Many optical instruments consist of a number of lenses. They are combined to increase the magnification and sharpness of the image. The net power (P) of the lenses placed in contact is given by the algebraic sum of the powers of the individual lenses $\mathrm{P}_1, \mathrm{P}_2, \mathrm{P}_3 \ldots$ as $\mathrm{P} = \mathrm{P}_1 + \mathrm{P}_2 + \mathrm{P}_3\ldots$ This is also termed as the simple additive property of the power of lens, widely used to design lens systems of cameras, microscopes and telescopes. These lens systems can have a combination of convex lenses and also concave lenses. (a) What is the nature (convergent / divergent) of the combination of a convex lens of power $+4 \mathrm{D}$ and a concave lens of power $-2 \mathrm{D}$ ? (b) Calculate the focal length of a lens of power $-2 \cdot 5 \mathrm{D}$ . (c) Draw a ray diagram to show the nature and position of an image formed by a convex lens of power $+0 \cdot 1 \mathrm{D}$ , when an object is placed at a distance of $20 \mathrm{cm}$ from its optical centre. OR (c) How is a virtual image formed by a convex lens different from that formed by a concave lens? Under what conditions do a convex and a concave lens form virtual images?