Question

spherical mirrors: the focal length of a concave mirror has a magnitude of 20 cm. what is its radius of curvature?

Answer 1

The radius of curvature of the concave mirror is 40 cm.

Step-by-step explanation:

To determine the radius of curvature of a concave mirror, we can use the relation R = 2f, where R is the radius of curvature and f is the focal length of the mirror. In this case, the focal length has a magnitude of 20 cm. Therefore, the radius of curvature of the mirror is 40 cm.

Answer 2

For a concave mirror with a focal length of 20 cm, the radius of curvature is 40 cm. If one wishes to place an object at the mirror's focal point with a focal length of 40 cm, the radius of curvature becomes 80 cm.

Step-by-step explanation:

The relationship between the focal length (f) of a concave mirror and its radius of curvature (R) is given by R = 2f. For a concave mirror with a given focal length of 20 cm, the radius of curvature would be R = 2 × 20 cm, which equals 40 cm. This relationship holds because the focal point is defined as the point where parallel rays of light either converge (in a concave mirror) or appear to diverge from (in a convex mirror), and it is located at half the distance of the radius of curvature from the mirror's surface.

In the specific example where it's desired to place the fluid-carrying pipe at the mirror's focal point, if the focal length is given as 40.0 cm, then the radius of curvature of the mirror would be R = 2f = 2 × 40.0 cm = 80.0 cm.