Power of a Lens: Is it Always Positive? | Concave, Convex & Combinations

Understanding Lens Power

Lens power is a fundamental concept in optics that determines the converging or diverging ability of a lens. The power of a lens is defined as:

$$P = \frac{1}{f}$$

where $P$ is power in diopters (D) and $f$ is focal length in meters

📏 Sign Convention (Cartesian):

Focal length is positive for convex (converging) lenses
Focal length is negative for concave (diverging) lenses
Power is positive for converging lenses
Power is negative for diverging lenses

Convex Lens Converging

Convex Lens - Positive Power

🔍 Characteristics:

• Thicker at center than at edges

• Converges parallel light rays

• Focal length (f) > 0

• Power (P) > 0 (Always positive)

• Forms real and virtual images depending on object position

🎯 Example Calculation:

Problem: A convex lens has focal length 20 cm. Find its power.

Step 1: Convert focal length to meters: $f = 20\text{ cm} = 0.2\text{ m}$

Step 2: Apply power formula: $P = \frac{1}{f} = \frac{1}{0.2}$

Step 3: Calculate: $P = +5\text{ D}$

Positive power indicates converging nature

Concave Lens Diverging

Concave Lens - Negative Power

🔍 Characteristics:

• Thinner at center than at edges

• Diverges parallel light rays

• Focal length (f) < 0

• Power (P) < 0 (Always negative)

• Always forms virtual, erect, and diminished images

🎯 Example Calculation:

Problem: A concave lens has focal length 25 cm. Find its power.

Step 1: Convert focal length to meters: $f = -25\text{ cm} = -0.25\text{ m}$

Step 2: Apply power formula: $P = \frac{1}{f} = \frac{1}{-0.25}$

Step 3: Calculate: $P = -4\text{ D}$

Negative power indicates diverging nature

Combination Advanced

Combination of Thin Lenses in Contact

📐 Formula Derivation:

Step 1: For lenses in contact, the equivalent focal length is given by:

$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} + \frac{1}{f_3} + \cdots$

Step 2: Since $P = \frac{1}{f}$, we get:

$P = P_1 + P_2 + P_3 + \cdots$

Step 3: The power of combination is the algebraic sum of individual powers

🎯 JEE Application Example:

Problem: A convex lens of power +5D is placed in contact with a concave lens of power -3D. Find the power of combination.

Solution: Using combination formula:

$P = P_1 + P_2 = (+5) + (-3) = +2\text{ D}$

The combination acts as a converging lens of power +2D

🚀 Problem-Solving Strategies

Key Points to Remember:

Power is NOT always positive - depends on lens type
Unit of power is diopter (D) = m⁻¹
Always convert focal length to meters
For combinations: algebraic sum of powers

JEE Exam Tips:

Watch sign conventions carefully
Practice combination problems with mixed lenses
Remember: Higher power = stronger lens
Check if answer makes physical sense

Advanced Applications Available

Includes lenses not in contact, power of mirror-lens combinations, and JEE Advanced level problems

📝 Quick Self-Test

Try these JEE-level problems to test your understanding:

1. A lens has power -2.5D. Is it converging or diverging? What is its focal length?

2. Two convex lenses of powers +4D and +6D are placed in contact. Find the power of combination.

3. A convex lens (P=+5D) and concave lens (P=-7D) are combined. What is the nature of combination?

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