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

[Jeremy D Rogers]

>> 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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