A convex mirror has a focal length of 19.0 cm. Determine the object location for which the image will be one-fourth as tall as the object.

i know that 1/f=1/do=1/di. when i put the numbers into the equation i keep getting 23.75 and its saying that its wrong. can you please help me?

To determine the object location for which the image will be one-fourth as tall as the object, we can start by using the mirror formula:

1/f = 1/do + 1/di

Where:
- f is the focal length of the convex mirror
- do is the object distance (distance between the object and the mirror)
- di is the image distance (distance between the image and the mirror)

In this case, the focal length is given as 19.0 cm:

1/19.0 = 1/do + 1/di

We are looking for the object location where the image will be one-fourth as tall as the object. This means the height of the image (hi) will be one-fourth the height of the object (ho):

hi = (1/4) * ho

Now, we can use the magnification formula to relate the object and image heights:

hi / ho = -di / do

Since we know that hi is one-fourth of ho, we can substitute the values:

(1/4) = -di / do

Rearranging the equation, we find:

di = -do / 4

Now, let's substitute this expression for di in the mirror formula:

1/19.0 = 1/do + 1/(-do / 4)

To simplify this equation, we can take the common denominator:

1/19.0 = (4 - 1) / (4do)

Now, cross-multiply the equation:

4do / (4 - 1) = 19.0

Simplifying further, we have:

4do = 19.0 * 3

do = (19.0 * 3) / 4

do = 14.25 cm

Therefore, the object location for which the image will be one-fourth as tall as the object is at a distance of 14.25 cm from the convex mirror.