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What geometric property makes a paraboloid focus a plane wave to a point?

  • A.The focal point lies exactly at the centre of curvature of the surface
  • B.Every path from the aperture plane to the focus is the same length
  • C.The surface reflects rays at an angle equal to the angle of incidence
  • D.The curvature of the surface increases steadily towards its outer rim

Answer: B

The defining property is that the total path from a plane across the aperture to the surface and on to the focus is constant, so all contributions arrive in phase. Equal angles of reflection are true of any mirror and explain nothing particular about the paraboloid, the curvature relationship stated is not the criterion, and the centre of curvature of a paraboloid is not its focus. Recognising that focusing is a statement about equal path lengths makes the extension to shaped and dual reflector systems straightforward.

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