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    cylinder question

    I'm trying to solve a problem for my board exam:
    A patient needs a cylinder correction of -4 at 90. Instead, a -4 at 85 lens was given. Where is the residual cylinder axis now?
    I would appreciate if you could also explain why. Thanks!

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    Quote Originally Posted by voxexo View Post
    I'm trying to solve a problem for my board exam:
    A patient needs a cylinder correction of -4 at 90. Instead, a -4 at 85 lens was given. Where is the residual cylinder axis now?
    I would appreciate if you could also explain why. Thanks!
    Using a calculator,

    http://64.50.176.246/tools/cylinders.php

    enter Plano -4 x 180 for the first lens and Plano +4 x 175 for the second lens. If I understand the question correctly, the answer is 43 (0.35 DS -0.70 DC × 43).

    http://64.50.176.246/files/memo_on_d...tolerances.pdf

    The above shows the formulas used, in particular equations #3 and #4. I was able to use equation #3 to find the cylinder power (8 * sin5 =.695), but no luck with equation #4. Math experts please help out here.

    IMO we'll only use calculators in the field, with graphical/vector type analysis and formulas used by only the lens designers.

    Hope this helps,

    Robert Martellaro
    Last edited by Robert Martellaro; 04-17-2017 at 10:21 PM.
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    You may not have access to the calculator during your exam, so go to this site: http://www.flashcardmachine.com/abo-optical4.html and scroll down a little way. You will find a chart that shows what percentage of cylinder is in effect for how many ever degrees off axis the lens is. When you first look at it, it seems impossible to memorize. But notice that the left side is just increments of five, and for the right side percentages, there is a memory key to help you. 1,2,4,5,6,7,8,8,9,9,8,8,7,6,5,4,2,1. The sequence is a mirror image of itself, which can make it easier to remember. The way it works, is that the percentage on the right side of the chart starts at 0. Add 1, 1%; add 2, 3%; add 4, 7%; add 5, 12% and so on. So in your problem, your lens was 5 degrees off axis, which tells us that 1% of the cylinder power is in effect at that meridian. .01 x 4 = .04 diopters.

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    I dont quite understand what is being asked here.

    The Patient RX is: +0.00 -4.00 X180

    But the patient is given: +0.00 -4.00 X175

    So the question is asking how much cylinder power the patient is experiencing at 90?

    If that is what is being asked you find the distance from the meridian you want to know the power at from the cylinder axis in degrees. ( you want to know the power at 90; the cyl axis is 175. So the distance would be 85)

    then use this equation: (((sin (distance from axis))^2)*cyl power)+ sph power

    So: (sin 85)^2= 0.992403876506104

    0.992403876506104 * -4.00 = −3.969615506024416

    the power at 90 is -3.97
    Last edited by Kujiradesu; 04-17-2017 at 07:25 PM.
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    The effective power @ 90 would be -3.96
    -3.97 to be more exacting, but what is 0.01 between friends? Kuji has it right. plc has an easier, no calculator method.
    Last edited by lensmanmd; 04-17-2017 at 07:34 PM.

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    OptiBoard Professional Kujiradesu's Avatar
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    Quote Originally Posted by lensmanmd View Post
    The effective power @ 90 would be -3.96
    -3.97 to be more exacting, but what is 0.01 between friends? Kuji has it right. plc has an easier, no calculator method.
    Dont mind me. I always quibble about CR-39 being 1.498 instead of 1.50. Po-tato; Po-Ta-toe. OR as we say in the shop "Good enough for the girls I go out with." (^_−)−☆
    Optical Cross: n. crucifixion apparatus used by the New Jersey State Board.

    "It is not knowing, but the love of learning, that characterizes the scientific [person]." -Charles Sanders Peirce

    "A concept is a brick. It can be used to build a courthouse of reason. Or it can be thrown through the window. -Gilles Deleuze

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    OptiBoard Professional Kujiradesu's Avatar
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    Quote Originally Posted by plculver View Post
    You may not have access to the calculator during your exam, so go to this site: http://www.flashcardmachine.com/abo-optical4.html and scroll down a little way. You will find a chart that shows what percentage of cylinder is in effect for how many ever degrees off axis the lens is. When you first look at it, it seems impossible to memorize. But notice that the left side is just increments of five, and for the right side percentages, there is a memory key to help you. 1,2,4,5,6,7,8,8,9,9,8,8,7,6,5,4,2,1. The sequence is a mirror image of itself, which can make it easier to remember. The way it works, is that the percentage on the right side of the chart starts at 0. Add 1, 1%; add 2, 3%; add 4, 7%; add 5, 12% and so on. So in your problem, your lens was 5 degrees off axis, which tells us that 1% of the cylinder power is in effect at that meridian. .01 x 4 = .04 diopters.
    The way I was taught this list was "drop the threes; double the eights".
    Optical Cross: n. crucifixion apparatus used by the New Jersey State Board.

    "It is not knowing, but the love of learning, that characterizes the scientific [person]." -Charles Sanders Peirce

    "A concept is a brick. It can be used to build a courthouse of reason. Or it can be thrown through the window. -Gilles Deleuze

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    Quote Originally Posted by Kujiradesu View Post
    I dont quite understand what is being asked here.

    The Patient RX is: +0.00 -4.00 X180

    But the patient is given: +0.00 -4.00 X175
    Hi Kujiradesu.

    Thanks for that- it only took me 3 days to forget that the cyl axis is ninety degrees opposite of what written. I corrected my post accordingly.

    The OP's example is asking for the residual astigmatism axis (and indirectly the power error), not the power in an alternative meridian, necessary when calculating for induced prism.

    The residual astigmatism axis is needed when calculating contact lens powers after an over-refraction, IOL implants, etc. It's essentially a problem concerning crossed cylinders.

    Best regards,

    Robert Martellaro
    Science is a way of trying not to fool yourself. - Richard P. Feynman

    Experience is the hardest teacher. She gives the test before the lesson.



  9. #9
    OptiBoard Professional Kujiradesu's Avatar
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    Quote Originally Posted by Robert Martellaro View Post
    Hi Kujiradesu.

    Thanks for that- it only took me 3 days to forget that the cyl axis is ninety degrees opposite of what written. I corrected my post accordingly.

    The OP's example is asking for the residual astigmatism axis (and indirectly the power error), not the power in an alternative meridian, necessary when calculating for induced prism.

    The residual astigmatism axis is needed when calculating contact lens powers after an over-refraction, IOL implants, etc. It's essentially a problem concerning crossed cylinders.

    Best regards,

    Robert Martellaro
    Thompson's Formula is the hard math way to do obliquely crossed cylinders, but there is also a way to graph this problem with much less math and to come to a reasonably close approximation of the answer (i.e. not exact. close.).

    Step #1 Transpose to plus cylinders
    Step #2 Arrange Cylinders in ascending Axis order

    Step #3 draw a horizontal line equal to scale for the first cyl power (also set your scale i.e. 1cm=1diopter)
    Step #4 Label the ends of the line A________B
    Step #5 from the right end of the line AB (point B) draw a scale line equal to the second cyl power and whose direction is such as to form the angle 2a from the elongation of line AB
    Step #6 label this line BE
    Step #7 connect points A and E
    STEP #8 measure line AE; to scale, it equals the resultant cyl power
    Step #9 measure angle BAE; this equals 2a'
    Step #10 2a' when divided in half equals the angle to be added to the axis of the lower of the two cyl axii to obtain the new axis
    Step #11 Use formula (see below) to obtain resultant sphere.
    Step #12 If necessary add all sph powers together to obtain final ans.

    formula for resultant sphere: D = (A+B-C)/ 2
    Where:
    D = resultant sph power
    A = power of the stronger of the two cyls
    B = power of the weaker of the two cyls
    C = power of the resultant cyl

    EDIT: I forgot to mention, although you can do this without a calculator you will most definitely need a ruler and a protractor.
    Optical Cross: n. crucifixion apparatus used by the New Jersey State Board.

    "It is not knowing, but the love of learning, that characterizes the scientific [person]." -Charles Sanders Peirce

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  10. #10
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    Toss your protractors and Apps when the cylinder powers are equal power.

    A patient needs a cylinder correction of -4 at 90. Instead, a -4 at 85 lens was given. Where is the residual cylinder axis now?
    Subtract 45 from 87.5 = 42.5 degrees.

    From: Borish's Clinical Refraction
    Attached Thumbnails Attached Thumbnails Res cyl axis.jpg  
    Science is a way of trying not to fool yourself. - Richard P. Feynman

    Experience is the hardest teacher. She gives the test before the lesson.



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