# Finding your differentials reduction through MATH ➕

Can I get some second opinions on what I’ve written here: https://wiki.endmyopia.org/wiki/Differentials#Complicated_way_with_math

I’m fairly sure it checks out.

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The math is fine. I would add that even if the math checks out, personal preference / work setup / whatever can change this, especially if you have complex prescription. So while theoretically the math is correct, the differential may not be comfortable and you need a bit different, so experimenting is needed.

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One note under “the simple way” it says to reduce more if you are further from the screen. Pretty sure you mean less. Otherwise looking great, I am excited about this wiki, wish it had existed when I was starting out!

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Hmm I did another take and something is not right. My full prescription is -3 (both based on Snellen and based on cm, I’m measured right now again, just to make sure I don’t have ciliary spasm). Currently I’m using -1 differential. That should mean that my edge of blur with them is 50 cm (I get -2 with the calculator if I input 50 cm and -3 - -2 = -1), but practically my edge of blur is clearly about 40 cm with this differential.

Can someone else check this too? In theory I don’t find any problem in the math, but the practice says otherwise.

Edit: did a try, I get 50 cm with -1.25 differential and about 60 cm with -1.5 differential. So the math seems to be:
(full prescription) - (number from the calculator) - 0.25 for me. Though I’m not sure why. Maybe vertex distance which @Lajos mentioned in one of his topic? ( How To: Choose Differentials Lens Power )
If I check the math based on that then I have to correct the -1 with the vertex distance, so: -1/(1- -0.015*-1) which is -1.015 which still not correct. Nor for -1.5 where I get -1.53

compare it to my topic that David linked to see if it checks out. you don’t need any link to any calculator, you can use windows calc or your smartphone if you understand the maths

also wondering why you did a new take on a perfectly good how to

vertex distance will not make much difference below around -4 D (i.e. low myopia)

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I also take the distance from the lens to my eye into account.
@halmadavid i am not sure this is the problem in your case, but would explain at least part of the difference between your measurement without glasses vs with glasses.

Example:
Without glasses. I measure 20cm to blur horizon. so that means that i should get 100/20 = 5D glasses for my full prescription? No, because the lens will be ~2cm from my eye, so i need to subtract that from my cm measurement.
20cm - 2cm = 18cm => 100/18 = 5.55D for full correction.

Let’s do another example with the numbers from @halmadavid.
If your full prescription is -3D based on cm, that means that you measured 100/3 = 33.33 cm
33.33cm - 2cm = 31.33cm => 100 / 31.33 = 3.19D
you are using -1D for diffs so:
-3.19 - (-1) = -2.19 => 100 / -2.19 = 45.6cm
So you should see clearly up to 45.6cm with your diffs. not 50cm.
So by taking into account the distance of the lens from your eye, you are taking that 5cm difference into account when converting cm to Diopters.

Of course, the lower the myopia the more negligible those 2cm become.
For high myopia, this is critical. as you can see, with 5D you can be inacurate by more than 0.5D!!!

Definitely didn’t read this before writing what I did. Maybe you or someone else should add it in?

tsk tsk, posting in how to without checking a few topics further down

I like the way you capitalised MATH like it’s some big scary thing that you would use as a last resort haha , also in the UK don’t we say maths instead? or you tryina make it USA-friendly

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With 2 cm reduction from the measured cm distance the math is correct, though I would calculate it this way:
Measured 33 cm - 2 cm = 31 cm -> with Endmyopia calculator: 3.25D
Want 50 cm, put into calculator -> -2 D

-3.25 D - (-2 D) = -1.25 which actually gives me 50 cm based on measurement (measuring from my eye with glasses on)

So @NottNott: maybe what need to added to the wiki is that unless you are 100% sure what you full prescription is (verified by optometrist or whatever), used the cm measurement - 2 cm for calculating for differentials.

@Lajos: your how-to is a bit advanced I think. If we want a wiki page with simple instruction for new / beginner users how to calculate differentials, it’s a bit too heavy in my opinion. So some rephrasing is necessary anyways.
Also I don’t get the same result with your calculations as if I do as I’ve written in the beginning of the post.

I like the way MATH just sounds like a hammer falling down onto you. Idk

I think if I write this it’ll probably get lost in translation between what you’ve written here and are trying to convey, and what I’ll end up writing. Recommending you can make a wiki account and edit yourself

busy time for me right now, but when it quietens down a bit I plan on making a wiki account for such editing…

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I think a slight feeling or almost like a hunch that you want to make me a wiki account and edit it myself… (did )

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To be pedantic… using math doesn’t mean typing numbers into an online gadget ! I’d be inclined to actually show the maths - all the gadget is doing is calculating the reciprocal and rounding. 100/60 is 1.6667 which you have to round to the nearest available optical lens strength - 1.50 (which is equivalent to 67cm) or 1.75, which is 57cm

But given that (for people starting out at least, which is who this is aimed at) the starting prescription is likely to be wrong, does it make sense to attempt to calculate a precise value for the differentials for a particular distance, as a delta from what is likely to be quite a loose approximation to an emmetropic eye ?

I’m really lucky in that I’m just starting out and it is becoming available just in time

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You are fortunate indeed, I started before the rough guide and now wiki and there was a steep learning curve for the first month or so, I was motivated enough to keep picking it apart and putting the pieces together but I certainly related to the frustration of many newbies trying to straighten things out. I thankfully didn’t have so many issues figuring out differentials though, I had basically badgered my optometrist into setting me up with a pair 15 months before finding EM, so I had a fairly solid start point.

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Since my background is physics, I’d also have mentioned the optics… 1/distance is the formula for the power of a lens. So that sort of implies that the distance is some sort of focal length. So what it is the focal length of…?

With your full prescription, your eye is relaxed when looking at a long distance (effectively infinity), so it wants the incoming light to be parallel. The lens strength that has been calculated is the (converging) lens that will take light from a point at its focal length equal to your preferred working distance (60cm) and make it parallel. And then your full prescription can comfortably take that parallel light and focus it on your retina with your eye lens fully relaxed.

And then since lenses in series just add in power, you add this lens strength to your prescription to get your (reduced) differential strength.

(This approach comes to the same numerical answer, but there is a small detail of a reversed sign. I’m adding a positive-powered lens which reduces the strength of the -ve lens. Your sum comes up with a -ve powered lens which you subtract. That might just be because the gadget produced a -ve number. Or there may well be a different story you can tell for which that makes sense. Such as first decomposing the full prescription ‘P’ into a pair of weaker lenses ‘D’ the differential, plus ‘X’ in series. Then calculate ‘X’ and rearrange to find ‘D’. Or something like that. It’s been a long time… )

Ah - got it… since ‘X’ is a diverging lens, it has a virtual rather than real focus. So D+X (plus your eye) together are able to focus light coming from infinity. You want eye + D to be able to focus light coming from 60cm. So X is the diverging lens that will take light from infinity and form a virtual focus 60cm behind it. So lo and behold, X is 100/-60 then D is P - X

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I’ve did some math I realized that we have two problems:

1. I have a screen distance which I want to use, what differential I need for that?
2. I have a differential glasses, what screen distance should I use?

We have the latter problem especially because glasses made in 0.25 increments. So they will never be correct for a given distance. I created formula for both:

For the calculations we need:

• cm measurement to edge of blur. Be honest yourself here, use varakari’s tool or some other red and green text and do a measurement as soon as the green gets blurry.
• a) desired distance for screen in cm -> if you have diopter gap between your eyes, calculate for both eye
• b) differential glasses diopter number you want to use -> if your differential is not equalized, it’s enough to use of the eye’s diopter. The other should give the same number, so you can use it to check your math.

First let’s calculate the full power glasses diopter:

• [full power glasses in diopter] = 100 / ( [cm measurement] - 2 )

We need to substract - 2, because the cm measurement gives you your full prescription at your eye level, so for contact lenses. Glass lenses sits about 2 cm before your eyes.

then
a) [differential glasses in diopter needed for the desired distance] = [full glasses] - 100 / [screen distance]
b) [distance in cm needed for given differential glasses] = 100 / ( [full glasses] - [differential glasses] )

Can someone check if my math is correct? If yes, I add it to the wiki page.

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Looks plausible. I think they’re rearrangements of the ‘X’ I mentioned above.
P = D + X
X = 100/distance_to_screen
=> distance_to_screen = 100/X = 100 / (P-D)

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Thank you so much @itamar. I found your eplaination very helpful. And I am a high myop:
-9.75 -4.00
-10.75 -3.25

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-7 glasses: full prescription is -8 D in contacts (-9 glasses).
In theory, -7 glasses is -6.5 D in contacts.
So 100 / (8 - 6.5) = 75 cm - edge of blur for vertical lines with -7 glasses should be 75 cm.
In practice, it’s only 40-45.

I composed a formula:
DfullContacts = 1000 / (1000 / (1000 / (1000 / Ddiffs - BVDmm) - (100 / distcm)) - BVDmm)

Where
Ddiffs - spherical diopters in differentials
BVDmm - back vertex distance in mm
distcm- desired edge of blur differentials should get you

If DfullContacts matches SPH value of your full correction contact lenses, you have chosen differentials correctly. Anyway, you need to test this on real lenses.

Example:
1000 / (1000 / (1000 / (1000 / -7 D - 12 mm) - (100 / 40 cm)) - 12 mm) ≈ -8 D.