Final answer:
The coils in the electric room heater are located approximately 26.32 cm from the concave mirror, calculated using the mirror equation and the given radius of curvature of the mirror.
Step-by-step explanation:
To determine the position of the coils using the information provided about the electric room heater, we can apply the mirror equation for a concave mirror. The mirror equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance (distance from the coils to the mirror), and di is the image distance (distance from the mirror to the image of the coils).
The radius of curvature (R) is given as 50.0 cm, which is related to the focal length (f) by the equation f = R/2. Since the image is formed 3.00 m away from the mirror, we must first convert this distance to centimeters (300 cm) to match the units of the focal length.
Plugging the known values into the mirror equation:
- f = 50.0 cm / 2 = 25.0 cm
- di = -300 cm (negative because the image formed by a concave mirror is on the same side as the object)
- 1/25.0 = 1/do - 1/300
- Upon solving, do = 26.32 cm (approximately)
Hence, the coils are located approximately 26.32 cm from the concave mirror.