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:

Solution

Physics sir · 3 steps

Lenses in contact just add their powers, so share the 25 D equally among the five lenses.

1. Powers add. For thin lenses kept in contact, the power of the combination is the sum of the individual powers. Five identical lenses each of power P give 5P.

   P_(eq) = 5P = 25 D ⇒ P = 5 D

2. Power to focal length. Power in dioptre is the reciprocal of focal length in metres: f = 1/P = 1/5 m = 0.2 m.
3. So. Each convex lens has f = 20 cm, which is option (b).

The idea to keep. For lenses in contact, add powers, not focal lengths. Always convert with f = 1/P in metres, and only then change to centimetres.

Answer from the NTA final answer key. Solution by PrepWiser.