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Thread: Toric lenses.....The sequel!

  1. #1
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    Toric lenses.....The sequel!

    Hi everyone, it's me again, with a slightly re-worded toric problem.

    A thin toric lens is made to the specification:
    +7.00DCx135/+9.50DCx45
    -3.50DS
    1. When a second thin lens of unknown power is placed in contact with the thintoric lens then the resultant power of the two thin lenses is: +2.25DS/-3.75DCx135. What is the power of the unknown second thin lens? Expressyour answer in negative sph-cyl form (6 marks)

      I can't quite get my head around what to do! I can't find an example in any of the text books quite like it.
      Any help is, as always greatly appreciated!
      Thanks
      Hannah
    Last edited by Hannah Doidge; 05-06-2016 at 06:47 AM.

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    Master OptiBoarder RIMLESS's Avatar
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    Quote Originally Posted by hannah doidge View Post
    hi everyone, it's me again, with a slightly re-worded toric problem.

    a thin toric lens is made to the specification:
    +7.00dcx135/+9.50dcx45
    -3.50ds
    1. when a second thin lens of unknown power is placed in contact with the thintoric lens then the resultant power of the two thin lenses is: +2.25ds/-3.75dcx135. What is the power of the unknown second thin lens? Expressyour answer in negative sph-cyl form (6 marks)

      i can't quite get my head around what to do! I can't find an example in any of the text books quite like it.
      Any help is, as always greatly appreciated!
      Thanks
      hannah
    -3.75 -1.25 x 135
    90% of everything is crap...except for crap, because crap is 100% crap

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    Quote Originally Posted by RIMLESS View Post
    -3.75 -1.25 x 135
    Hi, Thanks for replying!
    When I check my answer by adding -3.75/-1.25x135 to 6.00/-2.50x45 I get 1.00/-1.25x45, not +2.25/-3.75x135.
    Where am I going wrong?

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    Master OptiBoarder RIMLESS's Avatar
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    Your final resultant optical cross should have +2.25 on the 135 axis and -1.50 on the 45
    Your first lens cross should have +6.00 on the 135 and +3.50 on the 45
    The mystery lens should be the difference
    90% of everything is crap...except for crap, because crap is 100% crap

  5. #5
    ATO Member HarryChiling's Avatar
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    Quote Originally Posted by Hannah Doidge View Post
    Hi everyone, it's me again, with a slightly re-worded toric problem.

    A thin toric lens is made to the specification:
    +7.00DCx135/+9.50DCx45
    -3.50DS
    1. When a second thin lens of unknown power is placed in contact with the thintoric lens then the resultant power of the two thin lenses is: +2.25DS/-3.75DCx135. What is the power of the unknown second thin lens? Expressyour answer in negative sph-cyl form (6 marks)

      I can't quite get my head around what to do! I can't find an example in any of the text books quite like it.
      Any help is, as always greatly appreciated!
      Thanks
      Hannah
    We can simplify the first part of the problem, +7.00DCx135/+9.50DCx45:
    Code:
         +9.50 -2.50 x 135
    (+) -3.50
    ------------------------
         +6.00 -2.50 x 135
    Now your question is what gets added to this prescription to result in +2.25DS/-3.75DCx135

    Code:
         +6.00 -2.50 x 135
    (+) X
    -----------------------
         +2.25 -3.75 x 135
    This is an algebraic equation:

    Code:
          +2.25 -3.75 x 135
    (-)  +6.00 -2.50 x 135
    -----------------------
          X
    Luckily the axis are the same, so your task is easier, however if they weren't you could use Thompson's (yuk), a better way to add or in this case subtract two prescriptions is breaking them down into their MRE, C45, C180 components which all add and subtract simple then use, the trace and discriminant to compute the resulting spherocylinder I will post a link at the end to give you a better easier formula to remember assuming you are comfortable with matrix mathematics. For now, we march on and turnt he above into an addition so it's easier to comprehend:

    Code:
         +2.25 -3.75 x 135
    (+) -6.00 +2.50 x 135
    -----------------------
          -3.75 -1.25 x 135
    There is your answer: -3.75 -1.25 x 135

    Here is your link with calculator and explanation: https://makeoptics.com/harrychiling/...nder-summation

    PS - to check your answer add the three powers (since they are thin lens) in the caculator and the result should be equal:

    Code:
         +9.50 -2.50 x 135
    (+) -3.50
    (+) -3.75 -1.25 x 135
    ---------------------
         +2.25 -3.75 x 135
    Last edited by HarryChiling; 05-06-2016 at 12:00 PM.
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    Master OptiBoarder RIMLESS's Avatar
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    Quote Originally Posted by HarryChiling View Post
    We can simplify the first part of the problem, +7.00DCx135/+9.50DCx45:
    Code:
         +9.50 -2.50 x 135
    (+) -3.50
    ------------------------
         +6.00 -2.50 x 135
    Now your question is what gets added to this prescription to result in +2.25DS/-3.75DCx135

    Code:
         +6.00 -2.50 x 135
    (+) X
    -----------------------
         +2.25 -3.75 x 135
    This is an algebraic equation:

    Code:
          +2.25 -3.75 x 135
    (-)  +6.00 -2.50 x 135
    -----------------------
          X
    Luckily the axis are the same, so your task is easier, however if they weren't you could use Thompson's (yuk), a better way to add or in this case subtract two prescriptions is breaking them down into their MRE, C45, C180 components which all add and subtract simple then use, the trace and discriminant to compute the resulting spherocylinder I will post a link at the end to give you a better easier formula to remember assuming you are comfortable with matrix mathematics. For now, we march on and turnt he above into an addition so it's easier to comprehend:

    Code:
         +2.25 -3.75 x 135
    (+) -6.00 +2.50 x 135
    -----------------------
          -3.75 -1.25 x 135
    There is your answer: -3.75 -1.25 x 135

    Here is your link with calculator and explanation: https://makeoptics.com/harrychiling/...nder-summation

    PS - to check your answer add the three powers (since they are thin lens) in the caculator and the result should be equal:

    Code:
         +9.50 -2.50 x 135
    (+) -3.50
    (+) -3.75 -1.25 x 135
    ---------------------
         +2.25 -3.75 x 135
    ya ya ya that's just what I said without the circumlocution.....lol
    90% of everything is crap...except for crap, because crap is 100% crap

  7. #7
    ATO Member HarryChiling's Avatar
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    Quote Originally Posted by RIMLESS View Post
    ya ya ya that's just what I said without the circumlocution.....lol
    Nice, that's why I step on your shoulders so I can appear to be a giant!
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    Thanks you guys, it is very clear now! Which is handy since the big exam is tomorrow

  9. #9
    Master OptiBoarder RIMLESS's Avatar
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    Good Luck
    90% of everything is crap...except for crap, because crap is 100% crap

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