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

[Bexley Hall]

Greetings!

--- On Fri, 8/22/08, Jeremy D Rogers <jdrogers at optics.arizona.edu> wrote:

> >> 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.

And, (intuitive guess?) I can relate this to ratios of
"similar triangles" (re: angular extent)?  Sorry, I keep
thinking of 2D images (vaguely recalled from grade school)
showing the radii of the arcs that describe the sides of
the lens and how that related to focal pt, etc.

> 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.

OK.

> 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.

Understood.

> 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.

OK.  But, the angular extent can be seen (normalized?) to
similar units of the "diopters", right?  I.e., they're all
just similar triangles...  we're comparing tan()'s?

> Now, for a telescope, that work great, because
> the moon is 1/2 degree in the sky and with the telescope,
> you see how big it 'looks' and divide.

Right.  Distance to objective can't be changed (realistically)

> 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.

Yes.  Or, *anything* for that matter.  E.g., I can walk up
to a house and the house "looks bigger".  It hasn't really
changed physical size but it eats up a greater portion of
my field of vision.

> 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.

In theory, it would become "infinitely large" as it came into
contact -- just like the way tan() explodes (?)

> 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.

OK.

> 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.

But, would this be different than holding the item at a *different*
length?  Or, by moving the magnifier (or, does that just change
foxus?)

> 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.

So, presumably, *someone* has decided how to "normalize" these
figures -- so company X can't claim "3X" for their magnifying
glass while company Y claims 5X for the same exact glass!

I.e., is it akin to "circle of confusion"... you just pick some
*arbitrary* point on the curve and call that a reference?
(like 3dB down on a phase-magnitude plot)

> > 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.

Comparre *WHAT*? Magnifying glasses *or* (!) magnifying glasses
to "eyeglass diopters"?

> Assuming you want a WD of 20cm to avoid solder fumes,

Probably longer than that.  I also want to avoid burning
(melting?)my *hair*, etc.  :>  And, I usually want to be
able to see a bot more "context" when working -- if you
focus on one particular solder joint exclusively, you
later realize you've been working on the *wrong* joint!
(since, up close, they all look the same!  Hence, you want
to have more stuff in your field of view to "get our bearings")

> 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.

I.e., keeps you from crossing your eyes (at all!)

> 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)

OK, but, strictly reading your comments, I need to place the
*object* (target) within that focal length.  I am not averse to
putting the magnifying glass almost *on* the "work".  I can
usually get my hands/tools under it (and, often, this lets
me rest the hand that is holding the glass on the work
itself so I can kill two birds with one stone -- hold the
glass *and* the solder, etc.)

So, I should be able to move my head back comfortably...
Ah, but then "WD" increases (?) and the image shrinks?

> 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.

OK.  That places a lower limit on WD -- and, thus, an
*upper* limit on the magnification possible (for a given
lens), right?

> >> 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.

Which means the lens will be *honking* thick!  This is true of
the inspection lamps used on assembly llines (e.g., the lens
may be almost an inch thick, 4-5 inches in diameter).
This puts the kabosh on carrying it in your pocket!

> 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.

Yes.   The technical term is "SOL".  :<

> 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.

I have a 2-3X glass (3 inch?) that I use from time to time,
now.  It is "adequate" (i.e., I wouldn't run out and buy
another one like it!  :< ).  Except the morons who made it
opted to include a small "bifocal" (higher power) which
seriously hinders using it for the "full lens" capability.

> > 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. :-)

Ditto me re: my "work"!  I'll assume you are happy/challenged
with it, then!?

Thanks!
--don