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OPTI 201R 10 L27

# OPTI 201R 10 L27 - 27-1 8.4.1 Paraboloid Mirror Figure 8.18...

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OPTI 201R Fall 2010 27-1 8.4.1 Paraboloid Mirror Figure 8.18 Conic sections.

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OPTI 201R Fall 2010 27-2 Figure 8.19 Parabola surface in cross section. defines a parabola FS SM ! (8.29) " # " # 2 2 z f y f z \$ \$ % \$ ! \$ (8.30) 2 2 2 2 2 2 2 2 4 z fz f y f fz z y fz % % % ! \$ % ! \$ (8.31) (f is a positive value) 2 4 y z f \$ ! sag (exact) of a parabola (8.32) 2 2 y z R ! sag (paraxial approx.) of a sphere (8.33) 4 2 f R \$ ! so 2 R f \$ ! focal length of a parabola (positive) (R is the radius of curvature at the vertex) (R is the radius of curvature of the "base" sphere)
OPTI 201R Fall 2010 27-3 Figure 8.20 Plane wave is parallel to the directrix. Prove that every ray (not just in the paraxial region) comes to focus at F*: Prove that OPL off-axis = OPL on-axis :

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OPTI 201R Fall 2010 27-4 Consider a plane wave incident on the mirror, with the incoming wavefront at F*. Define the OPL as the distance from any point on this plane to the mirror, to the final focus at F*. As the wave propagates, and if the parabola images to a perfect point
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OPTI 201R 10 L27 - 27-1 8.4.1 Paraboloid Mirror Figure 8.18...

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