Final answer:
The focal length of a concave mirror is half its radius of curvature. For a mirror with a radius of curvature of 40.0 cm, the focal length is 20.0 cm. The correct answer is A) 20.0 cm.
Step-by-step explanation:
The question asks about the focal length of a concave mirror with a given radius of curvature. The relationship between the focal length (f) and the radius of curvature (R) of any mirror is given by the mirror equation R = 2f. Hence, to find the focal length of a concave mirror when the radius of curvature is known, you simply divide the radius of curvature by two.
For a concave mirror with a radius of curvature of 40.0 cm, the focal length is calculated as:
f = R/2 = 40.0 cm / 2 = 20.0 cm
Therefore, the correct answer is A) 20.0 cm.
Similarly, for practice problems, if a concave mirror has a radius of curvature of 0.8 m, we apply the same formula:
f = R/2 = 0.8 m / 2 = 0.4 m,
hence the focal length would be -0.4 m, considering the sign convention that focal lengths for concave mirrors are negative.
If you were to solve problem 109, you would use the combination of lenses and mirrors formulae. In problem 31, replacing an 800 mm telephoto lens with a mirror would require a mirror with a radius of curvature of 1600 mm because the focal length is half the radius of curvature.