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What is the focal length of a lens with power -2.0 D?

0.5 m

2 m

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics

Option A

0.5 m

Quick Summary:

The focal length of a lens is the reciprocal of its power when measured in meters · Given a power of $-2.0$ D, the focal length is calculated as $-0.5$ m, where the negative sign indicates a concave (diverging) lens.

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of power as the 'bending strength' of the lens; a higher number means more bending, and because they are inverse, a stronger lens actually has a shorter focal distance.

🧠 Memory Mnemonic / Shortcut Aid

P = 1/f (Power is the reciprocal of focus)

🔢 Key Formulas

$P = \frac{1}{f}$ — Power of a lens in Diopters where $f$ is in meters

$f = \frac{1}{P}$ — Calculation of focal length from power

⚙️ Working Principle

The relationship between power $P$ and focal length $f$ is defined by the lens power formula · Since $P = \frac{1}{f}$ , the focal length $f$ is derived as $f = \frac{1}{P}$ . The unit of power is Diopter (D), which is equivalent to $m^{-1}$ .

📌 Key Points

▸
A positive power indicates a convex lens (converging).
▸
A negative power indicates a concave lens (diverging).
▸
1 Diopter is defined as the power of a lens with a focal length of 1 meter.

✅ Advantages

▸
Diopters provide a simple additive way to calculate the power of combined lenses: $P_{total} = P_1 + P_2 +...$

❌ Disadvantages / Limitations

▸
This formula assumes the lens is thin and the medium is air; variations occur in dense media.

🛠️ Applications / Uses

▸
Prescription spectacles for myopia (nearsightedness) use concave lenses with negative power.
▸
Prescription spectacles for hypermetropia (farsightedness) use convex lenses with positive power.

📄 Additional Information

▸
The focal length is $-0.5$ m, which is equivalent to $-50$ cm.
▸
Wrong options: Options C and D are mathematically incorrect based on the inverse relationship $f = 1/P$ .

📊 Diagram / Illustration

✅

A is correct — The focal length is the reciprocal of the power, resulting in $-0.5$ m for a power of $-2.0$ D.

Core Concepts Used

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Optics Lens Power Focal Length

💡 EXAM TIP

Always pay attention to the sign in optics problems: negative power always signifies a diverging (concave) lens, while positive signifies a converging (convex) lens.

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