Question

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is 25 D. Focal length of each of the convex lens is :

• A. 20 cm
• B. 50 cm
• C. 500 cm
• D. 25 cm

Answer 1

Answer: (A)

20 cm

Answer 2

Total Power of Lenses in Contact:
When lenses are kept in contact, the effective power $P_{eq}$ is the sum of the individual powers of each lens:
$P_{eq} = \sum P_i$

Given that there are 5 identical lenses and the total power is 25 D, we have:
$5P = 25 \implies P = \frac{25}{5} = 5 \, \text{D}$
where $P$ is the power of each individual lens.

Calculate the Focal Length:
The focal length $f$ of a lens is related to its power $P$ by:
$P = \frac{1}{f}$
where $f$ is in meters if $P$ is in diopters (D).

Therefore:
$f = \frac{1}{P} = \frac{1}{5} = 0.2 \, \text{m} = 20 \, \text{cm}$

Conclusion:
The focal length of each convex lens is 20 cm.