Final answer:
The image will be formed 175 cm behind the mirror.
Step-by-step explanation:
In this problem, we are given that a small object is located 39.0 cm in front of a concave mirror with a radius of curvature of 50.0 cm. To determine where the image will be formed, 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.
Since the mirror is concave, the focal length (f) is positive. The object distance (do) is 39.0 cm. Plugging these values into the mirror equation, we can solve for the image distance (di). Once we have the image distance, we can determine where the image is formed in relation to the mirror.
Using the given values, let's solve for the image distance:
1/f = 1/do + 1/di
1/50.0 cm = 1/39.0 cm + 1/di
Now, we can simplify the equation and solve for di:
di = 50.0 cm x 39.0 cm / (39.0 cm - 50.0 cm)
di = 50.0 cm x 39.0 cm / -11.0 cm
di = -175 cm
Therefore, the image will be formed 175 cm behind the mirror.
Learn more about Concave mirrors