he focal length of a convex mirror is -20 cm. What is the radius of the curvature?

To find the radius of curvature of a convex mirror, you can use the mirror equation:

1/f = 1/r - 1/d

where:
- f is the focal length of the mirror,
- r is the radius of curvature,
- d is the object distance (distance between the object and the mirror).

In this case, you are given that the focal length (f) is -20 cm for a convex mirror. Since the focal length of a convex mirror is always negative, you can directly substitute this value into the equation:

1/-20 = 1/r - 1/d

Since the object distance (d) is not provided, I will assume it to be infinity. When the object distance is considered to be infinity, the equation becomes:

1/-20 = 1/r

To solve for the radius of curvature (r), we can simply rearrange the equation:

r = -20 cm

Hence, the radius of curvature of the convex mirror is -20 cm.