The Math of Reading/Computer Glasses?

A friend of mine recently got some "computer glasses" to go with his
regular glasses (he's nearsighted), and says that looking at his
computer for long periods doesn't make his eyes hurt as much anymore.
I may look into that myself, but what I'm immediately interested in is
the math of the thing.

The cylinder and axis numbers for the two pairs of glasses are the
same, which makes sense because he's equally astigmatic no matter what
he's looking at.

The sphere numbers for the distance glasses are:

right: -3.50
left: -4.75

and for the computer glasses they are:

right: -2.75
left: -4.00

It doesn't take too long to work out that the change is to add 0.75 to
the distance glasses to get the computer glasses. What I'm interested
in is "How did the Dr. arrive at that figure?" (When I asked the
question, he seemed astonished anyone would want to know.)

He said that he usually keeps his computer screen about 4 feet from
his face, and so that's the distance he gave the doctor. He wants that
to focus as if it were "infinity", thus allowing his ciliary muscles to
be relaxed even while looking at something not so far away. Sort of
like what you do with reading glasses, only not quite so much of it.

Best as we can figure, what's going on is that 4 feet is about 1.333...
meters, and 1/1.333... gives 0.75 -- that is, you picture the eye as
looking at infinity, where the rays of light coming from an object are
parallel. Then you flip that around, and picture the lens as picking
up parallel rays of light and focusing them at some distance, in this
case 1.333... meters. Put together, we have the object at 4 feet,
the light rays spreading out from it in all directions turned parallel
by the lens, and then those parallel lines go into the eye, which
focuses as if it were looking at something infinitely far away.

And if my friend had wanted reading glasses, then you might figure
for half a meter to hold a book, and thus add 2 diopters to the
distance prescription to get reading glasses. (He has no use for
reading glasses, because he only reads things on-line, so he didn't
bother.) Or if you had a really big monitor 6 feet away, you could
figure that as 2 meters and then go for a 0.5 diopter difference.

Does that sound right? If so, it may turn into a homework problem.


Darren Provine ! ! http://www.rowan.edu/~kilroy
"I told her she could ask anything but my weight. So she asked me,
`What was the last porn video you watched?', and I said `I weigh 122
pounds.'" -- Nancy Glass, describing an interview by Gail Shister

 

The basic concept looks exactly right, to me.

In your friend's case though, his eyes focus best on things that are
close to him, so with divergent rays. You can figure exactly how close,
from the original "distance" prescriptions. One eye naturally focuses at
1/3.5 meters, the other at 1/4.75 meters, or 11.2" and 8.26".

If he wore his distance-vision glasses, then added a pair of 0.75
diopter readers, you'd have the scenario you posted.

Dave

 

In reply to my question about the math of computer glasses, in
which I treated the 0.75D correction as a separate lens,

Hmm. That suggests that one could get a pair of spherical 0.75D
clip-on lenses and make "computer glasses" out of any pair of
prescription lenses. Is there any particular reason that wouldn't
be a good idea? It seems like it might save some money. And if
one's prescription changed, one could just keep the clip-ons instead
of buying two new pairs of glasses.

For that matter, it suggests that someone with 20/20 vision could
buy a pair of 0.75D glasses for use as computer glasses, just to
ease eyestrain. Do people do that? I've heard for some time that
it's bad to wear someone else's glasses, but would that apply to
a situation like this, where it's a standard correction?


Darren Provine ! ! http://www.rowan.edu/~kilroy
"One vision is produced by both eyes." -- Empedocles

 

Your ideas seem to be correct in principle. You are unlikely to find
0.75D reading glasses. The weakest ones I have seen seem to be about
1.00D.

I have tried using reading glasses over my distance glasses. I have my
monitor much closer than four feet so I have no problem finding cheap
reading glasses. When I do that, you can call me six-eyes. Nevertheless,
it is more awkward than having a separate pair of glasses around. I use
bifocals designed for looking at my screen through the upper parts of
the lenses. The bifocal add is only about 1.00D to look at things a bit
closer than my screen.

While strictly speaking arithmetic is part of mathematics, I cringe
whenever arithmetic is called mathematics in an attempt to elevate its
status closer to calculus or topology. Its status is that corresponding
to the 'rithmetic of the three R's taught more than a century ago in
one-room schools.

Bill

 

....but, sadly, seldom routinely taught today to any appreciable level of
proficiency even in schools with scores - or even hundreds - of rooms. At
least, not in my country - and neither, I daresay, in yours.

 

You can buy 0.75 D prescription glasses set to your eye's PD here. No
prescription is necessary and the optics are much better than over the
counter reading glasses (and the cost is cheaper too). I personally
bought several pairs at $8 each plus a low shipping cost. Two pair were
reading glasses set to move the far end of my focus range closer so that
I could hold books closer making my eyes work a little. This is the
only web site I've run into that does not require a prescription.

http://zennioptical.com/cart/home.php

 

I have been getting my off-the-shelf reading glasses at my local 99¢
store. They are good enough. I have also obtained them for $1 including
sales tax at a swap meet.

Bill

 

Certainly an economical choice, no doubt about that, and one that works
well for the right circumstances. I found problems with distortion and
swimming with over the counter reading glasses and wanting a
prescription pair with better optics that was fitted to my pupil
distance. Over the counter ones are set for 'average' pupil distance
which doesn't fit best for the majority of people.

I'm near sighted so I don't need any kind of reading glasses, but I
prefer to read at the far end of my focus range and that either requires
that I have LONG arms or used reading glasses to move that far end point
closer. I read by scanning my eyes back and forth (not moving my head
back and forth) and with over the counter glasses strong enough to move
the far end of my focus to about 10-15 inches, only a point about the
center of the over the counter glasses was undistorted. Everything up or
down or right or left was distorted with over the counter reading
glasses (tried a dozen or so brands) unless I moved my head to read or
the book back and forth to read. That was an unacceptable limitation of
over the counter reading glasses.

One additional factor is if one has any astigmatism, that can be correct
with prescription reading glasses, something that cannot be obtained
without a prescription in the US - a usually much more expensive option.
Internet discount options is the way I choose to reduce costs.

If one finds the lower quality optics or average pupil distance
acceptable (or only has a $1 or so in the budget), then the dollar store
is certainly the way to go.

 

In my usage, I sometimes wear the reading glasses over my prescription
glasses when needed. (Call me six-eyes.) Most of the time at my
computer, I usually use prescription bifocals to view the screen. When I
leave home, I might carry a pair of the $1 glasses.

I have not found optical quality to be a problem. Spectacle lenses are
not tightly toleranced compared to truly demanding optical applications.
The surface figure could be wavelengths off. Ophthalmic lenses are not
ordinarily shaped to minimize aberrations. For example, spherical
aberration is usually minimized by having the amount of refraction at
each surface designed to be equal. For the typical negative lens used to
correct myopia, the concave side (closest to the eye) and the convex
side combine to ENHANCE spherical aberration. Not a problem!

My guess is that the biggest problem arising from low cost lenses would
come from plastic lenses that are not cured or molded well.

Bill

 

Huh! I had their site open, about to order some spare glasses for a
daughter. I can pick up as low as +/- 0.25 diopter.

Dave

 

Dave
Thanks...I have it now.

 

Select the $8 glasses link and then select the first pair on the list.
You will be able to set the OD-Right and OS-Left to the prescription you
want. The choices are in 0.25 increments plus or minus.

 

Thanks...I get it now. Also found some info on accommodation in aiming
sports at

http://www.bullseyepistol.com/wong1.htm

which deals with the same problem in an empirical manner...