Why does focus of a spherical mirror does not depend on whether the rays are paraxial or not?
A concave mirror, or converging mirror, has a reflecting surface that bulges inward (away from the incident light). Concave mirrors reflect light inward to one focal point.They are used to focus light. Unlike convex mirrors, concave mirrors show different image types depending on the distance between the object and the mirror.
These mirrors are called "converging" because they tend to collect light that falls on them, refocusing parallel incoming rays, toward a focus. This is because the light is reflected at different angles, since the normal to the surface differs with each spot on the mirror.
Let us first consider the image formed by a concave mirror of a point O on the axis. It was assumed earlier that an optical device forms a sharp point image of a point object. In the case of a concave mirror, this is true only if the rays of light make small angles with the axis, i.e. strike the mirror close to the pole. Such rays are said to be paraxial. Rays outside the paraxial region do not converge to a sharp point, with the result that the image is blurred considerably, a defect known asspherical abberation. If the image is sharply defined, its location can be found by tracing out the paths of any two rays emanating from O. One of these may be conveniently chosen to be normal to the mirror, since it is just reflected back along the original path. Let the other ray strike the mirror at Q, making an angle q with the radius CQ , C being the centre of curvature of the mirror. The image I is located at the intersection of the two reflected rays. We shall assume, for the moment, that OP is greater than the radius of curvature . Denote by U and V, respectively, the distances of the object O and the image I from the pole P. It follows from the geometry that