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Nodal Points

Definition: points of an optical system for which an incoming ray, directed at a nodal point, leaves the system with the same direction.

German: Knotenpunkte

Category: general optics


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nodal points of a thick lens
Figure 1: The nodal points of a thick lens.

In Gaussian optics, one can define various types of cardinal points, including the nodal points. By definition, an input ray directed at a nodal point leads to an output ray which has the same direction, only possibly with a parallel offset. For that, an incoming beam from the input side must be directed to the front nodal point, and the corresponding output ray then appears to come from the back nodal point.

In the frequently encountered situation where the refractive index is the same in front of and behind the optical system, the nodal points coincide with the principal points.

Some examples of nodal points:

  • The nodal points of a curved interface between two optical media are located at the center of curvature of the surface – possibly far away from the surface.
  • For a thin lens, the two nodal points coincide in the center of the length. Therefore, a ray directed to that center will go through the lens without any deflection or parallel offset.

Seealso: cardinal points, Gaussian optics

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