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Cartesian Oval in Maple13 OR Mathematica7

  1. Jan 24, 2010 #1
    I'm attempting to get an output of a specific cartesian oval (or oval of descartes, the perfect imaging system in physical optics- viz. perfectly stigmatic imaging). Algebraically I've deduced the equation to be

    3/2 Sqrt[(30 - x)^2 + y^2] + Sqrt[x^2 + y^2] == 7/20 (Mathematica input).

    I'm kind of new to math programs, so for Mathematica I used the ContourPlot command- the website said it would work fine for implicit functions. I tried it on a simple circle and it worked fine. For the parameters I set up (-20<x<20, -20<y<20) it showed nothing.

    For Maple13, I input

    > implicitplot(7/(20)=sqrt( x^(2)+y^(2)) + 3/(2)sqrt((30-x)^(2)+y^(2)), x =-20..20, y=-20..20);

    and it reads

    Error, invalid >

    .

    For the oval there are four things that need to be known. index of refraction of both medium, and the object distance and image distance. From this point I'm solving for a triangle that has a base of the object and image distance summed, and the arms are equal to the distance traveled through air (medium 1) and the unknown medium 2 with refraction index 1.5. The object distance is 20 cm and the image distance is 10 cm. It first travels through air which has an index of 1.00

    Using pen and paper I see no reason why it would be an invalid function, even though implicit. For example, by definition of my cartesian system, the smallest value x (the distance of the object to the interface, which I define to be s0=20 cm) should yield a y value of 0. It does.

    The general function for any cartesian oval or oval of descartes is:

    n1*Sqrt[x^2+y^2] + n2*Sqrt[(s0+s1-x)^2 + y^2] == n1s0 + n2s1. The general function is attached as a .png file.

    Please help- this is the most frustrating feeling!
     

    Attached Files:

  2. jcsd
  3. Jan 24, 2010 #2
    ContourPlot[(3/2) Sqrt[(30 - x)^2 + y^2] + Sqrt[x^2 + y^2], {x, -20, 20}, {y, -20, 20}]

    This will return a contour plot in mathematica. However, attempting

    ContourPlot[(3/2) Sqrt[(30 - x)^2 + y^2] + Sqrt[x^2 + y^2]==7/20, {x, 10^100, -10^100}, {y, 10^100, -10^100}],

    returns a blank plot. Apparently there is no solution of 7/20 within this region of the plane.
     
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