Final answer:
The location of the image (q) is 44cm from the mirror, and the height of the image (h) is -6.0cm. The image is inverted and virtual.
Step-by-step explanation:
To solve the problem of locating the image of a mascara brush with a 3.0cm length held upright 22cm from a concave cosmetic mirror with a 44cm focal length, we use the mirror equation 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.
Rearranging the equation to solve for di gives us 1/di = 1/f - 1/do. By substituting the values in, we have 1/di = 1/44cm - 1/22cm, which simplifies to 1/di = 2/44cm - 1/44cm, giving us 1/di = 1/44cm. Thus, di = 44cm. This indicates that the image is formed at the same distance as the focal length, but on the same side as the object.
The magnification of the image, m, can be calculated using the formula m = -di/do, which yields m = -44cm/22cm = -2. This negative value indicates that the image is inverted and twice the size of the object. Hence, the height of the image, h, is m times the object height, so h = -2 x 3.0cm = -6.0cm.
Consequently, the image is inverted and virtual because the image distance is positive and the magnification is negative.