Two thin convex lenses of focal length 20 cm and 25 cm are placed at a finite distance apart. The power of the combination is 8D. Distance between the lenses is:
Answer & explanation
Correct answer: option 1
Here, f1 = 20 cm, f2 = 25 cm, P = 8D
Focal length of combination = $\frac{1}{8}$ m = $\frac{100}{8}$ cm
Now, using $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1 f_2}$
(where d is the distance between lenses),
we get $\frac{8}{100}=\frac{1}{20}+\frac{1}{25}-\frac{d}{20 \times 25}$
$\Rightarrow \frac{d}{500}=\frac{1}{20}+\frac{1}{25}-\frac{8}{100}=\frac{5+4-8}{100}=\frac{1}{100}$
or d = $\frac{500}{100}$ = 5 cm