The degree of convergence or divergence of light rays achieved by a lens is expressed in terms of its power. The power, $P$ of a lens is given by the relation,

$P = \frac{1}{f}$

where, $f$ is the focal length of the lens in metres.

Many optical instruments use a number of lenses. These lenses are combined to increase the magnification and sharpness of the images produced. The resultant or net power of the combination of lenses placed in contact with each other is given by the algebraic sum of the individual powers of each of the lenses. If the individual powers of two lenses are $P_{1}$ and $P_{2}$ , the resultant power, $P$ is given by

$P = P_{1} + P_{2}$

The focal length, $f$ of the combination of two lenses of focal lengths $f_{1}$ and $f_{2}$ is given by

$f = \frac{f_{1} f_{2}}{f_{1} + f_{2}}$

Suppose you are given three lenses $- A, B$ and $C$ with focal lengths $10 cm, 20 cm$ and $30 cm$ . $A$ and $B$ are convex lenses whereas $C$ is a concave lens. The three lenses are kept in contact with each other.

On the basis of the above information and what you have studied in the course, answer the following questions:

The combination behaves as a

Question

Column I	Column II
(a) Virtual, upright and larger than the object	(p) At $2 F_{1}$
(b) Real, inverted and larger than the object	(q) Beyond $2 F_{1}$
(c) Real, inverted and of the same size as the object	(r) Between $F_{1}$ and $2 F_{1}$
(d) Real, inverted and smaller than the object	(s) Between $F_{1}$ and the optical centre

Important Questions on Light - Reflection and Refraction