(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) Power of a lens is a measure of the degree of convergence or divergence of light rays falling in it.
Power of a lens depends on its focal length.
(b) Unit of power of a lens is dioptre.
One dioptre is the power of a lens whose focal length is 1 metre.
(c) f1 = 20 cm = 0.2 m
\(P_1\) = \(\frac{1}{f_1}\) = \(\frac{1}{0.2}\) = +5D
f2 = 40 cm = 0.4 m
\(P_2\) = \(\frac{1}{f_2}\) = \(\frac{1}{0.4}\) = +2.5D
f3 = -50 cm = -0.5 m
\(P_3\) = \(\frac{1}{f_3}\) = \(\frac{1}{-0.5}\) = -2D
Power of the combination
P = P1 + P2 + P3
= +5D + 2.5D + (-2D)
= +5.5D
Focal length of the combination
f = \(\frac{1}{P}\) = \(\frac{1}{+5.5}\)
= +0.1818M
= +18.18 cm