1. What power of a lens means
The power of a lens tells me how strongly the lens bends (converges or diverges) light. A lens with high power bends light a lot, while a lens with low power bends light only slightly.
This idea is especially useful in eyeglasses, microscopes and other optical systems where small changes in bending can make a big difference.
2. Definition of power
Power is defined as the reciprocal of focal length (in metres):
\( P = \dfrac{1}{f} \)
Here:
- \(P\) = power of the lens
- \(f\) = focal length in metres
Because power is the inverse of focal length, a smaller focal length means higher power.
3. Unit of power: dioptre
The SI unit of power is the dioptre (D). One dioptre means the lens has a focal length of 1 metre.
\( 1\,D = 1\,\text{m}^{-1} \)
If the focal length is shorter, the power increases. For example, a focal length of 0.5 m corresponds to:
\( P = \dfrac{1}{0.5} = 2\,D \)
4. Sign convention for power
The power of a lens follows the sign used for focal length:
- Convex lens → focal length positive → power positive
- Concave lens → focal length negative → power negative
So the sign of the power immediately tells me whether the lens is converging or diverging.
5. How power helps in real situations
Power is more convenient than focal length when dealing with eyeglasses or combined lens systems. It is easier to say “+2 D lens” than “lens with focal length 0.5 m”.
A positive number means the lens helps converge light (used for hypermetropia). A negative number means the lens diverges light (used for myopia).
6. Combination of lens powers
When two thin lenses are placed close to each other, their total power is simply the sum of their individual powers:
\( P_{\text{total}} = P_1 + P_2 \)
This rule makes calculations for optical instruments much simpler.
7. A simple example
If a convex lens has focal length \(f = +25\,\text{cm} = +0.25\,\text{m}\):
\( P = \dfrac{1}{0.25} = +4\,D \)
So it is a +4 dioptre lens.
If a concave lens has \(f = -50\,\text{cm} = -0.5\,\text{m}\):
\( P = \dfrac{1}{-0.5} = -2\,D \)
This is a -2 dioptre diverging lens.
8. Where I see lens power being used
Lens power appears in many optical systems and devices:
- Eyeglasses and contact lenses (power written as +D or –D)
- Ophthalmology prescriptions
- Magnifying glasses
- Microscope objectives
- Projector and camera lenses
Knowing the power helps me understand how strongly the lens bends light and what type of image it will form.