What is the power of a concave mirror (in diopters) located in air with a radius of curvature 20cm?

To find the power of a concave mirror, we use the formula for the mirror's focal length, which is derived from its radius of curvature. The relationship between the focal length (f) and the radius of curvature (R) for a mirror is expressed as:

f = R / 2

For a concave mirror, the focal length is considered negative. Given a radius of curvature of 20 cm, we calculate:

f = 20 cm / 2 = 10 cm

Since this is a concave mirror, we take the focal length as negative:

f = -10 cm

Next, we convert the focal length from centimeters to meters to use it in the power calculation:

f = -10 cm = -0.10 m

The power (P) of a lens or mirror is defined as the inverse of the focal length in meters:

P = 1 / f

Substituting the focal length:

P = 1 / (-0.10 m) = -10.00 D

Thus, the power of the concave mirror is -10.00 diopters, which corresponds to the concise understanding of how mirrors work, particularly with respect to their curvature and the sign convention for focal lengths. This