Question: Five identical convex lenses are placed one after the other in close contact. The power of this arrangement is 25 D. Then, what is the power of one such lens?
Options:
- 10 D
- 5 D ✅
- 125 D
- 20 D
Learn how to calculate the power of a convex lens when multiple lenses are placed in contact. This JEE Main 2024 Physics question includes a detailed explanation, key concepts, formulas, and additional practice problems to strengthen your understanding of optics.
JEE Main 2024 Physics Question with Solution
🔹 Understanding Power of a Lens
- The power (P) of a lens is defined as the reciprocal of its focal length ($f$) in meters: $P = \frac{1}{f}$
- When multiple lenses are placed in close contact, their combined power is the algebraic sum of their individual powers: $$P_{total} = P_1 + P_2 + P_3 + … + P_n$$
🔹 Applying the Formula to the Given Problem
We are given five identical convex lenses placed in close contact.
The total power of the system is given as 25 D.
Since all the lenses are identical, each lens contributes P to the total power: $$P_{total} = 5 \times P $$
$$25 = 5P$$ $$P = \frac{25}{5} = 5 D$$
Thus, the power of one such lens is 5 D.
Final Answer: ✅ 5 D
Important Points to Remember
✔ Power of a convex lens is positive, whereas for a concave lens, it is negative.
✔ Focal length (f) and power (P) are inversely proportional: A smaller focal length means higher power.
✔ When multiple lenses are in contact, their powers add up algebraically.
✔ Power is measured in Diopters (D), with the unit m⁻¹.
📌 Additional Practice Questions
🔹 Question 1: Two convex lenses of power 4D and 6D are placed in contact. Find the total power of the system.
🔹 Question 2: A concave lens of power -3D is placed in contact with a convex lens of power 7D. What is the effective power of the system?
🔹 Question 3: If a convex lens has a focal length of 20 cm, find its power.
Do You Know? 🤔
💡 The human eye lens is a convex lens with adjustable focal length, helping us focus on objects at different distances.
💡 Microscopes and telescopes use a combination of convex and concave lenses to magnify images.
💡 The lens formula $$\frac{1}{f} = \frac{1}{v} – \frac{1}{u}$$ is used to calculate the image position.
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