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Thread: Lenticular problem?

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    Lenticular problem?

    Accurately calculate the edge thickness of a thin -20.00D lens made with a plano front surface and a t= 1.0mm, n= 1.74 the lens is edged 42mm round,if the edge thickness is reduced by 50% using a plano tool find the diameter of the lens aperture produced?

    Am i right in saying you use sags to calculate the edge thickness, I just dont have anything to calc final aperture size?

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    Quote Originally Posted by westell8 View Post
    accurately calculate the edge thickness of a thin -20.00d lens made with a plano front surface and a t= 1.0mm, n= 1.74 the lens is edged 42mm round,if the edge thickness is reduced by 50% using a plano tool find the diameter of the lens aperture produced?

    Am i right in saying you use sags to calculate the edge thickness, i just dont have anything to calc final aperture size?
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    Master OptiBoarder Darryl Meister's Avatar
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    I would begin by determining the radius r of the back lens surface F2 (-20.00 D):



    You would calculate the sagitta of a -20.00 D lens surface at a semi-diameter d of 21 mm, given a refractive index of 1.74, using the sagitta formula:



    Add 1 mm to the thickness to allow for the center. Then divide the answer in half to arrive at the new edge thickness of the lenticular.

    Finally, after rearranging the sagitta formula to solve for the semi-diameter, calculate the semi-diameter d2 at which this edge thickness is obtained, less 1 mm for the center thickness, in order to determine the final aperture of the back surface (r):



    where s2 is now equal to half of the edge thickness, less 1 mm. If you need further help, just let me know, but this provide you with what you need to work out the problem.
    Darryl J. Meister, ABOM

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    ATO Member HarryChiling's Avatar
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    Quote Originally Posted by westell8 View Post
    Accurately calculate the edge thickness of a thin -20.00D lens made with a plano front surface and a t= 1.0mm, n= 1.74 the lens is edged 42mm round,if the edge thickness is reduced by 50% using a plano tool find the diameter of the lens aperture produced?

    Am i right in saying you use sags to calculate the edge thickness, I just dont have anything to calc final aperture size?
    I usually do it step by step, thin lens equation gives us:

    Power = Front Curve + Back Curve
    -20.00 = 0.00 + Back Curve
    Back Curve = -20.00D

    Then determine the radius of the back curve:

    Radius(m) = (n-1)/Back Curve (D)
    Radius(m) = (1.74 - 1)/-20.00
    Radius(m) = -0.037m
    Radius(mm) = 37mm

    Now determine the sag of the back curve:

    sag = radius - {radius2 - (diameter/2)2}1/2
    sag = 37 - (372 - 212)1/2
    sag = 37 - (1369 - 441)1/2
    sag = 37 - 30.5
    sag = 6.5mm

    Add the center thickness and divide for 50% of the edge thickness:

    Thickness(mm) = (sag + centerthickness) * 0.50
    Thickness(mm) = 7.5 * 0.50
    Thickness(mm) = 3.75mm

    Now subtract the center thickness from final thickness and we get the back curve sag:

    Back Curve Sag = 3.75 - 1.00
    Back Curve Sag = 2.75mm

    Now use the sag formula to find the diameter of the lens:

    Back Curve Sag = radius - {radius2 - (diameter/2)2}1/2
    2.75 = 37 - (372 - (diameter/2)2)1/2
    2.75 = 37 - (1369 - (diameter/2)2)1/2
    34.25 = (1369 - (diameter/2)2)1/2
    1173.06 = 1369 - (diameter/2)2
    (diameter/2)2 = 195.94
    (diameter/2) = 14.00mm
    Diameter = 28.00mm

    So the aperature is going to be 28mm with a plano back curve cut into it.

    Opps figures Darryl's got it.
    Last edited by HarryChiling; 04-01-2009 at 12:45 PM.
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