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D (diopters)
0.5
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50
cm
500
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D (diopters)
0.5
m
50
cm
500
mm
1
The Optical Power Calculator converts the focal length of a lens or curved mirror into optical power measured in diopters (D). Optical power quantifies how strongly an optical element converges or diverges light and is the standard unit used by optometrists, ophthalmologists, and optical engineers worldwide.
The optical power of a lens is defined as the reciprocal of its focal length in meters: $$P = \frac{1}{f}$$ where P is in diopters (D) and f is in meters. A converging (convex) lens has a positive focal length and positive power, while a diverging (concave) lens has a negative focal length and negative power. One diopter equals the power of a lens that brings parallel light to a focus at exactly one meter.
In ophthalmology, eyeglass prescriptions are written in diopters. A person who is nearsighted (myopic) receives a prescription with negative diopters (diverging correction), while a farsighted (hyperopic) person receives positive diopters (converging correction). Common prescriptions range from −0.25 D for mild myopia to −12 D or more for severe myopia. The diopter system makes it easy to combine lenses: the total power of two thin lenses in contact is simply the sum of their individual powers, Ptotal = P₁ + P₂.
Camera lenses are usually specified by focal length in millimeters (e.g., a 50 mm portrait lens), but optical designers often work in diopters when analyzing multi-element lens systems. Microscope and telescope optics are similarly analyzed using optical power to determine magnification and field of view.
This calculator accepts focal lengths in meters, centimeters, or millimeters and outputs the optical power in diopters along with the focal length in all three unit systems. It also indicates whether the optical element is converging (positive) or diverging (negative), providing a complete characterization at a glance.
Understanding optical power is essential for anyone working with lenses, from optometry students learning to write prescriptions to physics students solving lens combination problems to photographers selecting the right focal length for their creative vision.
The optical power of a thin lens or curved mirror is defined as the reciprocal of the focal length when the focal length is expressed in meters:
$$P = \frac{1}{f}$$
The unit of optical power is the diopter (D), where 1 D = 1 m⁻¹.
Sign convention:
Unit conversion: If the focal length is provided in cm or mm, it is first converted to meters:
$$f_{\text{m}} = f_{\text{cm}} / 100 = f_{\text{mm}} / 1000$$
Combining lenses: For two thin lenses in contact, the combined power is:
$$P_{\text{total}} = P_1 + P_2 = \frac{1}{f_1} + \frac{1}{f_2}$$
A high diopter value (e.g., +10 D) means a short focal length (0.1 m) and strong convergence—typical of magnifying glasses and strong reading lenses. Low diopter values (e.g., +0.5 D) mean a long focal length (2 m) and weak convergence. Negative values indicate a diverging element. In eyeglass terms, −2 D means mild myopia correction, while −8 D indicates significant myopia.
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A lens with a 50 cm focal length has an optical power of +2.0 D. This is a typical reading glasses strength for mild presbyopia (age-related farsightedness).
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A classic 50 mm camera lens has an optical power of +20 D. This high diopter value reflects the strong convergence needed to form a sharp image on a sensor just centimeters from the lens.
A diopter (D) is the SI-derived unit of optical power. It is defined as the reciprocal of the focal length in meters: 1 D = 1/m. A lens with a focal length of 1 meter has a power of 1 diopter. The diopter is named after the ancient Greek optical instrument dioptra and is used universally in optometry and optics.
Diopters have a practical advantage: the powers of thin lenses in contact simply add together. If an eye needs −3 D correction and −1 D for astigmatism, the total is −4 D. This additive property makes prescriptions easy to combine and adjust. Focal lengths, being reciprocals, do not add as simply.
A negative diopter value indicates a diverging (concave) lens. In eyeglass prescriptions, negative diopters correct myopia (nearsightedness) by spreading light rays slightly before they enter the eye, moving the focal point back onto the retina.
Yes. A curved mirror also has optical power. A concave mirror with focal length f has power P = 1/f (positive, converging), and a convex mirror has negative power (diverging). The formula is identical to that for lenses.
A flat (plane) surface has an infinite focal length, so its optical power is 1/∞ = 0 diopters. It neither converges nor diverges light. This is why a flat window does not magnify or distort images (ignoring thickness effects).
For two thin lenses placed in direct contact, the combined optical power is simply the sum: Ptotal = P₁ + P₂. For example, a +3 D and a −1 D lens in contact yield +2 D. If the lenses are separated by a distance d, the combination formula becomes P = P₁ + P₂ − d·P₁·P₂.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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