# Optical Forums > Ophthalmic Optics >  Vertex Distance and Prism

## Pete Hanlin

I'll be presenting a course on "Ophthalmic Application of Prism" at the OAA conference in June, and I want to make sure I have my "ducks in a row" before I answer a question that came up last time I talked about prism in a course...

Specifically, "Does a change in vertex distance affect the amount of prescribed prism?"  My answer was "No, because changes in vertex distance can only effect the elements of a prescription that involve focal lengths.  Since prism only refracts and does not converge or diverge light, it is unaffected by focal length."

Was this a correct assumption, or do I need to find the emails of all the attendees of that course (yeah, right)?

Thanks as always,
Pete

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## Bev Heishman

I believe you are correct.  Vertex would apply to the power of the lens.  Prism is independent of this function.

Good luck!

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## Darryl Meister

Hi Pete,

For prescribed prism... I don't believe that vertex distance affects the prismatic effect for distant vision, but I do believe it will affect the prismatic effect for near vision slightly. This has to do with a change in prism "effectivity" at near. If you want to know more, I can post the formula to calculate prism effectivity at near.

For induced prism... As the wearer looks away from the optical center of the lens, prism is induced according to Prentice's rule. As the vertex distance is increased, the eye moves across more of the lens surface for a given angle of view -- that is to say, the line of sight will move farther from the optical center, which will induce more prism, for the same angle of view.

Best regards,
Darryl

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## Diane

Pete,

I believe that I would be interested in seeing the formulas that Darryl has to post, because I believe that as the eye deviates away from the OC with perhaps different powers, that the prism effect would be different at different vertex distances.  If the refractive powers were similar, it wouldn't matter, but I believe if they are different, it would.  

Diane (Just wondering) Drake

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## shanbaum

I think the formula to which you are referring is:

ZC = Z / (1 - CV)

where ZC is the effective prism in diopters, Z is prism in diopters, C is the distance from the center of rotation of the eye to the prism in meters, and V is vergence in diopters.

This suggests that as vergence V decreases to zero (at distance), the effect of changes in vertex distance (which would also cause C to change) would diminish.





> Originally posted by Darryl Meister:
> *Hi Pete,
> 
> For prescribed prism... I don't believe that vertex distance affects the prismatic effect for distant vision, but I do believe it will affect the prismatic effect for near vision slightly. This has to do with a change in prism "effectivity" at near. If you want to know more, I can post the formula to calculate prism effectivity at near.
> 
> For induced prism... As the wearer looks away from the optical center of the lens, prism is induced according to Prentice's rule. As the vertex distance is increased, the eye moves across more of the lens surface for a given angle of view -- that is to say, the line of sight will move farther from the optical center, which will induce more prism, for the same angle of view.
> 
> Best regards,
> Darryl*

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## Pete Hanlin

Hi Everyone,
I'd like to see the formula, Darryl... [EDIT: oops, thanks shanbaum... you posted it just minutes before my post- talk about timely!] I realized that the prism inherent to the power of the lens would vary with vertex (at a standard vertex distance, a 2 degree turn equals about a mm on the lens surface, right?).   Also, as I understand it, each diopter of prism causes the eye to turn (or necessitates a turn) about 1/3mm towards the apex (which is why seg heights need adjustment when &gt;3diopters of verticle prism is prescribed)?  Is this correct?

Thanks,
Pete

[This message has been edited by Pete Hanlin (edited 05-26-2000).]

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## Darris Chambless

Hello to all,

Let me start by saying, Diane the bug is MINE! :-) Well, I feel better how about the rest of you.

Actually here's what I'm thinking (NOOOOOOO!!!! :-) and correct me if I'm wrong, but if I decrease vertex distance I will induce no additional prism because the eye will be closer to the optical plane. Therefore, you will have a larger optical field (perspectively speaking) with less prismatic effect from deviation, BUT you will increase the effect of marginal astigmatism because of how quickly the eye will move into an oblique axis (up = sagital. side to side = tangential. I think that's right) 

If I increase vertex distance I will decrease the marginal astigmatic effect. With a smaller optical field created (perspectively speaking) by the increasing distance you then create a more direct line of vision throughout the lens. In other words the more distance from the eye the more directly you will look through the entire lens area and reduce oblique astigmatism, but still no induced prism

If you can maintain the exact same level and angle throughout the vertex increase or decrease you would not have to worry about inducing prism. But, you have so many variables that could potentially cause induced prism such as height of the OC respectively, angle of tilt (panto or retro) not to mention the amount of prism that could be induced by the total power of the lens. In some cases the power may be low enough that you would have to move the lens a considerable amount (up,down, side to side) before you would ever have to worry about induced prism anyway. In higher scripts I would think that prism could be induced but not directly by vertex changes as much as the variables potentially caused by vertex changes.

HAVE I MADE MYSELF CLEAR!!!! :-)

Ya'll have a nice day and we'll be talkin' to ya,

Darris "Always with the stuff and the thing there." Chambless

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## Darryl Meister

> Originally posted by shanbaum:
> *I think the formula to which you are referring is:
> 
> ZC = Z / (1 - CV)
> 
> where ZC is the effective prism in diopters, Z is prism in diopters, C is the distance from the center of rotation of the eye to the prism in meters, and V is vergence in diopters.
> 
> *


Hi Pete and Robert,

The formula I have is:

E = P * w / (w + h)

Where E is the effective prism, P is the actual prism power, w is the working distance from the near object to the spectacle plane, and h is the distance from the spectacle plane to the center of the eye.

After some re-arrangement and substitution (e.g., V = 1 / w), you can see that this is equal to the right side of Robert's equation (neglecting sign convention).

Best regards,
Darryl

[This message has been edited by Darryl Meister (edited 05-26-2000).]

[This message has been edited by Darryl Meister (edited 05-26-2000).]

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## Darryl Meister

> Originally posted by Pete Hanlin:
> *Also, as I understand it, each diopter of prism causes the eye to turn (or necessitates a turn) about 1/3mm towards the apex (which is why seg heights need adjustment when &gt;3diopters of verticle prism is prescribed)?  Is this correct?
> *


Yes, Pete. You are correct (for a typical vertex distance). Remember that: A) 1 prism diopter deviates light 1 cm meter at a distance of 1 m, B) The spectacle plane is roughly 0.03 m from the center of the eye, so that C) 1 prism diopter deviates light 0.03 cm (or 0.3 mm) at the spectacle plane.

Best regards,
Darryl

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## Darryl Meister

Extending Mr. Shanbaum's point, I would also add the following: All of these effects at near are relatively negligible, especially for weak prism powers. Although vertex distance will affect prism effectivity, it will generally be by a very inconsequential amount.

Best regards,
Darryl

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## Darryl Meister

> Originally posted by Darris Chambless:
> *
> 
> If I increase vertex distance I will decrease the marginal astigmatic effect. With a smaller optical field created (perspectively speaking) by the increasing distance you then create a more direct line of vision throughout the lens. In other words the more distance from the eye the more directly you will look through the entire lens area and reduce oblique astigmatism, but still no induced prism
> *


Hi Darris,

Well, I don't know if I entirely followed you... ;-) But I will agree that reducing vertex distance for a given angle of view will increase the amount of oblique astigmatism -- at least according to my ray tracing sheet.

Best regards,
Darryl

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## Jeff Trail

Hey guys.. I think we are looking at it possibly "backwards"..We are taking "strict" rules and leaving out the "human" factor.                                            Lets start with the basics. we grind the amount of prescribed prism for the wanted correction(which usually is image placement)..now you're taking into account that it is for a "average" fitting, say a vertex of 12 mm to 14 mm..taking that into consideration you are using only a certian amount of actual "physical" lens surface..so the PD is important..NOW you have an increase of say 10 mm of vertex on top of the usual amount... the actual amount of lens surface used "physically" to get the same amount of visual field also increases, right?.. well technically you still will be seeing the same looking directly ahead BUT as you converge or look in the periphrel THEN thats where the problem would arise if they had "ground" prism.
       I think I would compare it to the same basic parameters used in an aspherical design. By keeping the vertex "short" and fitting the OC's and using a mono fit it makes all the difference in the world on the performence of the optics of that type of design...Notice how fitting an aspheric with a lot of vertex distance usually the patient complains about the oblique power problems?
So I would think it would apply the same to the question posted..technically the lens WOULD be the same the factor "changing" is the PERSON wearing it and how the would percieve the visual field?...

   "How about them apples"?..thats another optical technical term along with the great "ying-yang" debate from the old board..LOL

Jeff "Wears prismatic lens to the beach so I can see twice as many women" Trail :-)

[This message has been edited by Jeff Trail (edited 05-26-2000).]

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## Darris Chambless

> Originally posted by Darryl Meister:
> * Hi Darris,
> 
> Well, I don't know if I entirely followed you... ;-) But I will agree that reducing vertex distance for a given angle of view will increase the amount of oblique astigmatism -- at least according to my ray tracing sheet.
> 
> Best regards,
> Darryl*


Hello Darryl,

First let me say YOU HAVE A RAY TRACING SHEET!?!? You don't get out much do you? :-)(Just kidding) Secondly "effectivity"? Not sure what you're trying to say with that one, please clarify.

To clarify what I was saying, let's pretend for a moment shall we? Lets say we have a piece of clear, flat plate glass four inches square (with the edges safety beveled for obvious reasons, just so we know :-) and we squish it up against the boney orbit (no offense to anyone :-) on the right side of the face. Now then looking straight through the glass everything looks great but as I move my eye left, right, up or down to look at periferal edges I begin to blur a little because I'm looking through a thicker cross-cut section of the glass (hince marginal astigmatism). 

Now I take that same piece of safely manufactured glass and move it away from me to a distance of lets say 2ft. Perspectively (or in perspective, if you were ever an art student) the glass no longer covers the entire field of view and to the eye will only look two inches square (hypothetically speaking) Now as I deviate my gaze I'm clear all the way across because of my position to the glass. The cross-cut angle that I look through is now only a few degrees at the periferal points on the glass as opposed to 20 or 30 degrees up against my face.

These are of course extremes, but I hope you understand what I'm saying. I also realize that lenses are not flat, but this was the best example I could come up with under the circumstance ;-)

On the flip side Chad came up with another analogy in which the reverse would hold true. If you created a lens that followed the exact same curvature as the rotation of the eye (a psuedo sphere ;-) your clarity would be best at a minimal vertex distance and worse at a greater vertex distance. This would be because your cross-cut angle would be almost perpendicular throughout the lens when it was very close to the eye. When this lens is moved away from the eye the only perpendicular visual transmitance would be the apex and the rest would be a more severe cross-cut angle (distortion).

If these don't work to clarify let me know and I will come up with a different one :-)

Darris C.

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## shanbaum

> Originally posted by Darris Chambless:
> * 
> 
> &lt;snip&gt;
> 
> Secondly "effectivity"? Not sure what you're trying to say with that one, please clarify.
> 
> &lt;snip&gt;
> 
> Darris C.*


Paraphrasing Keating: this is the angle the eye must turn to keep a prism-deviated image on the fovea - the effect of the prism on the eye.

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## Texas Ranger

I really don't think vertex changes affect power, but I do believe that the "thickness" of the lens required to create the prism, creats magnification, which is affected by vertex. IMHO, Al.

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## Darris Chambless

> Originally posted by shanbaum:
> * Paraphrasing Keating: this is the angle the eye must turn to keep a prism-deviated image on the fovea - the effect of the prism on the eye.*


Hey Robert,

Thanks for the definition. I don't think I've ever heard of that particular word before and it threw me.

I have a more personal question for you. Weren't you in Australia the last time we spoke? I could have sworn that as recent as New Years you were living in Sydney, Austrailia. When did you move to the states or are you just here for a short term?

Talk to you later,

Darris Chambless

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## shanbaum

> Originally posted by Darris Chambless:
> * Hey Robert,
> 
> Thanks for the definition. I don't think I've ever heard of that particular word before and it threw me.
> 
> I have a more personal question for you. Weren't you in Australia the last time we spoke? I could have sworn that as recent as New Years you were living in Sydney, Austrailia. When did you move to the states or are you just here for a short term?
> 
> Talk to you later,
> 
> ...


No worries, mate.

...but ah'm uh native Texun, ol' son.

Maybe you're thinking of Robert Groche (sp?), who, I believe, may be one of them marsupial geeks lurking hereabout.

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## Darryl Meister

> Originally posted by Darris Chambless:
> *Now I take that same piece of safely manufactured glass and move it away from me to a distance of lets say 2ft. Perspectively (or in perspective, if you were ever an art student) the glass no longer covers the entire field of view and to the eye will only look two inches square (hypothetically speaking) Now as I deviate my gaze I'm clear all the way across because of my position to the glass. The cross-cut angle that I look through is now only a few degrees at the periferal points on the glass as opposed to 20 or 30 degrees up against my face.
> *


Hi Darris,

I see what you're saying... However, your analogy implies that the angle of view can change. If the plate of glass is pulled away while you maintain fixation on its edge, you have to reduce your angle of view as the plate moves farther away. However, our discussions up to this point have assumed that the angle of view remains constant. Remember, we're not fixating on the glass plate, we're fixating on the object beyond it -- which does not change its angle as the plate is pulled away from us (neglecting thickness).

Further, although shortening the vertex distance will increase oblique astigmatism, it will also increase as the vertex distance is increased. For a given angle of view and base curve, the oblique astigmatism will only be zero for one vertex distance.

Best regards,
Darryl

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