Difference between revisions of Diopters
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Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power | Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of the [[focal length]] in meters . The most common unit symbol for diopters is dpt, D, or m <sup> - 1 </sup> . | ||
<math>P = \frac{1}{f} = - \frac{1}{d}</math> | <math>P = \frac{1}{f} = - \frac{1}{d}</math> | ||
* We use the [[ cm measurement ]] to calculate the diopters needed to correct [[ refraction]] of the eye. If you can see clearly at 50cm, your diopters will be <math> - \frac{1}{0.50}= - 2 dpt</math> OR <math> - \frac{100}{50}= - 2 dpt</math>. | * We use the [[ cm measurement ]] to calculate the diopters needed to correct [[ refraction]] of the eye. If you can see clearly at 50cm, your diopters will be <math> - \frac{1}{0.50}= - 2 \ \text{dpt}</math> OR <math> - \frac{100}{50}= - 2\ \text{dpt}</math>. | ||
* Serial lenses add their powers: if you wear - 2 diopter contact lenses ( [[ vertex distance | adjusted for glasses strength ]] ) and put on reading glasses +1 diopter on the lenses you actually wear - 1 diopter. | * Serial lenses add their powers: if you wear - 2 diopter contact lenses ( [[vertex distance|adjusted for glasses strength]] ) and put on reading glasses +1 diopter on the lenses you actually wear - 1 diopter. | ||
**There are a few caveats such as vertex distance because moving the lens further away effectively gives you a weaker negative lens or a stronger positive lens. There's also shift, which induces a prism when the lens is moved sideways. These effects become negligible for weaker lenses. | **There are a few caveats such as vertex distance because moving the lens further away effectively gives you a weaker negative lens or a stronger positive lens. There's also shift, which induces a prism when the lens is moved sideways. These effects become negligible for weaker lenses. | ||
* According to the thin lens sign convention, the negative focal power is divergent and the positive focal power is convergent. | * According to the thin lens sign convention, the negative focal power is divergent and the positive focal power is convergent. | ||
** A lens with a negative diopter sign compensates for [[ myopia ]] while a lens with a positive diopter sign compensates for [[ hyperopia ]] . | ** A lens with a negative diopter sign compensates for [[myopia]] while a lens with a positive diopter sign compensates for [[hyperopia]] . | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ Approximate categorizations of myopia by [[ spherical ]] lens power : | |+ Approximate categorizations of myopia by [[spherical]] lens power : | ||
| - | | - | ||
| 0.00 to - 0.50 dpt || Not really considered myopic, probably doesn't need glasses | | 0.00 to - 0.50 dpt || Not really considered myopic, probably doesn't need glasses | ||
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==Technical Details== | ==Technical Details== | ||
This section is for the math - savvy people. It explains the concepts in more detail, but his knowledge is not strictly necessary to use the Reduced Lens method. | |||
=== Thin lens equation === | === Thin lens equation === | ||
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{{ See also |Astigmatism#Spherical equivalent }} | {{ See also |Astigmatism#Spherical equivalent }} | ||
Calculating the average value over all angles using an integral, the result <ref>Just integrate one or two periods: https://www.wolframalpha.com/input/?i=average+de+%28sin+x%29%5E2+de+0+à+2+pi</ref> is | |||
<math>P_{\text{avg}} = \lim_{T \to \infty} \frac{ 1}{2T} \int_{ - T}^{T} P_{\text{cyl}} (\sin{t})^2 \,dt = \frac{1}{2} P_{\text{cyl}}</math> | <math>P_{\text{avg}} = \lim_{T \to \infty} \frac{ 1}{2T} \int_{ - T}^{T} P_{\text{cyl}} (\sin{t})^2 \,dt = \frac{1}{2} P_{\text{cyl}}</math> | ||
C' is why the spherical equivalent has power equal to half the power of the cylinder. | |||
==== Adding/Combining Lenses ==== | ==== Adding/Combining Lenses ==== | ||
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See [[Vertex distance#Calculation|Vertex distance -> Calculation]] | See [[Vertex distance#Calculation|Vertex distance -> Calculation]] | ||
== References == | == References == | ||