Prismatic effect in bifocal lenses and the location of the near optical centre

A matrix expression is derived for the prismatic effect in the reading portion of a bifocal lens. Using this expression the problem of finding the location of the optical centre of the reading portion is examined. Matrix methods lead to a complete solution that holds in all circumstances within the usual limitations of first-order optics and thin lenses. Both the main and segment lenses may be astigmatic. In the usual case there is a unique near optical centre but situations can occur in which there is no near optical centre or an infinite number of them. These situations are examined systematically. Numerical examples illustrate the method.