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 ! kilroy@elvis.rowan.edu ! 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