Towards A More Progressive Viewpoint

No, not progressive politics, progressive eyeglasses. I got a pair recently, since I was having real trouble reading small print. Bifocals or reading glasses are one of those inevitable things in life: if you don't need them now, don't worry - you will, eventually. As we age, we all start having trouble focusing close and eventually we will need reading glasses or bifocal glasses to help us. It's called presbyopia, and everybody gets it sooner or later. Up until now I've had only a vague notion of what bifocals and reading glasses actually do.

At the top a lens - our eye, say, or a camera lens - is focusing on an object very far away. The light through a lens bends so that it all comes together at a point¹. When that point hits our sensors on the left (whether a piece of film, an electronic camera sensor or our retina) we get a sharp view of the object.

Below we've moved close to the object. The light from it now comes from much steeper angles. But the lens still bends light the same amount as before. The light rays on both sides act like a see-saw, with the lens itself as the center point. So the point of focus moves further away.

We need to change the focus depending on the distance. At the top is how a camera lens does it: the point of focus is behind the sensor, so we move the lens forward until the point of focus is on the sensor again.

The second picture illustrates how our eyes focus. Since the lens isn't bending the light strongly enough, we squish the lens so that it becomes thicker and bends light more. We can do that since our lenses are soft and jelly-like, unlike the glass lenses used in cameras.

Like many, many other people, I'm near-sighted. At the top we see the cause: the retina in the back of the eye sits too far away from the lens. Even when the lens is as flat as possible it still bends light too much to bring far-away things into focus. We can fix this with a convex lens, like the one on the right, that'll effectively weaken our own lens and let us focus far away. Think of it as the curve of the convex lens being subtracted from the curve of our own lens.

Presbyopia is the inability to focus close, and at the bottom we see the reason for it: as we age the lens gradually hardens, and it can no longer thicken enough to bend the light for close objects. The way to fix this is with a convex lens like the one on the right that will help make the eyes stronger. The curve of the concave lens is added to the curve of our own lens, effectively making the combination thicker.

So, with presbyopia you can use a convex lens to get closer focus. Cheap reading glasses sold here and there are exactly that². This is sufficient for people with otherwise good eyesight.

With nearsightedness you use a concave lens to get infinity focus. Now, here's a problem: what do you do if you're both near-sighted and presbyopic? As you can see in the figure above, the corrective lenses are opposites: one cancels out the other. How do you make a lens that corrects for both at the same time?

Well, you don't. A concave lens for near-sightedness worsens presbyopia - it makes the minimum focusing distance longer - while a convex lens for presbyopia worsens focus at infinity. This is why they're called reading glasses; you can't see far away wearing them so you only use them for close work.

Since glasses for near-sightedness worsens presbyopia, people can get around mild presbyopia simply by removing their glasses or looking below or above the rim when they read; you see this quite often. But once the presbyopia worsens it's no longer enough. People that have astigmatism as well - like me - need glasses at all viewing distances, so removing your glasses doesn't help much.

You could have two pairs of glasses of course, and switch between them. That's a hassle, though, so you'd really like to combine them into one pair. The traditional - and still best - method is simply to "cut out" the lower central part of concave lenses for near-sightedness and replace with convex lenses for presbyopia. That gives you those characteristic half-moon bifocal glasses that people instantly recognize as "old-folks glasses". While they're really the best type of glasses, they're not well liked.

Instead we have progressive glasses, so named because they go smoothly from a nearsighted concave lens toward the top to a convex (or at least less concave) lens at the bottom. This is actually very complicated; you want the change to be gradual, without too much visual bending, blurring or other weird effects during the transformation. We don't look through a point in the glasses, but through a whole area, so a single point in the lens may both be part of the lower edge of the concave near-sighted area toward the top, and part of the convex presbyopic area at the bottom at the same time. Add the astigmatic correction for people like me and the lens surface will get quite complicated.

There's apparently many progressive lens designs, but they are all compromises between conflicting goals. In my case I get far sight in the upper center; near sight in the lower center and towards the edges; and middle sight in a roughly H-shaped area in the very center and along the left and right edges.

One effect that creates problems for some people is that these are lenses, and they don't just move the focus forward or back. Concave lenses make things smaller, and convex lenses make them bigger - magnifying glasses are just strong convex lenses after all. Now, eye-wear lenses are typically fairly weak, but the effect is not negligible. The eyes of near-sighted people tend to look smaller, and the eyes of strongly far-sighted people can look huge behind their glasses.

This also means that the world looks a bit smaller and zoomed out when you wear concave lenses for near-sightedness. And the world looms a bit closer with convex reading lenses. This is normally fine; you quickly get used to it. But with progressive lenses the world gets smaller in some areas of your field of view and larger in other areas, like a funhouse mirror. And as you move around and move your head things shift between these areas to bend, stretch, distort and generally make you feel a little like you're drunk. People normally get used to this - I had no problems - but some people never really adapt. They're better off with bifocal glasses instead.

There are progressive contact lenses, by the way, where you get far vision in the very center and close vision around the edge, but people who've tried them don't seem too impressed. Another way is to wear a contact for far sight on one eye, and close on the other. Me, I'll just rather wear glasses; I've done so for most of my life after all, so this is no problem for me.

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#1 You have perhaps heard the term "diopter". It's a measure of how strong a lens is, and is really just the inverse of the distance from the lens to the point of focus when you focus on something infinitely far away. So a 1-diopter lens will bring the light together one meter behind the lens. A 2-diopter lens brings it to a point 1/2 meters away; a 10-diopter lens focuses infinity at 1/10 meter - ten centimeters - away and so on.

#2 As an aside, "macro filters" for cameras are the same thing too: an extra lens you screw in front of your ordinary camera lens so you can get closer and get a bigger picture of small things. They're an inexpensive way to play with macro photography.

For SLR cameras, you can also get "extension tubes". They're hollow tubes that fit between the camera and lens and simply move the lens further from the sensor so you focus closer than you normally could.