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Question

(a) What do you understand by the power of a lens? Name one factor on which the power of a lens depends.
(b) What is the unit of power of a lens? Define the unit of power of a lens.
(c) A combination of lenses for a camera contains two converging lenses of focal lengths 20 cm and 40 cm and a diverging lens of focal length 50 cm. Find the power and focal length of the combination.A optical instrument in which the above arrangement of convex lens is used is a convex lens used to burn paper by focusing sunlight.

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Solution

(a) The power of a lens is a measure of the degree of convergence or divergence of light rays falling on it. It is defined as the reciprocal of the focal length of a lens in metres.
i.e., Power = 1focal length of lens (in metre)

Therefore, the power of a lens depends on the focal length.

(b) The unit for the power of a lens is a dioptre (D). One dioptre is the power of a lens whose focal length is 1 metre.
(c) Focal length (f1) of the 1st converging lens = 20 cm = 0.2 m
Focal length (f2) of the 2nd converging lens = 40 cm = 0.4 m
Focal length (f3) of the diverging lens = -50 cm = -0.5 m (negative sign due to sign convention)
Power = 1focal length of lens (in metre)

Power (P1) of 1st lens = 10.2=5 D

Power (P2) of 2nd lens = 10.4=2.5 D

Power (P3) of diverging lens = 1-0.5=-2 D

Net power of the combination = P1 + P2+ P3 = 5 + 2.5 + (-2) = 5.5 D

Net focal length of the combination = 1net power=15.5=0.1818 m = 18.18 cm.

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