A refracting telescope uses two thin converging lenses. The larger lens acts as the objective and the smaller one as the eyepiece. The telescope is adjusted so that the final image is formed at infinity (normal adjustment).
(i) Draw a clearly labelled ray diagram of the telescope in this adjustment, marking the focal points of both lenses and the position of the intermediate image.
(ii) Starting from the geometry of the diagram, derive an expression for the magnifying power M of the telescope. Show that it can be written only in terms of the focal lengths of the two lenses.
(iii) Further show that the separation L between the objective and the eyepiece equals the sum of their focal lengths when the telescope is in normal adjustment.
(iv) State what the sign of the magnifying power conveys about the nature of the final image produced by the telescope.