(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 perging lens of focal length 50 cm. Find the power and focal length of the combination.

 Focal lengths, $f_2$ =  $+$40 cm = $+$0.4 m   $(\because lens\ is\ converging)$

 Focal lengths, $f_3$ =  $-$50 cm = $-$0.5 m    $(\because lens\ is\ diverging)$

To find: Power, $P$ and focal length, $f$ of the combination of the lenses.

Solution:

Power of the lens is given by-

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

Substituting the given value we get-

$P_1=\frac {1}{f_1}=\frac {1}{0.2}=\frac {10}{2}=+5D$

$P_2=\frac {1}{f_2}=\frac {1}{0.4}=\frac {10}{4}=+2.5D$

$P_3=\frac {1}{f_3}=\frac {1}{-0.5}=-\frac {10}{5}=-2D$

The power of the combination of lenses are-

$P=P_1+P_2+P_3$

$P=5+2.5+(-2)$

$P=7.5-2$

$P=+5.5D$

Now, the focal length of the combination of lenses are-

$f=\frac {1}{P}=\frac {1}{5.5}=\frac {10}{55}=+0.1818m=+18.18cm$

Thus, the power and focal length of the combination of lenses are +5.5 D and +18.18 cm respectively.