[Tfug] ... and, yet another, optics question! ;-)

[johngalt1]

I enjoyed reading this.

Excellent post, Jeremy.

----- Original Message ----- 
From: "Jeremy D Rogers" <jdrogers>
To: "Tucson Free Unix Group" <tfug at tfug.org>
Sent: Friday, August 22, 2008 8:12 PM
Subject: Re: [Tfug] ... and, yet another, optics question!
;-)


>>> Diopters is the optical power of the lens in inverse
>>> meters. Being
>>> near sighted, my glasses are -3 diopters, so they have a
>>> focal length
>>> of -1/3 meters or -30 cm. That would not help you.
>>
>> Are you playing fast-and-loose with terms or strictly
>> pedantic?
>> I.e., "optical power"... so, is a "2X magnifying glass"
>> (2 power?)
>> a "-2.00"?
>
> Sorry, I should have explained.. optical power of a lens
> is basically
> 1/f. Diopters is a measure of optical power, but
> specifically in units
> of meters. More generally, optical power could be measured
> in any
> inverse length scale.
>
> The optical power of a lens and the magnifying power are a
> little
> different. Let me explain. No, there is too much, let me
> sum up...
> Magnification is not magnifying power which is also not
> optical power.
> Optical power is 1/f. Magnification is only relevant when
> speaking of
> an object and image, so if you have a slide projector, you
> could
> measure the size of the slide and the size of the image on
> the screen
> and the ratio would be the magnification.
>
> However, nobody generally cares how big the image on your
> retina is,
> so instead of magnification, people like to talk about
> magnifying
> power which is the ratio of the angular extent of the
> object with the
> lens to that without. Now, for a telescope, that works
> great, because
> the moon is 1/2 degree in the sky and with the telescope,
> you see how
> big it 'looks' and divide. The problem is that with a
> small circuit
> board, you can put it closer to you face to make it have a
> larger
> angular size.
>
> But there is a limit to how close to your face you can put
> it, because
> your eye can not focus to something 1mm in front of it.
> For most
> people the closest they can focus (called the near point,
> see below)
> is about 10cm, but people who need reading glasses have
> lost the
> ability to focus so close and their near point may be arms
> length or
> more. So finally, if you put something as close as you can
> comfortably
> focus, and then measure the angular extent, then put the
> magnifier in
> front of it and measure the angular extent, that give you
> the
> magnifying power.
>
> Magnifying power can be described in terms of the focal
> length of the
> lens given your near point (assume 10 cm) or given a fixed
> object
> distance if you comfort level is also dictated by solder
> fumes. But it
> will be different if you change that distance, so this is
> why
> magnifying power tends to be loose term.
>
>> Or, am *I* playing fast-and-loose?  :-/
>>
>>> Glasses for far sighted people (reading glasses) are
>>> positive power which is what you want.
>>
>> Yes, which is why the thought struck me that I could just
>> buy some El Cheapo (reading) glasses and steal the
>> lenses...
>> But, how do I convert/compare diopters to "2X, 4X, 7X,
>> etc."
>> encountered on magnifying glasses?
>
> The only way to compare is to assume a working distance.
> Assuming you
> want a WD of 20cm to avoid solder fumes, the angular
> extent of an
> object of size d is roughly d/WD. Now if you have a lens
> of optical
> power 6 diopters, you have f=1/6m = 15cm. The highest
> magnifying power
> (largest apparent object size) comes from placing the
> object just
> inside the focal length of the lens which 'projects' the
> image to
> infinity, which is comfortable to your eye. So the angular
> extent is
> now d/f. So the magnifying power is (d/f)/(d/wd)=wd/f.
> Given wd=20cm
> and f = 15cm, you get a MP of  1.3x which isn't great. You
> see can see
> the problem that to get a good MP, you need a very short
> focal length
> lens (higher power) and it may be hard to find a pair of
> reading
> glasses with such high power.
>
>>
>>> A magnifying glass works by increasing the optical power
>>> of your eye
>>> or equivalently shortening the total focal length of the
>>> eye/lens
>>> system. Since I am near sighted, my glasses have a
>>> negative
>>> power.. so all I have to do is take off my glasses and
>>> put the
>>> object closer -- no pocket magnifier needed. :-)
>>
>> OK, I'm far sighted so don't normally need glasses for
>> close in
>> work.  *But*, reading the little tiny writing on surface
>> mount
>> components, etc. is now beyond me.  :<  Even bringing the
>> item
>> "up close" ... I just end up feeling like I am looking
>> cross-eyed!  :<
>>
>>> So what you want to look for is
>>> higher power or more diopters and you want them to be
>>> positive (which all reading glasses are).
>>
>>> The magnifying power that you get from a
>>> given lens depends on your eye's near point though.
>>
>> OK, what's a "near point"?
>
> Near point is the closest point your eye can focus. It
> differs from
> person to person and usually gets longer with age as your
> lens becomes
> less squishy and you loose the ability to accommodate.
> Typically, and
> average person has a near point around 10cm.
>
>>
>>> The only drawback
>>> to using a lens from a pair of glasses is that the lens
>>> is
>>> usually curved, so give a focal length, the thickness
>>> might be more
>>> than a lens made to be a magnifying glass. On the other
>>> hand,
>>> sometimes glasses use a higher index glass or plastic
>>> that requires
>>> less curvature to achieve the same focal length which
>>> would make
>>> it thinner. Probably your best bet is to play around
>>> with the
>>> pair of glasses in the store and see if it works for you
>>> better
>>> than what you have.
>>>
>>> One other thing you might look for is a loupe. This is
>>> what jewelers
>>> and such use, and it isn't flat, but it gives more like
>>> 10x and still
>>> is easy to carry around.
>>
>> I had such a thing (clipped onto my eyeglasses) when
>> younger.
>> But, realized I rarely needed it back then so...  :<
>
> I'm picturing christopher lloyd in back to the future.
> Sweet.
>
>> (I also used to have a nice *metal* shoe horn that I
>> never
>> needed but sorely mis now!)
>>
>> The problem I have found with most things (like *worn*
>> reading
>> glasses is that I end up with the lens close to my eye
>> and.or
>> the "target" close to my face.
>>
>> Ideally, I want to be able to hold something (lens) in my
>> hand
>> at a comfortable distance with my head far back from
>> both.
>> For exemple, I may be trying to solder a component on a
>> circuit
>> board -- I don't want my face so close that I can feel
>> the heat
>> (and fumes!) from the soldering iron.
>>
>> And, I think (?) to get any decent magnification, I would
>> have
>> to have a large (diameter) lens so both eyes could see
>> through it
>> if it was close to my face -- hence a smaller diameter
>> lens would work
>> if it was close to the "target" (i.e., both eyes could
>> converge on
>> the lens more easily).
>
> That all sounds reasonable. Large diameter, high power
> lens should
> work for you as long as you.  The biggest problem will
> probably be
> finding a lens with short enough focal length. And given
> the index of
> refraction of most glasses and plastics, you will find
> that a short
> focal length lens will either be small diameter, or for
> larger
> diameter, it will need to be thicker. Since your goal is
> to find
> something thin that you can put in your pocket, you may be
> stuck. But
> I still say it's worth a try. Maybe you will find that you
> don't need
> 10x, and you can live with 2x as long as its convenient to
> carry.
>
>>
>> Sorry my explanation isn't very precise.  :-/  I don't
>> know enough
>> about the science to put it in better terms.
>
> Not at all... as may be apparent by my long winded email,
> I like
> talking about lenses. :-)
>
> Good luck,
> JDR
>
>>
>>
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