Final answer:
To project an image of herself on the garage wall 1.80 m behind her, she should hold the hubcap approximately 5.68 cm from her face.
Step-by-step explanation:
To project an image of herself on the garage wall, she needs to use a concave mirror. The distance at which she should hold the hubcap from her face can be determined using the mirror equation: 1/f = 1/di + 1/do, where f is the focal length of the concave mirror, di is the distance of the image from the mirror, and do is the distance of the object (hubcap) from the mirror. In this case, the image distance should be equal to the distance of the garage wall (1.80 m) behind her, and we can assume the object distance is the distance at which she holds the hubcap from her face. Solving for do, we get:
1/(-f) = 1/1.80 - 1/do
Simplifying, we get:
1/do = 1/1.80 + 1/f
Since the object distance (do) is what we need to find, we can rearrange the equation to solve for it:
do = 1 / (1/1.80 + 1/f)
The exact distance will depend on the specific focal length of the concave mirror being used. Let's assume the focal length is 10 cm:
do = 1 / (1/1.80 + 1/10)
Calculating this, we find that she should hold the hubcap approximately 5.68 cm from her face in order to project an image of herself on the garage wall 1.80 m behind her.