Are plus lenses heavier than minus?

[Darryl Meister]

Still for a shaped lens you could probably argue that the plus lens would be heavier, though the actual magnitude of the difference would depend upon several factors.

I should clarify that this statement holds true for lenses of moderate to high power, or in frames requiring a great deal of decentration or a relatively large minimum blank size. As the powers drop below +/-3.00 D, or the decentration becomes negligible, the advantage in thickness can actually reverse in favor of plus lenses.

Best regards,
Darryl

[Robert Martellaro]

Still for a shaped lens you could probably argue that the plus lens would be heavier, though the actual magnitude of the difference would depend upon several factors.

And that's exactly why my program was misreporting the weight of plus lenses. The program I use allows me to choose from ten different shapes, and plots the edge thickness at eight equally spaced points around the clock. This seems to be working properly for minus powers but when I choose round for the shape in plus powers the lens weight is higher than if I choose a square shape, which is just the opposite of what one would expect with plus powers. I guess I'll have to trial and error each shape and re-map the keyboard.

Darryl,

Thanks for spending so much time and effort putting this matter to rest. Thanks also for pointing me towards the OpticsLite program. Many useful tools.

Respectfully

[Darryl Meister]

Thanks for spending so much time and effort putting this matter to rest

No prob! It was an interesting exercise.

Best regards,
Darryl

[DrG]

I should clarify that this statement holds true for lenses of moderate to high power, or in frames requiring a great deal of decentration or a relatively large minimum blank size. As the powers drop below +/-3.00 D, or the decentration becomes negligible, the advantage in thickness can actually reverse in favor of plus lenses.

Best regards,
Darryl

I'm sorry to have taken so long to respond, but I think you are agreeing that plano/concave lenses have less mass than plano/convex lenses, all things being equal including the minimum thickness. And that the difference in mass increases with increasing sag, and approaches zero as the sag approaches zero....or the base curve approaches a cone -- on a theoretical basis, of course.

I do appreciate the different perspectives from a practical point of view, though.

Best regards,
DrG

[Darryl Meister]

Here is a summary of my conclusions:

1. For uncut, knife-thickness plano-concave and plano-convex lenses, there is no practical difference in volume. As the diameter or power of the lens blank increases, the plano-convex lens would normally increase in volume slightly faster than the plano-concave lens of the same curvature (refer to the mathematics above). However, plus lenses must be reduced in curvature somewhat in order to compensate for the gain in vertex power caused by thickness. As it turns out, the reduction in volume as a consequence of this reduction in curvature very nearly equals the gain in volume produced as the mathematical approximation breaks down. I had a look at a +10.00 D plano-convex lens and a -10.00 D plano-concave lens, both at a 70 mm diameter, and the difference in volume was only 0.02 cm^3. This is even less than it was for +/-4.00 D lenses at 60 mm.

2. For shaped lenses of typical thickness and base curvature, minus lenses generally produce less volume in moderate to high powers than plus lenses. For powers below +/-3.00 D, plus lenses will generally have similar -- and often less -- volume (factoring in the smaller minimum thickness) than minus lenses, unless the frame requires significant decentration or is of an unusual shape.

Best regards,
Darryl

[drk]

Great thread. I always assumed that a plus lens weighed more than a minus, but I've been incorrect.

How about this twist: are aspheric plus lenses flattened greater than aspheric minus lenses are steepened? In other words, on the whole, has the industry produced higher eccentricity plus lenses than minus? It would seem so.

My preconceived notion is that aspheric design benefits plus much more than minus.

[Steve Machol]

Is it possible that because the center of gravity in a plus lens is farther from the face it would appear to be heavier (i.e., more pressure on the nose) than a similarly powered minus lens? Just a thought.

[Darryl Meister]

My preconceived notion is that aspheric design benefits plus much more than minus

I think the biggest issue with plus versus minus aspheric lens designs is the fact that base curves for minus lenses are already relatively flat, and don't require a great deal of modification from "best form" shapes. Further, asphericity on the back surface of a minus lens will result in maximum thickness reduction (and vice versa for aspheric plus lenses), though most semi-finished aspheric lens blanks are aspheric on the front.

Nevertheless, the asphericity required to improve the optical performance of a minus lens results in nearly as much thickness reduction as it does for a comparable plus lens -- even when the asphericity is on the front surface. However, the reduction in volume (and weight) is not as significant as with plus lenses. (At least according to the simple aspherics I tested in OpticsLite.)

Although I'd have to sit down and think about it, this could be due to the fact that the bulk of the volume and thickness of a plus lens is fixed by its center thickness, which is in turn fixed by the sagittal depth of the front surface for a given back curve and edge thickness. A shallower aspheric curve reduces the center thickness and volume by an amount equal to the difference in height between a spherical surface and an aspherical surface at the same diameter. However, asphericity on the surface of a minus lens rolls off the thickness toward the edge. Consequently, the reduction in thickness (and volume) as a result of the increasing asphericity of the surface only becomes pronounced as you get farther and farther out.

Think of it like this: The smaller you edge an aspheric minus lens down, the less the edge thickness will vary from the edge thickness of a comparable spherical design. However, the reduction in center thickness for an aspheric plus lens is fixed, regardless of how much you edge the lens down.

Is it possible that because the center of gravity in a plus lens is farther from the face it would appear to be heavier (i.e., more pressure on the nose) than a similarly powered minus lens?

Interesting thought. This might make the lenses more likely to "tip off," since moving the center of gravity forward would make the weight of the lenses work against the temples by using the nosepads act as a fulcrum. The downward force on the nose would be similar, though there might be a new torsion component against the bridge of the nose as a result of the weight of the lenses applying torque to the nose pads (which are acting as that fixed fulcrum).

Best regards,
Darryl

[Tom Hubin]

Hello,

This is my second attempt to post to this thread. Let's see if I can do this right this time.

I am new to this list so may not be strictly proper.

In the 1970's I was an Army optician in Denver and a civilian optician in Maryland with a Virginia license. I also taught opticianry with Ken Wagner and Jim Matthews at Essex Community College in Baltimore. These days I am an optical engineer but still poke my nose into old interests.

I was referred to this list when I asked at sci.med.vision for info and manuals for the Essilor MBX edger. I still need that info but probably need to find the right place to ask.

I just happened onto this thread regarding the weight of lenses. I too did some math in the 1970's to figure out how much a pair of glasses might weigh. At first this was just to help teach but later I cleaned it up and published the article referenced below in a Washington DC based trade magazine.

"Weight of Lenses", T. Hubin, THE DISPENSING OPTICIAN, Jul 1978

I have a copy here someplace but no idea where at the moment. Darryl just told me how to post a file so I will try to find it, scan it, and post it as a JPG file or something like that. Wish me luck.

BTW, my math was similar to that posted in this thread for sections of spheres but I doubt that I actually put that much math detail into the published article.

Tom Hubin
thubin@earthlink.net

[HarryChiling]

The equations that I have go as follows:

Rf=front curve radius
Rb=back curve radius
p=eccentricity of lens (asphericity)
Et=edge thickness
Vf=volume of front
Vb=volume of back
Sb=sag of back
Sf=sag of front
d=diameter of lens
den=density of lens
min=minimum edge thickness

First I start with the getting the sag for both surfaces

Sf = Rf/p - √[ (Rf/p)2 - (d/2)2 / p ]
Sb = Rb - √[ Rb2 – (d/2)2 ]

Then I determine the Edge Thickness

(+) Et = min
(-) Et = Sb – Sf + min Then I will find the volume (convert all variables into centimeters before equations)

Vf = π*Sf2 *( 3*Rf – p*Sf )/3
Vb = π*Sb2 *( 3*Rb – Sb )/3

Then we find the weight (diameter and Et is in mm)

Weight = den * ( Vf – Vb + π*d2*Et/4000 )

For reference I used Mo Jalies article "How to ensure the thinnest lensses" Optics Today April 22 2005 and various internet resources, as well as Darryls Optics Lite. I checked it to make sure everything was correct with Darryls software Optics Lite.

[QDO1]

depends how clever the surfacer is... generally there is no difference between plus and minus, if looked at theoretically, but the crux comes when a plus lens is surfaced. surfaced poorly, it will be thicker, surfaced to a "on the edge knife edge", and optimised it can be thinner... why? because the minus lens has a set CT that cant be made thinner, because the lens crashes out in surfacing/polishing/glazing



if the lens is aspheric, then the answer is in the math, and it really depends what aspheric curve was used, but all things being equal, the plus lens is generally thinner if well surfaced

explained another way - the smaller the lens, the more the CT of the minus lens effects overall thickness of the minus lens