Question

Two thin lenses of focal lengths $20cm$ and $25cm$ are placed in contact. The effective power of the combination is

• A. $9D$
• B. $2D$
• C. $3D$
• D. $7D$

Answer 1

Answer: (A)

$9D$

Given: $f_1=20cm$ and $f_2=25cm$

The focal length of the combination of lenses:

$\Rightarrow \frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$

$\Rightarrow \frac{1}{F}=\frac{1}{20}+\frac{1}{25}$

$\Rightarrow F=\frac{100}{9}$ $cm=\frac{1}{9}$ $m$

Effective power of the lens, $P=\frac{1}{F}=\frac{1}{1/9}=9D$