Find the focal length of a convex mirror whose radius of curvature is 32 cm.

The relationship between the focal length (f) and the radius of curvature (R) for a spherical mirror is given by the mirror equation:

1/f = 1/R

For a convex mirror, the radius of curvature (R) is considered negative. Given that the radius of curvature is R =−32cm, we can substitute this value into the mirror equation to find the focal length (f):

1/f = 1/(-32)

Now, solve for f:

f = -32/1

Therefore, the focal length of the convex mirror is f =−32cm. The negative sign indicates that the focal point is on the same side as the reflective surface, which is typical for convex mirrors.