• Figure shows the ray diagram considering three rays. It shows the image A′B′ (in this case, real) of an object AB formed by a concave mirror.
• Thus, point A′ is image point of A if every ray originating at point A and falling on the concave mirror after reflection passes through the point A′.
• We now derive the mirror equation or the relation between the object distance (u), image distance (v) and the focal length ( f ).
• From Figure, the two right-angled triangles A′B′F and MPF are similar. (For paraxial rays, MP can be considered to be a straight line perpendicular to CP.) Therefore,
• Equation (3) is a relation involving magnitude of distances. We now apply the sign convention. We note that light travels from the object to the mirror MPN. Hence this is taken as the positive direction.
• To reach the object AB, image A′B′ as well as the focus F from the pole P, we have to travel opposite to the direction of incident light.
• Hence, all the three will have negative signs. Thus,
B'P = -v, FP = -f, BP = -u
Using this convention in eqn. (3), we get
