).

So clearly, we need to start by finding the distance at which the image appears. To do such , we use the lens formula:

we replace   with 12 cm, f with the given "-6 cm" (recall that diverging lenses carry negative focal distance), and proceed to solve for the unknown ( ). We will skip writing the units (cm) of both known distances, having present that the distance we find will therefore come in cm:

where the negative sign is telling us that the image appears on the "object side" of the lens.

Now that we know , we can estimate the magnification (M):

The magnification is positive (this means that the image is upright - not inverted) but smaller than one, which tells us that the image is smaller than (one third of) the object's size.

Then, if the object's size is 15 cm, the image's size will be one third (1/3) of it, that is: 5 cm and upright.

Then you need to select the last of the choices given: 5.0 cm

it has to be b, about 97 percent.