# Optical Forums > Ophthalmic Optics >  spectacle magnification

## sevalav

Hello!

This is Spectacle magnification equation:
SM=[1/(1-(t/n)*Df)]*[1/(1-h*D)]
where h is verteks distance ("*Vertex distance* is the measurement from the back of the spectacle lens to the front of the eye", that means to the apex of the cornea
- http://onlineopticianry.com/wordpres...p2pdf.php?p=37 ).
But, in several places I find that this "h" ("*g"* or* "d"*) is "distance from the back of the lens to the entrance pupil" ( http://www.drdrbill.com/downloads/op...nification.pdf )
Can someone explain me this difference?

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## HarryChiling

It is from the back vertex of the lens to the entrance pupil, you caught a typo that I will correct.  Usually you could use the vertex distance and add about 3mm to that.

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## chip anderson

Actually unless Distometers or lids have changed since the '50's.  Vertex is back of lens to front of lid +1 mm for lid thickness.  And yes, I know most lids are a little thicker than this.

Chip

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## HarryChiling

> Actually unless Distometers or lids have changed since the '50's. Vertex is back of lens to front of lid +1 mm for lid thickness. And yes, I know most lids are a little thicker than this.
> 
> Chip


To the stop or entrance pupil, is what it was supposed to read.

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## chip anderson

With anterior chamber depths varying so much how would anyone measure this at least with the tools a dispenser has at his discression?

I mean they don't exactly give us sonograms to work with.

And the anterior cornea is the next refractive surface after the spectacle lens, not the lens of the eye.

Chip

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## sevalav

Thanks for explanation!

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## HarryChiling

> With anterior chamber depths varying so much how would anyone measure this at least with the tools a dispenser has at his discression?
> 
> I mean they don't exactly give us sonograms to work with.
> 
> And the anterior cornea is the next refractive surface after the spectacle lens, not the lens of the eye.
> 
> Chip


Well your right no exact measure, but Gullstrand gives us 0.5mm for corneal thickness, and then posterior cornea to anterior lens is given as 3.1mm the 3-4mm seen in many texts is really just an estimate.

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## Barry Santini

It is the image of the eye's pupil, formed by the cornea, as seen by an observer.  Harry is correct.  It is the *entrance pupil* that is the correct reference point for calculating VD and for use in other calculations, such as image size.

Barry

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## tmorse

> It is from the back vertex of the lens to the entrance pupil, you caught a typo that I will correct. Usually you could use the vertex distance and add about 3mm to that.


I don't quite get it... the 3mm added corresponds to the eye's primary nodal point? 
Yet this is a spectacle magnification question that doesn't involve the eye, just the parameters of the lens, front curve, index, thickness, vertex distance and back vertex power. The only reason the back vertex power is there as a lens parameter is the it was refracted at the Dr's office as that power at that specific vertex distance. And the vd supplied by the Dr. is only the distance from cornea to back of eyeglasses (with the eye's nodal point 3mm in already taken into account). 
If you moved this lens out a few mm, the effective power of this lens would change depending on change in vd =h, but not by h+3mm. 
The image vergence leaving the lens would strike the front of the cornea and then be refracted by all the internal surfaces and indices and eventually strike the retina. The 3mm in question would be taken into account then, no? :Confused:

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## lensgrinder

> I don't quite get it... the 3mm added corresponds to the eye's primary nodal point?


The 3mm is added to account for eylid thickness.  When you take a vertex distance it is taken with the eyes closed.

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## HarryChiling

> The 3mm is added to account for eylid thickness. When you take a vertex distance it is taken with the eyes closed.


That would account for a mm at most and distometers have eyelid thickness calc'ed in. The measure is to the aperature, stop, pupil, entrance pupil, roughly about 3 mm behind the corneal surface.

Look at the image from http://www.drdrbill.com/downloads/op...nification.pdf

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## chip anderson

Check your distometer.  I don't think they have anything cancelled or figured in.  Take a caliper and see how the distometer measures between the caliper points.  Bet it's gonna be near right on.

Chip

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## HarryChiling

> Check your distometer. I don't think they have anything cancelled or figured in. Take a caliper and see how the distometer measures between the caliper points. Bet it's gonna be near right on.
> 
> Chip


Chip it's not in the tool but the supplied rotateing chart/wheel thingy. Take a look at it and calc the differences sometime. I think we already discussed this some time ago and I ended up calipering my distometer and it is accurate up till about 20mm and doesn't factor in the lid thickness but I had someone confirm that the wheel does factor in thickness and the proper use of the tool is to use both parts.

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## tmorse

> That would account for a mm at most and distometers have eyelid thickness calc'ed in. The measure is to the aperature, stop, pupil, entrance pupil, roughly about 3 mm behind the corneal surface.
> 
> Look at the image from http://www.drdrbill.com/downloads/op...nification.pdf


I've seen this image in Darryl's excellent treatise. So thanks Harry, but I'm looking for an expanation of 'why'. 

As to the distometer issue, the last time I bought one it came with a booklet of instruction... and the scale on the distometer does indeed take the thickness of lid (about 1mm) into account.:cheers:

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## Oedema

> It is the image of the eye's pupil, formed by the cornea, as seen by an observer.  Harry is correct.  It is the *entrance pupil* that is the correct reference point for calculating VD and for use in other calculations, such as image size.
> 
> Barry


Barry is correct here.  Spectacle mag is generally calculated with reference to the entrance pupil, this is one of the reasons that you still have spectacle magnification with contact lenses despite the fact that they sit right on top of the cornea (they still have ~3mm of vd!).

That said, day-to-day it's not really a very important consideration.  Even if you're dealing with aniseikonia as long as you're using the same type of VD for each eye it should not really matter.

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## chip anderson

Seems to me that unless one is interested in some sort of isoconic ballance the rule of thumb which is good enough for practical concideration is :  .25 magnification (both to the observer and the patient) for every 1 diopter of power.   Inversly .25 of minification of every diopter of minus.  Can be varied with vertex but not enough to really get all hot and bothered about.

Chip

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## tmorse

> Barry is correct here. Spectacle mag is generally calculated with reference to the entrance pupil, this is one of the reasons that you still have spectacle magnification with contact lenses despite the fact that they sit right on top of the cornea (they still have ~3mm of vd!)


Yet when they compensate for change in vertex distance from glasses Rx to CL Rx they don't add in this extra 3mm. :Confused:

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## Oedema

> Yet when they compensate for change in vertex distance from glasses Rx to CL Rx they don't add in this extra 3mm.


Those 3mm are irrelevant when considering the power change for vertex.  Either you can consider going from a VD of 15 mm with spectacles to 3mm with CL, or 12mm to 0, either way what is important is how much you're CHANGING the vertex distance- you get to the same place in the end.

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## chip anderson

Could be that they don't add it in CL because contact lens companies and practioners have gotten so lazy that they check front vertex which would add addittional Plus to plus lenses and less Minus to minus lenses.
Most Vertex conversion charts for contact lenses today are laid out for front vertex.

Chip

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## HarryChiling

> So thanks Harry, but I'm looking for an expanation of 'why'.


Spectacle Magnification = Retinal Image Size in Corrected Eye / Basic Height of Image in Uncorrected Eye

"The basic height of a retinal image is determined by the limiting ray through the centre of the eyes exit pupil. As we saw in Chapter 12, the angle _u'_ which theis ray makes with the optical axis bears a constant ratio (for any given eye) to teh angle _u_ made with the optical axis by the conjugate incident ray directed towards the centre of the entrance pupil. Thus the basic height of the retinal image is directly proportional to the angula rsubtense of the of the object at this point." *pg 229 Clinical Visual Optics*

Basically a shortcut from ray tracing the eye.

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## tmorse

> Spectacle Magnification = Retinal Image Size in Corrected Eye / Basic Height of Image in Uncorrected Eye


Great picture. Many thanks, Harry.:cheers:

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