Question

A convex lens of focal length 10 cm is placed in contact with a concave lens of focal length 20 cm. The focal length of this combination of lenses will be:
(a) +10 cm
(b) +20 cm
(c) −10 cm
(d) −20 cm

Answer 1

-10 is the answer....

Answer 2

The focal length of this combination of lenses will be +20 cm.

Explanation:

It is given that,

Focal length of a convex lens, f = +10 cm

Focal length of the concave lens, f' = -20 cm

Let P and P' are the power of the convex and concave lens respectively. So,

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

$P=\dfrac{1}{10}$

P = 0.1 D

And

$P'=\dfrac{1}{f'}$

$P'=\dfrac{1}{-20}$

P' = -0.05 D

Let p is the power of the combination of lenses such that,

$p=P_1+P_2$

$p=0.1+(-0.05)$

p = 0.05 D

Let F is the focal length of this combination of lenses. it is given by :

$F=\dfrac{1}{p}$

$F=\dfrac{1}{0.05}$

f = 20 cm

So, the focal length of this combination of lenses will be +20 cm. Hence, this is the required solution.

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