FP ( PM = AB) ( . ) Since APB = A PB , the right angled triangles A B P and ABP are also similar. Therefore, B A B P B A B P ( . ) Comparing Eqs.
( . ) and ( . ), we get B P – FP B F B P FP FP BP ( . ) Equation ( .
) 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 FIGURE . Ray diagram for image formation by a concave mirror. 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 these in Eq. ( . ), we get – – – v f v f u – or – v f v f u v u f ( . ) This relation is known as the mirror equation .
The size of the image relative to the size of the object is another important quantity to consider. We define linear magnification ( m ) as the ratio of the height of the image ( h ) to the height of the object ( h ): m = h h ( . ) h and h will be taken positive or negative in accordance with the accepted sign convention. In triangles A B P and ABP, we have, B A B P BA BP With the sign convention, this becomes – – h v h u – so that m = – h v h u ( .
) We have derived here the mirror equation, Eq. ( . ), and the magnification formula, Eq. ( .
), for the case of real, inverted image formed by a concave mirror. With the proper use of sign convention, these