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Medical Forum / General / Vision / February 2006

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Why is ONLY 20/20 Vision so important?

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Christopher Zoettl - 01 Feb 2006 13:34 GMT
I have been watching this newsgroup for sometime and always seen quotes
that "20/20 vision" is THE best to have. Here in Europe we use a "visus
table". I'll point out:

20/70 = aprox.    Visus of 0.28
20/60 = aprox.    Visus of 0.3
20/40 =     Visus of 0.5
20/20 =     Visus of 1.0
20/15 = aprox.     Visus of 1.3
20/13 = aprox.     Visus of 1.6

My question is why do optometrist only try to correct to 20/20 even
though through full correction much higher vision would be possible?
In europe it is very common to prescribe full correction to maximize
vision. I would like to debate this with the following example:

acemanvx@yahoo.com wrote:
> I dont care what you say, seeing just shy of 20/20 is
> not considered having trouble seeing.

Theoreticaly by seeing 20/20 you can still have an error of i.e. -0.50
to -1.00 dpt. (Which means everything what is further then two to one
meters away gets blurry).
When correcting this, glasses would boost you up to a visus of 1.6 (20/13).

> I would not even consider 20/40 trouble seeing except in extreme
> situations like if I wanted to be a
> pilot, join the army, be a spy or anything that requires 20/20.

20/40 would be equal seeing things at 50%!?! I don't know how it is with
you, but seeing objects with 50% wouldn't satisfy me. And i think no
matter which situation (extreme or common) you should always have the
best vision possible.

> I consider trouble seeing starting at 20/70 to 20/100.
> My brother is 20/60 and he can see just fine. I have pointed out things in the
> distance and hes able to see almost anything he wants. He only wears
> glasses for driving and occasionally to see lectures in college
> classes.

Of course he can see anything he wants... For example he would see a
car. He would know it is a car because it moves and has four black
things which your brain tells him that are wheels. BUT he couldn't see
which brand it is or what the driver looks like. He couldn't make a
difference if the car has a silver or light blue painting. You loose all
the details (see http://de.wikipedia.org/wiki/Bild:Sch%C3%A4rfe_optik.jpg)
-----------------------------------

So why do people think seeing things with 20/30, 20/40 is enough? Why do
refractie surgeons only aim for 20/20 or 20/30 even though the patients
could have much better vision with conatacts or glases?
Maybe something to consider...

Best regards

Chris
John - 01 Feb 2006 14:04 GMT
test
Neil Brooks - 01 Feb 2006 17:38 GMT
>test

Aw, crap.  I didn't study ;-)
Signature

Live simply so that others may simply live

Yasar, Mehmet C PFC B Co 602d ASB - 03 Feb 2006 01:51 GMT
Ah bummer... What a refreshing change, nothing changed on this NG... :)
acemanvx@yahoo.com - 01 Feb 2006 14:27 GMT
You are forgetting not everyone is correctable to 20/20. Surgeons aim
for 20/20 because its the golden standard of perfect vision. Many
people arent capable of this and a few may be capable of better, such
as 20/15 and occasionally 20/13 or 20/10. Not only that, since all
laser surgury induces more high order aberrations, you may experience a
loss in quality and sometimes also accuracy of vision. I cant tell you
how many people lose one or two lines of BCVA. They never see 20/20
again after lasik.

20/30 to 20/40 is not quite perfect but considering you can be 20/400
or count fingers without glasses, its a very big improvement and will
greatly reduce your dependancy on glasses if not eliminate them.

http://upload.wikimedia.org/wikipedia/de/4/42/Sch%C3%A4rfe_optik.jpg

This looks like the 20/40 I see.

http://upload.wikimedia.org/wikipedia/de/4/42/Sch%C3%A4rfe_optik.jpg

Looks like 20/200 vision to me.

"My question is why do optometrist only try to correct to 20/20 even
though through full correction much higher vision would be possible?"

Optometrists try to correct the best your eyes are capable of. This
means if they are capable of 20/15 then he will get you there. If they
only see 20/40 then thats all you can be corrected to. They first try
to get you to 20/20 because for many people, this is the point where
they achieve plano. Optometrists assume if you dont get to 20/20 you
arent plano yet and keep trying a few times then say thats your BCVA.
Mine tried like 3 or 4 times to get me to 20/20 but I cant correct to
perfect vision and neither can my mother, father nor brother.

"Theoreticaly by seeing 20/20 you can still have an error of i.e. -0.50

to -1.00 dpt. (Which means everything what is further then two to one
meters away gets blurry)."

I would not even call it a blur. Someone whos -1 and seeing 20/10 would
of course be capable of seeing better than 20/20 with correction.
Another person may be plano and see 20/20. Both people at 20/20 will
see equally well from a distance reguardless of pescription. The
exception is lasik 20/20 which may not be the same quality as 20/20
with virgin eyes. I know this lady whos -.75 and sees 20/20 without
glasses, 20/15 with glasses and says the difference is very very small.
Shes upset she got pescribed glasses and was told to wear them. Shes
seeing an ophthamologist for a 2nd opinion and in the meantime shes
been going much of the time without glasses.

"When correcting this, glasses would boost you up to a visus of 1.6
(20/13)."

Then you can wear glasses on occasion but they are highly optional if
you meet the DVM of 20/40(and especially if you exceed it)

"20/40 would be equal seeing things at 50%!?! I don't know how it is
with
you, but seeing objects with 50% wouldn't satisfy me. And i think no
matter which situation (extreme or common) you should always have the
best vision possible."

If a person sees 20/40, at 20 feet from the chart that person can read
letters that a person with 20/20 vision could read from 40 feet away.
The 20/40 letters are twice the size of 20/20 letters; however, it does
not mean 50% vision since 20/20 sounds like it is one half of 20/40. If
20/20 is considered 100% visual effiency, 20/40 visual acuity is 85%
efficient.

My comments: While 20/40 is half the visual acuity of 20/20, its 85% as
functional or efficient as 20/20. People who see 20/40 are quite
functional despite half the acuity. If you are already wearing glasses
and they are too weak, get stronger glasses. But if you arent wearing
them, you dont have to if your not having trouble seeing. I know tons
of friends with a -1 pescription and some with even -2 and they go
without glasses. Why? you ask? They dislike glasses, simple as that.

"Of course he can see anything he wants... For example he would see a
car. He would know it is a car because it moves and has four black
things which your brain tells him that are wheels. BUT he couldn't see
which brand it is or what the driver looks like. He couldn't make a
difference if the car has a silver or light blue painting."

He could see everything including what the driver looks like. He can
see the color of the car, heck even I can without glasses and im 20/400
without. of course he does wear glasses to drive, but even that he
doesnt have to but does it for good measure. 20/70 is legal to drive
here so he isnt restricted because hes 20/60. He chooses to wear
glasses for driving, nothing wrong with that when it comes to safety
but for anything else, he doesnt wear glasses.

By the way, whats your pescription and how well do you see with and
without glasses? My pescription is below:

left eye: -4.5 sphere, -.75 cylindar(140 axis) correctable to 20/30
right eye: -3.5 sphere, -1.5 cylindar(55 axis) correctable to 20/40
otisbrown@pa.net - 01 Feb 2006 15:46 GMT
Dear Chris,

Subject:  Does a minus lens have an "effect" on the refractive
state of the natural eye.

Re:  #1  Dynamic concept -- proven with the primate eye -- YES!

Re:  #2  Box-camera (frozen eye) concept -- not proven, but assumed --
NO!

There are two schools of "though" about the natural eye's behavior
as described above.

The reason you whould NOT go for a strong minud (creating
20/10 in a 20/30 eye) is because of the concern that
that minus will (as a secondary effect) create stair-case myopia,
and the cynamic eye controls its refractive state to BOTH
a "confined" environment with that environment made even
more "confined" by the minus lens.

But it is very difficult to resist the urge to give the person
very, very sharp vision as you state.

There is repeated "Gnashing of teeth" over this issue
as you might have understood from reading some of these
posts.

There is NO RESOLUTION to this issue, so "practice" becomes
the "majority opinion" (Theory number 2) and the second-opinion,
concept number 1.

There are good reasons (in young children) to be very "careful"
with that minus.  See:

www.chinamyopia.org

for this second-opinion.

As always, enjoy our pleasant analytical discussions
about the natural eye's proven behavior as a matter
of fundamental science.

Best,

Otis

++++++++++++++++++

> I have been watching this newsgroup for sometime and always seen quotes
> that "20/20 vision" is THE best to have. Here in Europe we use a "visus
[quoted text clipped - 52 lines]
>
> Chris
Quick - 01 Feb 2006 17:31 GMT
"effect"
"though"
"confined"
"confined"
"Gnashing of teeth"
"practice"
"majority opinion"
"careful"

Quote count: 8
Post size: small/tiny
otisbrown@pa.net - 01 Feb 2006 20:08 GMT
Dear Quick,

Please add the words

"Paradigm"

"Semantics"

"Refractive state" not Refractive "error",

"Paradigm-shift"

"Second-opinion"

"Informed choice"

Best,

Otis
Christopher Zöttl - 03 Feb 2006 15:36 GMT
Dear Otis,

please look at this link and answer me the following questions:

http://www.usherbrooke.ca/ophtalmologie/images/Predoc/Erreurs_refraction/myopie.jpg

As you might know a fully corrected or emmotropic eye the light beams
come to a stop in the fovea centralis. So why should a plus lens or no
lens at all help? You would even get more blurry vision. How would it
prevent an eye from getting stair case myopia?

Best regards

Chris

otisbrown@pa.net schrieb:
> Dear Chris,
>
[quoted text clipped - 101 lines]
>>
>>Chris
otisbrown@pa.net - 03 Feb 2006 16:34 GMT
Dear Chris,

Subject:  The dynamic nature of the living eye.

Re:  Picture of a "box-camera" use to represent the (presumed)
living eye.

Scientific research proves that the living eye changes its
refractive state (in a negative direction) when you place
a minus lens on it.  What this proves that the living eye
is a highly-accurate auto-focused camera.  (Refractive state is
measured
with "classical" atropine.  Refractive state can be plus or minus,
and the living eye completely normal.  Refractive states IN THE WILD
run from zero to +2 diopters, (normal, or gaussian distribution) and
are completely normal.)

You have shown a "frozen" box camera, and the picture would
be true -- if the living eye were proven to be a "box camera".

But no proof exists that the living, or natural eye is like that -- at
all.

Thus if the eye has a refractive state of EXACTLY ZERO (very rare),
then a "plus 2" would in fact blur the eye-chart to about 20/140.
True enough.

For the "near" enviroment, the +2, for objects at 20 inches, would
in effect be moved to optical "infinity".

In fact, if you read NEI advocacy you will find that they realize
that a "near" environment is a "problem" for the living, natural
eye.  So they make the statement that you should
"look up" for 6 minutes out of every 60 minutes.  (10 percent of
the time looking at "infinity".)

When I suggest that a 2 dipoter plus be used for all this
"close work", it is simply to say that you should be
"looking up" for 60 of the 60 minutes.

And then the majority-opinion OD EXPLODE.

That is clearly not "medicine" nor is this plus lens
a "prescription".

It is simply scientific common sense.

Why do these majority opinion ODs have a problem with that?

In fact, this becomes more a matter of personal choice or
"judgment" that a "medical" issue.  Why make it into
a "medical" issue?

Best,

Otis
acemanvx@yahoo.com - 03 Feb 2006 17:34 GMT
Hey Christopher Zoettl, did you see my long reply below your post? I
said everything I had to. I disagreed on alot of what you said!
Christopher Zöttl - 05 Feb 2006 00:13 GMT
acemanvx@yahoo.com schrieb:
> Hey Christopher Zoettl, did you see my long reply below your post? I
> said everything I had to. I disagreed on alot of what you said!

Dear Acemanvx,

I also disagree on a lot of what you said. But I respect your opinion.

Best regards,

Christopher Zoettl
Quick - 03 Feb 2006 18:11 GMT
> That is clearly not "medicine" nor is this plus lens
> a "prescription".

legal disclaimer? just in case it's quackery?

> It is simply scientific common sense.

Scientific common sense? I didn't know that science
involved common sense. I thought common sense was
what you used to make decisions in the absence of
objective facts or insufficient information.

> Why do these majority opinion ODs have a problem with
> that?

Probably because it's not based on science and you have
no common sense?

> In fact, this becomes more a matter of personal choice or
> "judgment" that a "medical" issue.  Why make it into
> a "medical" issue?

Bzzzt, no legal out here. You're now saying that you're only
suggesting a personal choice and not addressing a medical
issue?  Sounds like you're back peddaling.

-Quick
A Lieberman - 03 Feb 2006 22:58 GMT
> When I suggest that a 2 dipoter plus be used for all this
> "close work", it is simply to say that you should be
> "looking up" for 60 of the 60 minutes.

Dear Christopher,

Please disregard Otis.  He is not in the medical profession nor in any
position to give medical advice.

Thank you.

Allen
Christopher Zöttl - 05 Feb 2006 00:46 GMT
otisbrown@pa.net schrieb:
> Dear Chris,
>
[quoted text clipped - 52 lines]
>
> Otis

Dear Otis,

the eye might not be a box camera, and the lens of the eye may be able
to adapt.
But what if the cornea has to much refraction. I mean a
Gullstrand-Cornea has a refraction of 43.05 dpt, what if an eye has a
refraction of 45 dpt? Then no matter if the eye were living or a box
camera, the light beams would be to short, because the cornea makes a
static refractive error ->
http://www.usherbrooke.ca/ophtalmologie/images/Predoc/Erreurs_refraction/myopie.jpg

What purpose would resolve for me by looking 10% of then time to infinity?
If I have a +2 lens infront of me this would resolve only in an angular
magnification of 0.5x . Which means everything would get smaller. How
should this be helping the eye?

Best regards

Chris
otisbrown@pa.net - 05 Feb 2006 02:24 GMT
Dear Chris,

I see you have the same book that I do -- concerning Kepler's
first "assumption" the an un-desired refractive state of the
living eye was an "error", and that analysis carried forward
through the years to the "Gullistrand" paradigm.

And excellent analysis -- of an assumption.

Until you realize that you are analizing your false (but honest)
assumption about the living eye -- not much preventive-progress
can be made.

If you "accept" that the living eye must be a dynamic system,
and build a "working model" of it -- then the "picture" becomes
profoundly different.

This type of "change" is called a "paradigm" shift or "change"
described by Thomas Kuhn, in "The Structure of Scientific Revolutions".

When the "paradigm" changes, then even the word we use
to describe the living eye must change also -- which
is why I insist on describing the living eye has having
"refractive states" -- and completely normal -- as least
from -1 to +2 diopters.

All these refractive refractive states are called "ametropia"
as Dom insists.

Thus the effect of the "Kepler" assumption is to make
all natural and living eyes "defective" because of
our assumptions.

And that does include the Gullistrand model.

Do not get me wrong.  It is nice to calculate
curvature to 6 significant figures -- but
it does not mean very much because
it can not possibly repesent the proven
behavior of the primate eye.

Further the "accommodation" model -- could never
"work", and could NEVER be made to work either.

The total power of the eye is controled by micro-blur
sensed at the surface of the retina, and the "sharp"
image is maintained by continuous feed-back from
retina to lens.

But that is why you can not specifiy "'length" and
should stick to what is measured, i.e., refractive
state, and not extrapolate a state into a "length".

Best,

Otis

But what if the cornea has to much refraction. I mean a
Gullstrand-Cornea has a refraction of 43.05 dpt, what if an eye has a
refraction of 45 dpt? Then no matter if the eye were living or a box
camera, the light beams would be to short, because the cornea makes a
static refractive error ->
Dan Abel - 01 Feb 2006 21:20 GMT
> I have been watching this newsgroup for sometime and always seen quotes
> that "20/20 vision" is THE best to have.

20/20 is normal.  It is better to have normal vision than worse vision.  
No informed person here would claim that 20/20 is the best.


> My question is why do optometrist only try to correct to 20/20

I believe it is more of a language problem.  I have never had a
refraction where an OD stopped trying to get better vision at 20/20.  No
OD on this group says that they do this, either.

> acemanvx@yahoo.com wrote:
> > I dont care what you say, seeing just shy of 20/20 is
> > not considered having trouble seeing.

Quoting what aceman says will not make you friends on this group.  He is
trying very hard to learn as much as he can about vision, but many of
his posts are far from correct.

> Theoreticaly by seeing 20/20 you can still have an error of i.e. -0.50
> to -1.00 dpt. (Which means everything what is further then two to one
> meters away gets blurry).
> When correcting this, glasses would boost you up to a visus of 1.6 (20/13).

20/20 simply means that you see at 20 feet what a normal person sees at
20 feet.  20/30  means that you see at 20 feet what a normal person
could see at 30 feet.  20/15 means you can see at 20 feet what a normal
person can only see at 15 feet.  In all three cases, the measurement is
taken at 20 feet, and says nothing at all about what you can see at one
or two meters.  Despite the conversion chart published on this group by
aceman, converting Snellen results to diopters, it doesn't always work
that way.  

> So why do people think seeing things with 20/30, 20/40 is enough? Why do
> refractie surgeons only aim for 20/20 or 20/30 even though the patients
> could have much better vision with conatacts or glases?
> Maybe something to consider...

Is this your actual experience, or just based on what the wackos on this
group have posted?

As far as refractive surgery goes,  there are reasons to undercorrect
myopes.

Signature

Dan Abel
dabel@sonic.net
Petaluma, California, USA

Dom - 02 Feb 2006 10:09 GMT
> My question is why do optometrist only try to correct to 20/20 even
> though through full correction much higher vision would be possible?
> In europe it is very common to prescribe full correction to maximize
> vision. I would like to debate this with the following example:

> So why do people think seeing things with 20/30, 20/40 is enough? Why do
> refractie surgeons only aim for 20/20 or 20/30 even though the patients
[quoted text clipped - 4 lines]
>
> Chris

Optometrists always try to give the best vision possible, whether it's
20/20, 20/15 or 20/30. Or whatever. And patients love it if you can get
them to a good 20/15 instead of plain old 20/20.

Some patients who are say 20/30 uncorrected might be quite happy to live
with that and avoid glasses, and that's fine. But others want the best
possible vision - different individuals have different expectations.
What is acceptable to one individual (e.g. Aceman) may be seen as
entirely unacceptable to another. People are different.

Refractive surgeons don't aim for an acuity (e.g. 20/20), they aim for a
refraction (e.g. 0.00 or -0.75). If they subsequently achieve 20/20 then
they are satisfied. 20/15 would be a bonus.

Dom
Dr. Leukoma - 03 Feb 2006 03:16 GMT
Dear Chris,

The term "20/20" is more akin to a metaphor for the BCVA, which is the
"best corrected visual acuity."  For most people, the BCVA is 20/20 or
1.0 decimal, for some it is 20/15 or 1.3 decimal, and still fewer can
go to 2.0 or 20/10.
otisbrown@pa.net - 03 Feb 2006 03:25 GMT
Dear Chris,

The definition of 20/20, was established
by a Dr. Snellen.  It is not a "metaphore".

It means that you can read characters
that subtend 5 minutes-of-arc at 20 feet.
No more, not less.

There are two defintions of "passing"
the 20/20 line.  They are

1.  You read 1/2 the letters correctly -- the
DMV

2.  You read 4 out of 5 --  the military.

Thus 20/20 is 3/8 inch letters and 20/40 is 3/4 inch letters.

Metric is 0.9 mm and 1.8 mm at 6 meters.

That is measurement in engineering terms.  I do not know how DrG
converts objective measurements into a metaphore.

Best,

Otis
Dr. Leukoma - 03 Feb 2006 03:55 GMT
The term 20/20 does indeed have both a scientific, as well as a
non-scientific meaning.  In scientific terms, it is the size of a
letter subtending 5 minutes of arc at any distance, and not just 20
feet, mind you.  Of course, the test distance will determine the SIZE
of the letter required to subtend 5 minutes of arc.

In common use, i.e. lay terms, 20/20 is often used to express the BCVA,
as most people consider that 20/20 is the best possible resolution.

Otis, you should quite while you are ahead.

DrG
http://coppellfamilyeyecare.com
Quick - 03 Feb 2006 05:47 GMT
This is it folks... the grand prize winner!

> a "metaphore"

Think about that. Putting quotes around metaphore...

-Quick
Glenn - USAEyes.org - 03 Feb 2006 08:07 GMT
>This is it folks... the grand prize winner!
>
[quoted text clipped - 3 lines]
>
>-Quick

ROFLOL

Glenn Hagele
Executive Director
USAEyes.org

"Consider and Choose With Confidence"

Email to glenn dot hagele at usaeyes dot org

http://www.USAEyes.org
http://www.ComplicatedEyes.org

I am not a doctor.
otisbrown@pa.net - 03 Feb 2006 14:35 GMT
Dear Quick,

A metaphore, is making a statement like,  The ship "ploughed" the sea.
THAT is a metaphore.

I do not agree with DrG's use of the word to describe an objective
chart, and the reading of that chart (1/2 the letters).  That is
objective --
not a "metaphore".

The issue is one of sematics -- as the basis of a scientific
argument about scientific proof.  (A subject we should
discuss at some future time.)

Best,

Otis
Dr. Leukoma - 03 Feb 2006 15:37 GMT
The very same person who regularly turns the medical dictionary on its
head would defend the correct usage.  That's called irony.

DrG
drfrank21@gmail.com - 03 Feb 2006 16:07 GMT
> Dear Quick,
>
[quoted text clipped - 13 lines]
>
> Otis

Otis, try spelling metaphor correctly in order to gain more
credibility. Hey, if you're
going to be nitpicking on grammatical issues at least spell the word
correctly.
I guess everybody but you understood what Dr.G meant (metaphor is
actually a type
of analogy).

How about an implicit metaphor for you.  "Shut your trap!"  qualifies
and
sure seems appropriate to me in this case.

frank
Mike Tyner - 03 Feb 2006 18:57 GMT
> A metaphore, is making a statement like,  The ship "ploughed" the sea.
> THAT is a metaphore.

> The issue is one of sematics -- as the basis of a scientific

If you're going to lecture us on "sematics" as well as medicine and science,
please check your spelling.

-MT
otisbrown@pa.net - 04 Feb 2006 03:42 GMT
Dear Mike,

Thanks, it is metaphor.

Given the "quality" of the post here -- I agree, please prescribe
for the sharpest vision possible.

That is the only thing that you can do.  Any preventive
work would truly be impossible.

Best,

Otis
p.clarkii@gmail.com - 04 Feb 2006 23:40 GMT
not to mention ineffective also.
dragonlet - 07 Feb 2006 16:47 GMT
Someone here really messed up the forums by providing some fault
information.  Obviously the people in the know are quite frustrate
it and I'm having trouble comprehending when there's exces
information about metaphors and semantics.

I'll start by trying to answer the actual question

20/20 was determined when the eye is at it's relaxed state, starin
into the distance that an object should focus to a point on the bac
of the eye.  This optimal distance was decided at 20 feet.  So
measurement of how clear or unclear a person's visual acuity is no
measured by 20/20.  You see at 20 feet what you SHOULD be seeing a
20 feet.

Some people's eyes are capable of seeing things at 20 feet what th
norm should be seeing at 15 feet.  So you see better!.. and som
people eyes are not as good because of one reason or another and the
see 20/30.. so you see something sharp at 20 feet when others see i
at 30 feet.

A lens put in front of your eye, being contact lens or eyeglasses wil
"BEND" the light accordingly so that the light focuses where i
should.  With people who are far sighted, the image focuses past th
point where it should.  People who are near sighted, the imag
focuses before the point where it should.  LENSES, help push thi
focus point to where it should be for the best vision possible

Some people can deal with 20/30 sight because most of their lifestyl
maybe more critical for near vision .. and less for far vision.  Tha
is why some people don't mind it even though it's less than optimal.

Optometrists or Ophthalmologists will try to correct for 20/20 .. i
you can see better than that, then they will correct for it.. bu
most people don't need it.  Even if you put a higher prescription i
front of someone's eye will not make it sharper for them.. it wil
most likely make their eyes more tired by the end of the day.

Hopefully that explains things

FURTHERMORE, Chris a plus lens... +2.00D does not make things smaller
A +2.00 lens is basically a magnifying lens and therefore will mak
objects look larger.
Robert Kopp - 08 Feb 2006 17:19 GMT
> I have been watching this newsgroup for sometime and always seen quotes
> that "20/20 vision" is THE best to have. Here in Europe we use a "visus
[quoted text clipped - 11 lines]
> In europe it is very common to prescribe full correction to maximize
> vision. I would like to debate this with the following example:

If refractive error is exactly neutralized, you get the best you can get. If
you don't have the best you can get, either the corrective lens is too
strong or it isn't strong enough.

In this case (for myopia), I would prefer a lens that isn't quite strong
enough, since this at least makes reading more comfortable. If it's too
much minus, that doesn't help for any task.
Signature

Robert T. Kopp
http://analytic.tripod.com

 
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