Final answer:
To determine the magnification of a makeup mirror held 20 cm from a woman's face with a radius of curvature of 120 cm, the focal length is calculated as half of the radius of curvature (-60 cm). Using the magnification formula m = -di/do, and assuming a magnification of 1 for typical makeup mirror usage, the image distance di is found to be -20 cm, indicating the image is virtual and formed behind the mirror.
Step-by-step explanation:
To calculate the magnification of the image that a woman sees when she holds a makeup mirror a certain distance from her face, we need to use the mirror equation and magnification formula. The mirror equation relates the object distance (do), the image distance (di), and the focal length (f) of the mirror. It is given by 1/do + 1/di = 1/f. The magnification (m) is given by m = -di/do, where a negative magnification means the image is inverted.
First, we need the focal length of the mirror. The radius of curvature (R) is given as 120 cm, thus the focal length f is R/2, which is 60 cm or 0.6 m. Since the mirror in question is a convex mirror, the focal length will be negative, so f = -0.6 m.
Now, we can use the mirror equation to find the image distance di. Assume the object distance do is negative because it's a virtual object in this case (the woman's face), hence do = -20 cm, so:
1/do + 1/di = 1/f
1/(-0.2 m) + 1/di = 1/(-0.6 m)
Since di is difficult to measure directly in this case, we'll use the magnification formula to find di.
The desired magnification is not given, but we can infer that if the mirror is being used as a makeup mirror, a typical magnification might be 1 (where the image size is equal to the object size). Solving for di yields:
-di/do = m
-di/(-0.2 m) = 1
di = -0.2 m
Thus, the image is formed at the same distance as the object, but behind the mirror.
Note that in reality, the magnification seen would vary depending on how the individual is using the mirror.