A thin lens is placed with its optical centre at the origin on the principal axis, the incident light being taken to travel from left to right. Using the Cartesian sign convention, answer the following questions without performing any numerical calculation.
(a) For a converging lens that produces a real image on a screen to the right of the lens, state with reasons the algebraic signs (positive or negative) of:
(i) the object distance u, (ii) the image distance v, (iii) the focal length f.
(b) For a diverging lens that produces a virtual image on the same side as the object, state with reasons the algebraic signs of u, v and f.
(c) Explain how the sign of the linear magnification m indicates whether the image is erect or inverted in each of the above two situations.