If we perform ray tracing of rays incident on a spherical mirror, we find that in the paraxial approximation at least, parallel incoming rays are all reflected together at one point (or appear to come from one point in the case of a convex mirror). Spherical mirrors thus act very much like lenses, but they also reverse the direction of light propagation. The focal length of the mirror is half its radius of curvature, as shown in the diagram below. I recommend that in treating mirror problems you "open out" the rays and treat the mirror as a lens and see what happens to the transmitted rays. Convex surfaces act like diverging lenses, concave surfaces act like converging lenses. Mirrors have the advantage over lenses of a focal length that does not vary with wavelength. You may wish to consider how the convex mirror used in car side mirrors is used to give a wider field of view than a plane mirror. Where is the image formed by such a system?
The first part shows how the reflection off the curved surface of a horizontal incoming leads to the ray being reflected through the focal point, which is half a radius of curvature from the mirror. This is analagous to the action of a spherical lens, but with a change of direction (now going right to left) added in. The second two parts show a more general ray, and how we can "open out" a spherical mirror to show its lens-like properties.
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