Please teach me an easy method for combining cylinders... let's say +2.00 x 120 and -2.25 x 030. and +2.00 x 120 and -2.25 x 080 Thanks!
the equation for this is absolutely heinous.... but lemme look through my notes and see if they "dumbed it down" the EASY way to do this... take these two as trial lenses, throw them on your lensometer and see what comes out.
Andrew, The equation is hideous. Your best bet would be to contact Coopervision and request their Toritrack program, which is also available for your palm. You plug in the numbers and voila, it calculates it for you. The CD/program is free and theyd be more than happy to mail it right to you
We learned about the equation, but I personally never use it - too many variables! If you know about vector addition (and are comfortable with it), I've found that is the easiest way. We also learned how to combine them via matrices, if that makes it any easier. If you want any more info on either of these methods, let me know...
The first two cylinders you wrote down are easy because their axes are 90 degrees apart - just draw out a power cross to determine the resultant. +2.00x120 + -2.25x030 = -0.25x030 To combine cylinders that are not 90 degrees apart via the vector method, resolve each cylinder into its horizontal and vertical components - but make sure to multiply the axis component by 2, i.e. for+2.00x120 Horizontal is: +2.00cos2(120) Vertical is:+2.00sin2(120) Do the same for -2.25x030 Horizontal is -2.25cos2(030) Vertical is -2.25sin2(030) Then add horizontal and vertical components to get x and y components - then resolve into one component as per normal vector addition. i.e. Cyl = sqrt(xsq. + ysq.) Use the sign of the horizontal component for the resultant cylinder. The resultant axis is then 1/2arctan(y/x) I don't know if this helps or not - it looks a lot longer than it is, but once you get an algorithm down, it takes about 30 seconds to do and there is very little chance of making a mistake. As well, if you are unsure of whether or not an answer makes sense, you can draw out the vectors just to make sure you're on the right track. UW - so proud that they have the most hours of optics instruction at any optometry school in North America....
The answer for the combination of +2.00 x 120 and -2.25 x 030 is +2.00 with -4.25 x 030 This doesn't quite fit with your answer above.
Argh! Sorry about that - I was in the midst of studying for my 7th final last night. Brain's not working too well anymore. Thank goodness only 1 final left. Anyhow, scratch what I said about just adding the vectors together using a power cross. Use the vector method - you will get the right answer. +2.00x120/-2.25x030 MOR = (+2.00/2) + (-2.25/2) = -0.125 Cx = (+2.00cos2(120)) + (-2.25cos2(030)) = -2.125 Cy = (+2.00sins(120)) + (-2.25sin2(030)) = -3.68 Cr = sqrt(-2.125sq + -3.68sq) = +-4.25 Theta(r) = 1/2tan(-3.68/-2.125) = 30 degrees Resultant sphere: Sr1 = MOR - C/2 = -0.125 - 4.25/2 = -2.25 Sr2 = MOR + C/2 = -0.125 + 4.25/2 = +2.00 The more positive resultant sphere is used for minus cylinder form while the more negative resultant sphere is used for plus cylinder form. The degree resultant applies to the negative cylinder form of the combination (if the resultant degree was negative though, you'd have to add 180 to it and apply it to the plus cyl form and then use transposition to find the minus cyl form - if that makes sense). So minus cyl form is: +2.00-4.25x030 Plus cyl form is: -2.25+4.25x120 My answers for your second problem using this method (but running on very little sleep are ): Minus cylinder: +1.25-2.73x057 (+1.25-2.75x057) Plus cylinder: -1.49+2.73x147 (-1.50+2.75x147)
Thanks for your help! If the cyclinders are 90 degrees apart, then it works with a power cross. I can do that. If they are not 90 degrees apart, then I must use the equation above.
Just remember, it is statistically to your advantage to choose a DEFAULT answer before you take the test. If you have no idea of the answer, it is better to choice the same answer for all the ones you don't know instead of picking an answer at random. I'm a B-man myself. Of course if you can narrow it down do that. But if you are just guessing...go with "B."
