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

The Correct Option is A

Total Power of Lenses in Contact:
The effective power \( P_{eq} \) of lenses in contact is the sum of their individual powers:
\[ P_{eq} = \sum P_i \]

For 5 identical lenses with a total power of 25 D:
\[ 5P = 25 \implies P = \frac{25}{5} = 5 \, \text{D} \]
Here, \( P \) denotes the power of a single lens.

Calculate Focal Length:
The relationship between power \( P \) (in diopters) and focal length \( f \) (in meters) is:
\[ P = \frac{1}{f} \]

Consequently:
\[ f = \frac{1}{P} = \frac{1}{5} = 0.2 \, \text{m} = 20 \, \text{cm} \] 

Conclusion:
Each convex lens has a focal length of 20 cm.