Final answer:
The magnification of the heater element can be calculated using the mirror equation to first determine the object distance and then applying the magnification equation, magnification (m) = -image distance (d_i) / object distance (d_o).
Step-by-step explanation:
To find the magnification of the heater element in Example 25.9, we use the mirror equation and the magnification equation. Since the problem gives us the radius of curvature of the mirror (50.0 cm) and the image distance (3.00 m or 300 cm), we can find the focal length (f) which is half of the radius of curvature, so f = 25.0 cm. With the focal length and the image distance, we can calculate the object distance (do).
Using the mirror equation:
1/f = 1/do + 1/di or 1/25 = 1/do - 1/300
Solving this equation gives us the object distance do. Now, the magnification (m) is given by the equation m = -di / do. Substituting the values for di and do will give us the magnification, which according to the problem statement is of large magnitude and helps to spread out the reflected energy. Since we don't have complete numerical details here, an exact value cannot be provided, however, you would select the answer choice with the calculated magnification value assuming all required information was present.