A concave lens of focal length $25 c m$ and a concave lens of focal length $25 c m$ and a concave lens of focal length $10 c m$ are placed in close contact with one another.
(a) What is the power of this combination ?
(b) What is the focal length of this combination ?
(c) Is this combination converging or diverging ?

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Solution

$f_{1} = 25 c m = 0.25 m$
$P_{1} = \frac{1}{f_{1}} = \frac{1}{0.25} = 4 D$
$f_{2} = - 10 c m = - 0.1 m$
$P_{2} = \frac{1}{f_{2}} = \frac{1}{- 0.1} = - 10 D$
(a) Power of the combination :
$P = P_{1} + P_{2}$
$= 4 D + (- 10 D)$
$= - 6 D$
(b) Focal length of the combination:
$f = \frac{1}{P} = \frac{1}{- 6} = - 0.1666 m = - 16.66 c m$
(c) The combination has negative focal length , so it is diverging.

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f1=25cm=0.25m P1=1f1=10.25=4D f2=−10cm=−0.1m P2=1f2=1−0.1=−10D (a) Power of the combination :P=P1+P2 =4D+(−10D) =−6D (b) Focal length of the combination:f=1P=1−6=−0.1666m=−16.66cm (c) The combination has negative focal length , so it is diverging.