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This might sound really stupid (!)

  1. Nov 6, 2005 #1
    Ok...well, here goes:
    Let's say we draw a slope-field for

    [tex] \frac{{dy}}{{dx}} = \frac{x}{{k - y + \sqrt {x^2 + \left( {k - y} \right)^2 } }} [/tex]

    Now, let's say a ray of light traveling in the direction [tex] \left\langle {0, - 1} \right\rangle [/tex] "hits" one of the slope segments we drew. However, each "slope segment" is a actually a short planar mirror!!

    And so,

    *Regardless of which segment this light ray strikes, will the light ray be reflected through the point [tex] (0,k) [/tex] ?
    (assuming this ray strikes one and only one "mirror"/slope-segment)
    Last edited: Nov 6, 2005
  2. jcsd
  3. Nov 22, 2005 #2
    Rewrite the equation for dy/dx taking dy/dx=C where C is an arbitrary constant, what curve the resulting equation represents? What properties has such a "mirror"? To what point the ray will be focused?
    Last edited: Nov 22, 2005
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