Image in a Convex Mirror

If we can find the focal length of the convex mirror formed by the cornea, we can find its radius of curvature (the radius of curvature is twice the focal length of a spherical mirror). We are given that the object distance is $d_{\text{o}}=\mathrm{12.0\; cm}$ and that $m=0.0320$. We first solve for the image distance $d_{\text{i}}$, and then for $f$.

$m={\mathrm{–d}}_{\text{i}}/d_{\text{o}}$. Solving this expression for $d_{\text{i}}$ gives

Entering known values yields

Substituting known values,

This must be inverted to find $f$:

The radius of curvature is twice the focal length, so that

The radius of curvature found here is reasonable for a cornea. The distance from cornea to retina in an adult eye is about 2.0 cm. In practice, many corneas are not spherical, complicating the job of fitting contact lenses. Note that the image distance here is negative, consistent with the fact that the image is behind the mirror, where it cannot be projected. In this section’s Problems and Exercises, you will show that for a fixed object distance, the smaller the radius of curvature, the smaller the magnification.

The three types of images formed by mirrors (cases 1, 2, and 3) are exactly analogous to those formed by lenses, as summarized in the table at the end of Image Formation by Lenses. It is easiest to concentrate on only three types of images—then remember that concave mirrors act like convex lenses, whereas convex mirrors act like concave lenses.