Final answer:
The focal length of the convex mirror is -22.0 cm, indicating that it is a virtual focal point situated on the same side of the mirror from which light originates. The magnification is approximately 0.36, which means the image is upright and smaller than the object.
Step-by-step explanation:
When an object is placed 38.5 cm in front of a convex spherical mirror, and a virtual image forms 14.0 cm behind the mirror, we can use the mirror equation to determine the mirror's focal length. The mirror equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. For a convex mirror, the image distance (di) is considered negative.
Using the given distances, we substitute do = 38.5 cm and di = -14.0 cm into the mirror equation to find the focal length (f):
1/f = 1/38.5 + 1/(-14.0)
1/f = 0.025974 - 0.071429
1/f = -0.045455
f = -22.0 cm
The negative value indicates that the focal length is on the same side as the direction from which light is coming, which is characteristic for a convex mirror. Furthermore, the magnification (m) can be calculated using the magnification formula, m = -di/do, which, in this case, yields:
m = -(-14.0)/38.5
m ≈ 0.36
This means the image is upright and 0.36 times smaller than the object.