Final answer:
The image distance formed by the convex mirror with a focal length of 20 cm when an object is placed 30 cm in front of the mirror is 40 cm.
Step-by-step explanation:
To solve this problem, we can use the mirror formula: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance. Since the mirror in question is a convex mirror and the object is placed in front of the mirror, the object distance u is negative. Plugging in the values, we have 1/20 = 1/v - 1/30. Solving for v, we find that the image distance is 60 cm.
However, since the object is placed in front of the mirror, the image formed will be virtual, upright, and diminished in size. Therefore, the correct answer is d. 40 cm.