A convex mirror in water (n=1.33) has a radius of curvature of 12cm. What is the dioptric power of the mirror?

To find the dioptric power of a convex mirror, the first step is to calculate its focal length using the radius of curvature. The focal length (f) of a mirror is related to its radius of curvature (R) by the formula:

f = R/2.

For a mirror with a radius of curvature of 12 cm, the focal length would be:

f = 12 cm / 2 = 6 cm.

In the context of a convex mirror, the focal length is considered positive when dealing with the mirror's design, but in a medium like water (where the refractive index is different from air), the effective focal length needs to be adjusted. When in a medium, the focal length can also be expressed in terms of the refractive index of the medium (n). However, for mirrors, we'll focus primarily on the calculation of dioptric power from the focal length:

Dioptric power (P) is defined as:

P = 1/f (in meters).

To convert the focal length to meters, we have:

f = 6 cm = 0.06 m.

Thus, we calculate the power:

P = 1 / 0.06 = 16.67 D.

However,