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Thread: Hi Index Lens Formula

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    Question Hi Index Lens Formula

    Does anyone know a formula that can calculate the refractive index of a lens given its surface powers (measured with a lens clock set for n=1.523), its minimum thickness, and its overall power in diopters. The actual formula was not published and nobody, not even the original publication, seems to know of it. Is anyone familiar with this formula?

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    Master OptiBoarder Jeff Trail's Avatar
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    Re: Hi Index Lens Formula

    SMW said:
    Does anyone know a formula that can calculate the refractive index of a lens given its surface powers (measured with a lens clock set for n=1.523), its minimum thickness, and its overall power in diopters. The actual formula was not published and nobody, not even the original publication, seems to know of it. Is anyone familiar with this formula?
    Two ways to do it, and we really went into this a while back for another member (haya) the easiest is if you had a "cheap" version of a surfaca program and you could run a "reverse" system plugging in the known numbers (sags and curves) and tinker with the index of refraction to get them to all match...

    The one you asked for was provided by JRS, SEE that I'm more than happy to give credit to someone else for this complicated mess.. OH and you still need to figure in the CT and how that will effect power.. BUT here is a paste and snip from our other thread, it was back around the middle of last year some time...

    ALL JRS posting from here on down:p



    Due to the complexity of the calculations, this formula is broken down into useable fragments for a handheld calculator. The Power piece equals lensometer (digital readout preferred) power achieved.

    Frd = ABS (530 / True Base Curve)
    Rrd = ABS (530 / True Rear Curve)
    A1 = Frd - Rrd - Center Thickness
    B1 = 1000 * (Frd - Rrd) + (Rrd * Power) * (Frd - Center Thickness)
    C1 = 1000 * Rrd * Frd * Power
    If Power < 00.00 then............ Index = (-B1 + SQRT (B12 - 4 * (A1 * C1))) / (A1 * 2)
    otherwise............................... Index = (-B1 - SQRT (B12 - 4 * (A1 * C1))) / (A1 * 2)
    JRS gave an example using the formula


    As requested Haya, I worked up an example for you. One note though... in looking over the last lines (INDEX=), I discovered that the returned value was expressed as just the value to the right of the decimal. So I modified that line to convert to a index that comes out the way you expect it to look like. Works either way, just understand the reading. So here 'tis.

    Here is what you know going in;
    1) Rx
    2) Center Thick
    3) Lens Analyzer Readout

    1) –2.00 –1.00 x 075
    2) 1.7 mm
    3) –2.037 –1.027 x 075 (unrounded best)

    For this formula cylinder is disregarded, so;

    Using a good digital sag gauge (mine is a 40mm ball tip), we measure for TBC and REAR SPHERE (base) values

    TBC = 4.26 D (1.631 sag)
    REAR = -6.12 D (2.386 sag)

    Moving into the formula then….

    Frd = ABS(530/4.26) Frd = 124.41315
    Rrd = ABS(530/-6.12) Rrd = 86.530612
    A1 = 124.41315 – 86.530612 – 1.7 A1 = 36.182533
    B1 = 1000 * (124.41315 – 86.530612) + (86.530612 * -2.037) * (124.41315 – 1.7) B1 = 16252.764
    C1 = 1000 * 86.530612 * 124.41315 * -2.037 C1 = -21929416.5

    Since Power < 0 (minus), then
    INDEX = 1+ (-16252.764 + SQRT(16252.764^2 – 4 * (36.182533 * -21929416.5))) / (36.182533 * 2) INDEX = 1.585665109 (or 585.665109 using the original INDEX= from above posting)

    Rounded to 3 places past decimal = 1.586. Hence we have a poly lens

    Hope this helps. I have now created a small Excel sheet, so my brain can go back to sleep (normal state).
    You might want to go find that thread on the whole thing. If you can not find it I'll see if I can and tell you which one it was..I took the "short cut" to find the answer, JRS likes to make you work hard for the answer, he is probably right though, you should know the hard way to do it and understand it before "cheating" and doing it a lab rats back door cheating way;) Hope this is what you wanted...

    Jeff"see I'm willing to give credit where credit is due"Trail

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    Forever Liz's Dad Steve Machol's Avatar
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    Master OptiBoarder Shwing's Avatar
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    This was posed as a question to a electronic newsletter called: "Optical Dispensing News" and was answered in today's edition by none other than the Master himself:

    FINDING THE REFRACTIVE POWER OF THE LENS
    The response below relates to last week's request for help in finding a formula that can calculate the refractive index of a lens given its surface powers (measured with a lens clock), its minimum thickness, and its overall power in diopters.

    Clifford W. Brooks, O.D.
    Indiana University School of Optometry
    To subscribe to Optical Dispensing News, please visit:
    http://www.opticaldispensing.com/
    Shwing

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    Forever Liz's Dad Steve Machol's Avatar
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    Sorry Schwing but since that was a copyrighted article I needed to remove if from your post. :(


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    Master OptiBoarder Shwing's Avatar
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    NO problemo!

    I finally found what I was looking for:

    Lens clock excercise for glass lenses only:

    How to tell if a lens is high index with clocking a lens (you must know the power of the lens before clocking)

    ie: you know a lens is -6.00D (by lensometery); you clock it and clock net nominal power of -5.25D, therefore known power is higher than clocked power.

    -5.25/(divided by)-6.00 = 88%; therefore the ratio is 10-12% difference; so the lens is a 1.60 material

    The rule to remeber then is:

    - if ratio is higher than 80% difference, lens is lower index (1.6)
    - if ratio is 75% difference, lens is 1.70 glass
    - if ratio is 66% difference, lens is 1.80 glass
    - if ratio is 55-60% difference, lens is 1.90 glass

    This only works for glass as lens clocks calibrated for glass (plus mineral lenses) are more stable than organic.
    Last edited by Shwing; 01-21-2003 at 12:40 PM.
    Shwing

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