Derive an expression relating the focal length f, of a convex mirror to the object distance, u, and image distance, v.

Derive an expression relating the focal length f, of a convex mirror to the object distance, u, and image distance, v.

Solution

Consider the incidence of ray OX on to a convex mirror from a point object O placed along the principle axis and then suddenly reflected in the direction XK making an angle q with the normal XN.