Encyclopedia … combined with a great Buyer's Guide!

Sponsors:     and others

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

Author:

How to cite the article; suggest additional literature

URL: https://www.rp-photonics.com/nodal_points.html

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

Questions and Comments from Users

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here; we would otherwise delete it soon. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.

Your question or comment:

Spam check:

  (Please enter the sum of thirteen and three in the form of digits!)

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.

preview

Share this with your friends and colleagues, e.g. via social media:

These sharing buttons are implemented in a privacy-friendly way!

Code for Links on Other Websites

If you want to place a link to this article in some other resource (e.g. your website, social media, a discussion forum, Wikipedia), you can get the required code here.

HTML link on this article:

<a href="https://www.rp-photonics.com/nodal_points.html">
Article on Nodal points</a>
in the <a href="https://www.rp-photonics.com/encyclopedia.html">
RP Photonics Encyclopedia</a>

With preview image (see the box just above):

<a href="https://www.rp-photonics.com/nodal_points.html">
<img src="https://www.rp-photonics.com/previews/nodal_points.png"
alt="article" style="width:400px"></a>

For Wikipedia, e.g. in the section "==External links==":

* [https://www.rp-photonics.com/nodal_points.html
article on 'Nodal points' in the RP Photonics Encyclopedia]