# This might sound really stupid (!)

1. Nov 6, 2005

### bomba923

Ok...well, here goes:
Let's say we draw a slope-field for

$$\frac{{dy}}{{dx}} = \frac{x}{{k - y + \sqrt {x^2 + \left( {k - y} \right)^2 } }}$$

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Now, let's say a ray of light traveling in the direction $$\left\langle {0, - 1} \right\rangle$$ "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 $$(0,k)$$ ?
(assuming this ray strikes one and only one "mirror"/slope-segment)

Last edited: Nov 6, 2005
2. Nov 22, 2005

### mathphys

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