# Optical Forums > General Optics and Eyecare Discussion Forum >  Dioptric power vs. magnification power

## plculver

Does anyone know how to convert diopters to magnification power?  I mean, if I have a 4x magnifying glass, how many diopters is that?  Or if I have a 30 diopter plus lens, what magnification power is it?

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## mlm

For simplicity's sake, it's times 4.

4x magnifier = 16 D
30 D lens = 7.5x

(If I remember right, it's not exactly 4, but it's the easiest way to calculate it quickly.)

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## braheem24

From what I remember there are 2 standards and Asian and a German standard both of which have different conversions but both fall in the 4-5D range.

Good Luck

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## Ginster

Thanks Guy's I was wondering this myself, excellent question!;)

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## Barry Santini

The Scientific conversion: magnification reference (comparative) distance is 25cm (10 inches). 4D = 1X magnification.

This means that a lens that permits an object to be in focus at 10 inches away yields an approximately-equivalent retinal image size to an un-aided eye that focuses at the same distance. 

If there reference distance is changed, say to 8 inches (approx 20 cm), then 5D = 1X magnification

Then, add in marketing by magnifier companies that couldn't explain or find persuasive the concept that a 4D lens only yields 1x mag, and they decided to create the formula:

Magnication (of a simple maginifier) = Dioptric power of lens/ 4 "+" *1* = magnifying power.

In this example, a 4D lens = 2X.

This is all for "linear" magnification.  Angular magnification is something else.

FWIW

Barry

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## xiaowei

> The Scientific conversion: magnification reference (comparative) distance is 25cm (10 inches). 4D = 1X magnification.
> 
> This means that a lens that permits an object to be in focus at 10 inches away yields an approximately-equivalent retinal image size to an un-aided eye that focuses at the same distance. 
> 
> If there reference distance is changed, say to 8 inches (approx 20 cm), then 5D = 1X magnification
> 
> Then, add in marketing by magnifier companies that couldn't explain or find persuasive the concept that a 4D lens only yields 1x mag, and they decided to create the formula:
> 
> Magnication (of a simple maginifier) = Dioptric power of lens/ 4 "+" *1* = magnifying power.
> ...


This IS actually one of the few cases where it´s not (only) marketing, but there is some true optics behind it.;)

The first formula applies to the case, where the eye itself is focussed to infinity. The "+1" enters for the more realistic case, where the eye is already focused to 25cm and you use of the magnifier, meaning you also need to move the object a bit nearer to the lens (In that latter case, actually the distance eye-magnifier lens enters, the "+1" is an approximation for the limiting case where the magnifier lens is straight in front of the eye). 

小卫

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## Barry Santini

> The first formula applies to the case, where the eye itself is focussed to infinity. The "+1" enters for the more realistic case, where the eye is already focused to 25cm and you use of the magnifier, meaning you also need to move the object a bit nearer to the lens (In that latter case, actually the distance eye-magnifier lens enters, the "+1" is an approximation for the limiting case where the magnifier lens is straight in front of the eye). 
> 
> 小卫


This *is* interesting! So, by "straight in front of the eye", do you mean that the magnifier is being used almost as a "loupe" (wherein the magnifying lens is at the plane of the eye, and the object is placed just inside the fcous point of the magnifier/eye combination?)

barry

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## xiaowei

> This *is* interesting! So, by "straight in front of the eye", do you mean that the magnifier is being used almost as a "loupe" (wherein the magnifying lens is at the plane of the eye, and the object is placed just inside the fcous point of the magnifier/eye combination?)
> 
> barry


Yes, basically, if the distance between both lenses is zero and all componenents can be treated as "thin lenses", you can easily see why it increases the magnification by just 1:

If the eye focusses to 25cm instead of inf, the eye lense adds just another 4dpt to the whole power of the system. This is the same overall effect as leaving the eye focussed at inf and using a loupe of 4 more dpt. In the moment the distance is not zero, powers do no longer simply add and things become more complicated, but as long as the distance is small compared to the focal length of the magnifier, it´s a good approximation.

It also means, that a young person can go higher than +1 extra by accommodating stronger when using a loupe (and vice versa for the 40+ generation!:(), it´s just a standard!

小卫

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## Dave Nelson

This is an interesting discussion. What about proximity magnification, also known as "relative distance" magnification. The closer an object gets, the bigger it looks, or the larger the retinal image. Thats how "ready-made" readers work...they are commonly but mistakenly called "magnifiers" by the public. Any magnification they provide is incidental. What they actually do is allow the presbyope to hold the reading material CLOSER, making the image larger, but they allow the wearer to FOCUS the image. Bifocals do the same thing, and hand-held magnifiers do the same again, when they are placed directly in front of the eye. When a hand-held magnifier is held away from the eye and near the object of study, typically reading material, the magnifier is best held at its working distance, This is the same as the focal length, which, as has already been pointed out, is related to its dioptric value, and its magnification. To clarify an important point with hand held magnifiers: If the focal length is 10 centimeters, (4 inches) that means that PARELLEL light rays are brought to a focal plane at 10 centimeters, thus light rays with a vergence equal to 10 cm will leave the magnifier PARELLEL. The end result? Remember this always:
people using a hand-held magnifier at its proper working distance, DO NOT NEED ACCOMODATION or MULTIFOCAL CORRECTION. They will get the best effect looking through the distance part of their prescription, because the light rays are parellel, just as light rays from infinity are held to be.

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## Barry Santini

> Yes, basically, if the distance between both lenses is zero and all componenents can be treated as "thin lenses", you can easily see why it increases the magnification by just 1:
> 
> If the eye focusses to 25cm instead of inf, the eye lense adds just another 4dpt to the whole power of the system. This is the same overall effect as leaving the eye focussed at inf and using a loupe of 4 more dpt. In the moment the distance is not zero, powers do no longer simply add and things become more complicated, but as long as the distance is small compared to the focal length of the magnifier, it´s a good approximation.
> 
> It also means, that a young person can go higher than +1 extra by accommodating stronger when using a loupe (and vice versa for the 40+ generation!:(), it´s just a standard!
> 
> 小卫


Thank you for this terrific clarification and explanation!

barry

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## xiaowei

> This is an interesting discussion. What about proximity magnification, also known as "relative distance" magnification. The closer an object gets, the bigger it looks, or the larger the retinal image. Thats how "ready-made" readers work...they are commonly but mistakenly called "magnifiers" by the public. Any magnification they provide is incidental. What they actually do is allow the presbyope to hold the reading material CLOSER, making the image larger, but they allow the wearer to FOCUS the image. Bifocals do the same thing, and hand-held magnifiers do the same again, when they are placed directly in front of the eye. When a hand-held magnifier is held away from the eye and near the object of study, typically reading material, the magnifier is best held at its working distance, This is the same as the focal length, which, as has already been pointed out, is related to its dioptric value, and its magnification. To clarify an important point with hand held magnifiers: If the focal length is 10 centimeters, (4 inches) that means that PARELLEL light rays are brought to a focal plane at 10 centimeters, thus light rays with a vergence equal to 10 cm will leave the magnifier PARELLEL. The end result? Remember this always:
> people using a hand-held magnifier at its proper working distance, DO NOT NEED ACCOMODATION or MULTIFOCAL CORRECTION. They will get the best effect looking through the distance part of their prescription, because the light rays are parellel, just as light rays from infinity are held to be.


TRUE. This is the case when that extra "+1" does not count/change much, this especially applies to strong magnifiers (10x and up). In any case, the definition of magnification IS actually arbitrary as it compares the (largest) retinal image you could get using the magnifier of an object to the largest image you get when held at the "near point" of your bare eyes, which is simply defined as standaedized 25cm. Young people ot high myopes that can focus to a few cm would actually need a different definition of loupe magnification.

This is different from the magnification of a telecope, which is *absolute* angular magnification, while it again appears in microscopes with visual observation, because defining the magnification of the eyepiece has the same problems. (Not to mention the magnification values given for microscopic images in books or - today - on screens, that often are not really true *absolute* values (what page size/screen size is/was used?), but likely the microscope "was set to 1200x" so the image shown "must be at 1200x too, isn´t it?"

小卫

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## au

about the magnification, is it ok with either aspheric or aspheric lens ?

eg, if pt have +5.00D and pl on Rx, can we calculate the magnification size of image ?

thanks for help.

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## Darryl Meister

You can actually download an article on magnification that I wrote several years ago from this post. The article also explains how magnification is rated.

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## HarryChiling

> You can actually download an article on magnification that I wrote several years ago from this post. The article also explains how magnification is rated.


Just what the doctor ordered thanx Darryl.

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## mwatson817

I am so glad that I found help help here.  There is a study guide out there that says to find the dioptric power of a magnifying glass that one should multiply the "x" power by 2.5, however several sources say to multiply by 4, so thank you all.  

I do have a few questions that I am certain can be answered here.

1.  If an image in a mag lens is clearer at 5cm from the page, what is the mag power of the lens?

2.  If a patient has a 30D hand mag, what distance should they hold it from the page to get the clearest image?

Thanks once again

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## drk

Eliminating accommodation effects and assuming magnifier held at focal plane:
a. 1/5cm = 20 D
F/4 +1 = 6X ("conventional magnification") or F/4 = 5x ("relative magnification")

b. 1/30 D = 3.3 cm

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## heritage972

Brief comment on the statement by Dr. Santini:  This is all for "linear" magnification.  Angular magnification is something else."
Actually the magnification discussed is angular magnification.  That is what the patient is interested in.
Everything I see on this thread correctly points out that the formula assumes a near point (NP) of 25 cm.  For an older patient, typically with a larger NP, the generalization is  angular magnification = NP x diopter + 1.
The equations for this, assuming a thin lens, are in many references on the web, e.g. http://www.phy-astr.gsu.edu/cymbalyuk/Lecture4.pdf (I have no association with this university, this was just the first reference that popped up on google.)  There is a small typo in the formula for magnification, where the symbol 'q' should be 'f' but everything else is OK.  Picture are nice.

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## Darryl Meister

> Everything I see on this thread correctly points out that the formula assumes a near point (NP) of 25 cm.  For an older patient, typically with a larger NP, the generalization is  angular magnification = NP x diopter + 1


Just keep in mind that the formula for _conventional_ or _maximum_ magnification, F / 4 + 1, assumes that the image vergence leaving the magnifier will be equal to the 25 cm reference distance. So I believe that the patient will need to either wear bifocals with close to a +4.00 D add power or make up the difference with ocular accommodation (if available).

The attached article provides some of the specific mathematics involved:

Best regards,
Darryl

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