A brief description about cardinal points with videos principal points, nodal points, focal points

1. Cardinal points
Prepared by
Loknath Goswami
B.Sc. Optom 2nd year
Ridley College of Optometry, Jorhat

2. Light
• Light is that part of electromagnetic radiation
that is capable of causing a visual sensation
and has wavelengths from about 380 to about
780 nm

3. • Light travels in a straight line
• In vacuum, light travels with a speed of 3x108
m/s
• When a ray of light travels from a rarer
medium to a denser medium, then at the
point of incidence it bends towards the
normal at the point of incidence

4. Rules for refraction
• Any incident ray traveling parallel to the principal
axis of a converging lens will refract through the
lens and travel through the focal point on the
opposite side of the lens.
• Any incident ray traveling through the focal point
on the way to the lens will refract through the
lens and travel parallel to the principal axis.
• An incident ray that passes through the center of
the lens will in effect continue in the same
direction that it had when it entered the lens.

5. Refraction by a Convex lens

6. Refraction by a Concave lens

7. Introduction
• The analysis of an optical system using
cardinal points is known as Gaussian optics,
named after Carl Friedrich Gauss
• For an optical lens system – Characteristics are
defined by its “cardinal points”
• By knowing the location of the cardinal points
we can find out the image produced by an
object passing through optical lens

8. • The cardinal points lie on the optical axis of
the optical system
• Each point is defined by the effect the optical
system has on rays that pass through that
point

9. History
• Listing and Gauss, while studying refraction by
lens combinations, concluded that for a
homocentric lenses’ system, there exist 3 pairs
of cardinal points, which are
• 2 principal foci
• 2 principal points
• 2 nodal points
– All situated on the principal axis of the system

10. • The models of schematic eyes developed by
Listing, Tschering and Helmholtz greatly
advanced the understanding of the optics of
the eye
• However, it was Gullstrand who developed the
most authoritative model of the eye

11. Cardinal data of the Gullstrand’s
schematic eye
• Principal foci F1 and F2 lie 15.7 mm in front of
and 24.4 mm behind the cornea, respectively
• Principal points P1 and P2 lie in the anterior
chamber 1.35 mm and 1.60 mm behind the
anterior surface of cornea, respectively
• Nodal points N1 and N2 lie in the posterior
part of lens 7.08 mm and 7.33 mm behind the
anterior surface of cornea, respectively

12. Gullstrand schematic eye

13. The reduced eye
• The Gullstrand’s model of schematic eye had
definitely enhanced the understanding of the
optics of eye, but the calculations were still
cumbersome
• Listing simplified the data by choosing single
principal point and single nodal point lying
midway between two principal points and two
nodal points, respectively

14. The reduced eye

15. Comparison

16. Classification
• Every optical system has 6 cardinal points
– Focal points – primary & secondary
– Principle points – primary & secondary
– Nodal points – primary & secondary

17. Focal points
• The front focal point of an optical system, by
definition, has the property that any ray that
passes through it will emerge from the system
parallel to the optical axis.
• The rear (or back) focal point of the system
has the reverse property: rays that enter the
system parallel to the optical axis are focused
such that they pass through the rear focal
point.

18. Focal points

19. Principal points
• The two principal planes have the property that a ray
emerging from the lens appears to have crossed the rear
principal plane at the same distance from the axis that that
ray appeared to cross the front principal plane, as viewed
from the front of the lens
• This means that the lens can be treated as if all of the
refraction happened at the principal planes
• The principal planes are crucial in defining the optical
properties of the system, since it is the distance of the
object and image from the front and rear principal planes
that determines the magnification of the system. The
principal points are the points where the principal planes
cross the optical axis

20. • If the medium surrounding the optical system has
a refractive index of 1 (e.g., air or vacuum), then
the distance from the principal planes to their
corresponding focal points is just the focal
length of the system.
• In the more general case, the distance to the foci
is the focal length multiplied by the index of
refraction of the medium.
• For a thin lens in air, the principal planes both lie
at the location of the lens.

21. • The point where they cross the optical axis is
sometimes misleadingly called the optical
centre of the lens.
• Note, however, that for a real lens the
principal planes do not necessarily pass
through the centre of the lens, and in general
may not lie inside the lens at all.

22. Location of Principal points in
different form of lenses

23. Principal and Focal points

24. Nodal points
• The front and rear nodal points have the
property that a ray that passes through one of
them will also pass through the other, and
with the same angle with respect to the
optical axis.
• If medium on both sides of the optical system
is the same (e.g. air), then the front and rear
nodal points coincide with the front and rear
principal planes, respectively.

25. Nodal points

26. Nodal points

27. Surface vertices
• The surface vertices are the points where each
optical surface crosses the optical axis.
• They are important because they are the
physically measurable parameters for the
position of the optical elements, and so the
positions of the cardinal points must be
known with respect to the vertices to describe
the physical system.

28. • In anatomy, the surface vertices of the
eye's lens are called the anterior and
posterior poles of the lens.

29. References
• Eugene Hecht, Optics, 4th edition, chapter 6
• Theory and practice of optics and refraction
• https://youtu.be/Wq0eMr_Lib0
• https://youtu.be/2EUzr8fP0TA
• http://www.physicsclassroom.com/Class/refrn
• www.dictionary.com/browse/light
• https://en.wikipedia.org/wiki/Cardinal_point_
(optics)