Final answer:
The image distance for an object placed at 20 m in front of a concave mirror with a radius of curvature of 40 m is -20 m, indicating a virtual image created behind the mirror.
Step-by-step explanation:
If an object is placed at 20 m in front of a concave mirror with a radius of curvature of 40 m, we can use the mirror equation to find the image distance. The mirror equation is given by 1/f = 1/do + 1/di, where f is the focal length of the mirror, do is the object distance, and di is the image distance. We know that the focal length (f) is half of the radius of curvature (R), so f = R/2 = 40 m / 2 = 20 m.
Applying the values to the mirror equation, we get:
1/20 m = 1/20 m + 1/di
Solving for di, we find:
1/di = 0 - 1/20 m
1/di = -1/20 m
di = -20 m
Thus, the image distance is -20 m, indicating that the image is formed 20 m behind the mirror and is therefore a virtual image.