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How to approximate a lens shape

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  • How to approximate a lens shape

    I'm trying to make an optical center-punch with the lathe, so I want to approximate a lens shape on the end of some some cheap plastic (acrylic?) rod that I got from Tap plastics.

    This doesn't need to be great. Realistically just a non-magnifying flat on the end of the rod would work OK, but I figure someone other there might have a bright idea on how to approximate a proper lens shape without a CNC machine.

    So far I've made a couple trials freehanding with a file roughing out an approximate lens shape, and it sort of worked, although not very magnified and it was somewhat distorted.

    Maybe make a CAD drawing, printing out to scale, and using that as a gauge?

    First things first though, need to figure out the refractive index, and then figure out how to calculate what the desired shape is supposed to be for some magnification.

    Any ideas floating around out there?

  • #2
    Plastic lens

    Make a rod the length of the radius you want for your lens surface with
    points on both ends. Center punch your cross slide for one point and a
    matching place on your headstock for the other. With the rod set in the
    two punch marks, keep pressure on the rod with the carriage feed as
    you traverse the plastic with the cross feed. Start with the rod in line
    with the ways and you will get a spherical surface.
    This works for small parts of a sphere since if you go too far the points
    will come out of the punch marks.
    Polish with finer and finer abrasives and then Brasso or Simichrome
    to get it clear. Charlie

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    • #3
      A spherical lens works fine for an optical punch so I use a ball cutter to rough it out.

      See: http://www.gadgetbuilder.com/OpticalPunch.html
      Location: Newtown, CT USA

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      • #4
        I'd start here:

        Edmund Optics (EO) has been a leading producer of optics, imaging, and laser optics for 80 years. Discover the latest optical and imaging technology.


        ... In a prior life designing and making electro-optical-mechanical lab instruments I'd often need to do something with light I'd never done before. Cracking the Edmunds and Opto-Sigma catalogs almost invariably gave me the answer and at least pointed me in the right direction.
        "Lay on ground-light fuse-get away"

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        • #5
          I have used a shop built radius tool to make lenses, and also used cad to lay out coordinate charts for turning ellipses and parabolic curves. You stair step your cuts with a square end, spray it with marker or paint, and then carefully file down to eliminate the lines left by the paint.
          Location: Jersey City NJ USA

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          • #6
            optical punch lens

            I made an optical center punch that works great and I only have one kink to add. No matter how you form your lens shape, if it is approximately a circular arc you should be fine. I freehanded mine with a clean six inch mill file with no particular trouble. If I had to guess, perhaps an inch or so for the radius. The surface against the work needs to be dead flat and highly polished. I got sneaky and after I got the lens polished to a consistent translucent haze i put it back into the lathe and flame polished it with a wooden kitchen match. Just enough heat to self level without distortion, worked great. On the flat side I drilled a wooden 'lapping block' to hold it perpendicular while I polished it on 2000 grit silicon carbide wet/dry automotive sandpaper. I think I just used a little water.

            Also, for the reticule, don't bother with trying to make crosshairs. I made a very, very small trepanning tool and scored an annular reticule about fifty thousandths in diameter. I filled it in with black ink from a sharpie marker and repolished to remove any 'overspray'. Again, works great and your eye likes to naturally center things anyway.

            Hope this is of some use.

            Cheers,

            Jim

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            • #7
              Here's some theoretical stuff to determine your radius of curvature.

              The basic equations are Snell's Law (the Wikipedia article is good on this) and the thin lens approximation (again, see Wikipedia).




              If you crunch through those you find that for a thin plano-convex lens of a material with an index of refraction of 1.5, the focal length is very close to twice the radius of curvature of the convex surface. "Very close" means within a few percent.

              A thick plano-convex lens used as a contact magnifier, with one convex end and a flat end butt up against the object plane (the thing you're looking at), has a focal length very close to 2.5 times the radius of curvature of the convex surface.

              The index of refraction of the acrylic plastics is usually quoted in the 1.497 - 1.500 range. I've seen one number down around 1.300 but that may be bogus. Everyday plate glass is about 1.500. Optical glasses run 1.500 to maybe 1.800. The exact number wouldn't seem to be important in your application.

              As for what focal length you want, Bausch & Lomb gives these figures for its line of Hastings Triplet magnifiers -

              7x - 1.5"
              10x - 1"
              14x - 0.8"
              20x - 0.5"

              Bausch + Lomb is one of the world's largest suppliers of contact lenses, lens care products, prescription pharmaceuticals, intraocular lenses and other eye surgery products.


              These basic figures should be good for any magnifier, although a simple lens will have more aberrations than the Triplet, and these would become more pronounced at higher magnifications.

              So to determine the radius of curvature of your convex face, pick a magnification (which from the B&L data determines the focal length), assume your index of refraction is 1.5, and divide the focal length by 2.5.

              For a 10x magnifier, the radius of curvature is then 0.4". A hemisphere with a diameter of 0.8" would do it, although at that aperture your spherical aberration is going to make the image almost useless. The 10x B&L triplet has a lens diameter of .62", but your simple lens would have to be smaller than that. Spherical aberration will make your focussed image fuzzy.

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              • #8
                R=(n-1).H / n
                Where R is the radius
                H is the height of the piece and
                n is the refractive index of plexiglass. Which is 1.49. So n=1.49

                No. I'm not that smart. This is from the Oct/Nov. 2006 machinist Workshop. Page 45

                by Jeorg Hugel. The real smart guy.

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                • #9
                  I just put on two pairs of glasses.
                  Free software for calculating bolt circles and similar: Click Here

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                  • #10
                    I used a very fine file to rough in an acrylic dowel, then I sand papered it with increasingly finer grit, then finished it off on the buffing wheel with rouge. Even a circular form factor will produce results - the trick is to do it without melting the plastic.

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                    • #11
                      Some good info here:
                      http://www.gadgetbuilder.com/Coddington.html
                      specifically here:
                      Internet,Hosting,Phone,DSL.Cable,Business,Residential,Fiber,Dialup,Consulting,WordPress,VPS,SSL,Domain registration,Reseller,Website Design
                      Last edited by Swarf&Sparks; 03-01-2007, 03:17 AM.
                      Just got my head together
                      now my body's falling apart

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                      • #12
                        Successfully (3rd attempt !) made a rectangular Perspex lens for a Bike route holder. 1 inch rod turned between two centres (as far apart as I could get on the end of the rod). Polished with fine wet & dry then metal polish. Magnified text better than the photo would indicate.

                        Mark
                        Hey Swarf&Sparks - good to have another Escher fan on the board.
                        What you say & what people hear is not always the same thing.
                        www.remark.me.uk

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                        • #13
                          Just noticed your location Mark. After 3 pints o' that scrumpy, everything takes on an Escheresque perspective!
                          Just got my head together
                          now my body's falling apart

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                          • #14
                            BTW, a good source of linear lenses is old fax machines.
                            Rgds, Lin
                            Just got my head together
                            now my body's falling apart

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                            • #15
                              Lin - At my age a couple of pints is enough, although I'm really a Bunderberg OP man (when I can get it) and as Dean Martin said "I'm not drunk if I can lie on the floor without holding on"
                              Mark
                              What you say & what people hear is not always the same thing.
                              www.remark.me.uk

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