The power of a lens is one of the most fundamental yet crucial concepts in optics. Whether you're preparing for board exams, competitive tests like NEET and JEE, or simply want to understand your eyeglass prescription better, this guide breaks down the topic in an easy-to-understand, exam-ready format.
What Is the Power of a Lens?
The power of a lens refers to its ability to converge (bring together) or diverge (spread out) light rays. This ability depends directly on the focal length of the lens.
In simple terms:
- A strong lens bends light more.
- A weak lens bends light less.
Mathematically, the power P of a lens is given by:
P = 1/f,
where f is the focal length in metres.
SI Unit of Lens Power
The SI unit of power of a lens is dioptre (D).
- If a lens has a focal length of 1 metre, its power is 1 D.
- Dioptre is represented as 1D = 1 m⁻¹.
This unit helps opticians and physicists express the lens’s refractive strength.
Convex vs Concave Lenses: How Power Differs
| Lens Type | Nature | Power Sign | Focal Length | Light Behavior |
|---|---|---|---|---|
| Convex Lens | Converging lens | Positive (+) | Shorter f | Converges light rays |
| Concave Lens | Diverging lens | Negative (−) | Shorter f | Diverges light rays |
Example:
- A lens with +2.0 D has a focal length of 0.5 m, and it is convex.
- A lens with −2.5 D has a focal length of −0.4 m, and it is concave.
Visual Clarity: Power & Focal Length
Think of a convex lens like a magnifying glass — it brings objects into focus by converging rays. The shorter the focal length, the more sharply it bends light, hence more power.
A concave lens, on the other hand, spreads rays outward — often used in glasses for short-sightedness (myopia).
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Real-Life Applications of Lens Power
1. Eyeglasses Prescriptions
Eye doctors use the dioptre system to prescribe lenses. A −3.00 D prescription means the patient needs a concave lens for correction.2. Cameras & Telescopes
In professional photography and astronomy, lens power determines clarity and range.3. Microscopes
Objective lenses with different powers (10X, 40X, 100X) help in magnifying specimens at various scales.4. Projectors
High-power lenses are used to focus and project sharp images over distances.Important Formulae at a Glance
| Formula | Description |
|---|---|
| P = 1/f | Power in dioptres (f in metres) |
| f = 1/P | Focal length derived from power |
| D = 100/f(cm) | For focal length in centimetres |
How Opticians Use Power of a Lens
Lens prescriptions are typically written in this format:
- Right Eye (OD): –2.00 D
- Left Eye (OS): +1.50 D
This indicates that the right eye needs a concave lens, while the left eye needs a convex lens.
Lens Power in Combination
When two lenses are placed in contact:
Total Power = P₁ + P₂
If you combine a +2.0 D lens with a –1.0 D lens, the net power is +1.0 D — behaving like a weak convex lens.
People Also Ask (PAA) for Featured Snippets
Q: What is the formula for the power of a lens?
A: Power of a lens is calculated as P = 1/f, where f is the focal length in meters.Q: What is the unit of power of a lens?
A: The SI unit of power of a lens is Dioptre (D).Q: How do you identify if a lens is convex or concave from its power?
A: If the power is positive, it is a convex lens. If it is negative, it is a concave lens.Frequently Asked Questions
What is the power of a lens with 50 cm focal length?
Convert to metres: 50 cm = 0.5 m
So, P = 1 / 0.5 = 2.0 D
If a lens has a power of −4 D, what is its focal length?
f = 1/P = 1/(-4) = −0.25 m
This is a concave lens.
Is a higher dioptre lens more powerful?
Yes, higher dioptre means shorter focal length and more bending power.
What power of lens is used for hypermetropia?
Convex lenses (positive power) are used to correct farsightedness.
