dioptric power (original) (raw)

Author: the photonics expert (RP)

Definition: the inverse of the focal length

Alternative terms: power, focusing power

Category: article belongs to category general optics general optics

Related: focal length

Units: m−1

Formula symbol: ($\varphi$)

Page views in 12 months: 737

DOI: 10.61835/d8s Cite the article: BibTex BibLaTex plain text HTML Link to this page! LinkedIn

Content quality and neutrality are maintained according to our editorial policy.

What is a Dioptric Power?

The dioptric power of a focusing or defocusing optical element is defined as the inverse of its effective focal length. Sometimes it is just called power, but this is ambiguous because power occurs with various different meanings, e.g. magnification or optical power.

The dioptric power is measured in units of m−1, also called diopters (dpt). It is common to specify the dioptric power of prescription glasses, for example, whereas the focal length is usually specified for standard lenses, microscope objectives and photographic objectives.

In many cases, the dioptric power is a more natural quantity than the focal length because stronger focusing action implies a higher dioptric power but a shorter (smaller) focal length. For example, the dioptric power of the thermal lens in a laser crystal is proportional to the dissipated power. The width of the stability zones of a laser resonator with respect to dioptric power of the thermal lens depends only on the minimum mode radius in the laser crystal and on the optical wavelength, whereas the stability range in terms of focal length has a more complicated dependence.

Some additional aspects come into play when the medium before and after the optical system is not the same. For example, we may consider an underwater camera, where the object side is filled with water, while the interior of the camera is filled with air. In that situation, the front focal length of the camera objective is larger than the back focal length. The dioptric power must be calculated from the effective focal lengths, which is related to the case ($n = 1$). One thus takes the inverse of the back focal length, which is the same as the refractive index of water divided by the front focal length.

The dioptric power of a single interface between two media is the difference of refractive index divided by the radius of curvature of the surface.

The combination of two thin lenses at a close distance (with air or vacuum between them) has a dioptric power which is simply the sum of the powers of the two lenses. If the distance ($d$) is not negligible, the total dioptric power is: \phi = {\phi _1} + {\phi _2} - {\phi _1}\;{\phi _2}\;d$$

Example: Dioptric Power of Prescription Glasses

Simple calculations can be done concerning the required dioptric power of prescription glasses under different circumstances.

A well-functioning human eye can view distant objects with the relaxed eye's lens, but can also accommodate to shorter viewing distances by increasing the dioptric power of the eye. For a minimum viewing distance of 20 cm, for example, the dioptric power needs to be increased by 1 / 20 cm = 5 dpt. Considered in the context of geometrical optics, this is because 5 dpt are required for transforming rays which originate from an object at a distance of 20 cm into parallel rays (as would be obtained for a very distant object).

With increasing age, the eye increasingly loses its capability to accommodate to different distances, i.e., it can vary its dioptric power only in a rather limited range of e.g. 1 dpt width. If the relaxed eye can comfortably see distant objects, for reading text at the distance of only 50 cm, for example, one will require prescription glasses with 1 / 50 cm = 2 dpt, well beyond the remaining accommodation power of the old eye. For reading text on a computer monitor at a more convenient distance of 80 cm, one requires only 1 / 80 cm ≈ +1.2 dpt. However, it may be that the relaxed eye already requires some correction (some positive or negative dioptric power) to comfortably view distant objects, and that correction would also have to be added for reading at shorter distances.

In practice, the situation can become more complicated for various reasons:

The eye may have some astigmatism, which implies that it requires different dioptric powers in different directions. An ordinary spherical lens will provide good enough vision only for sufficiently weak astigmatism.
The two eyes may require different corrections.
The distance between the lens centers for the two eyes should be appropriately adjusted because otherwise one obtains an additional change in viewing direction. That aspect becomes more critical for glasses with large dioptric power.

Frequently Asked Questions

What is a dioptric power?

The dioptric power of an optical element is the inverse of its effective focal length. It quantifies the degree to which the element converges or diverges light.

What is the unit of dioptric power?

The unit of dioptric power is inverse meters (m⁻¹), which are also called diopters (dpt).

Why is dioptric power a useful concept?

It is often more intuitive than focal length, as a stronger focusing action corresponds to a higher dioptric power. Also, the combined power of two thin lenses in close contact is simply the sum of their individual powers.

How is dioptric power used for prescription glasses?

It specifies the refractive correction needed for sharp vision at a target distance. For example, 2 additional diopters are needed for vision at a 50 cm distance instead of infinity.

How can one calculate the total dioptric power of two separated lenses?

For two thin lenses with powers (${\phi _1}$) and (${\phi _2}$) separated by a distance ($d$), the total dioptric power is (${\phi} = {\phi _1} + {\phi _2} - {\phi _1}{\phi _2}d$).

Questions and Comments from Users

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.