Find equation for shape of reflecting surface

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SUMMARY

The discussion focuses on deriving the equation for a reflecting surface that produces parallel rays from a point light source located at (d, 0). The axis of the mirror is aligned with the x-axis, intersecting at the origin (0, 0). Utilizing Fermat's Principle, participants are encouraged to confirm the approach taken to establish the mathematical representation of the reflecting surface. The conversation emphasizes the importance of visual aids in understanding the geometric configuration involved.

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  • Understanding of Fermat's Principle in optics
  • Basic knowledge of coordinate geometry
  • Familiarity with the concept of reflecting surfaces
  • Ability to interpret and create mathematical equations
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  • Research the application of Fermat's Principle in deriving optical paths
  • Study the properties of parabolic mirrors and their equations
  • Explore geometric optics and ray tracing techniques
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Physicists, optical engineers, and students studying geometric optics who are interested in the mathematical foundations of light reflection and surface design.

CaptainQuaser
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Here is the question, I just need verification, don't know how to make the fancy formulas here so bear with me...

Consider a reflecting surface that produces parallel rays from a point source of light. The axis of the mirror lies on the x-axis which passes through the mirror at x=y=0. The source is at x = d, y=0 and rays of light are produced paralled to the x axis. Using Fermat's Principle, derive the equation of the relecting surface.

I am doing this on my palm pilot right now, so I will try to draw a picture of my thoughts.
 

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Anyone? Am I on the right track?
 

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