Final answer:
The image distance is found to be approximately -22.9 cm using the mirror equation, indicating a virtual image for a concave mirror with a given object distance and focal length.
Step-by-step explanation:
To determine the image distance for a concave mirror when an object is placed in front of it, we can 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. In this case, the focal length f is 15 cm, and the object distance is 40 cm. Plugging these values into the equation yields:
∑1/15 = 1/40 + 1/di → 1/di = 1/15 - 1/40 → 1/di = (8.67 cm)∑ .
The image distance for a concave mirror with a focal length of 15 cm and an object placed 40 cm in front of it is -24.0 cm.
Therefore, the image distance di is approximately -22.9 cm, indicating that the image is formed 22.9 cm behind the mirror, and is virtual and upright.