The document defines and describes the cardinal points of an optical system, which characterize its imaging properties. It discusses the focal points and planes, where light rays converge or pass through unchanged. It also covers the principal points and planes, which define where refraction appears to occur. The nodal points are defined as points where light rays pass through undeflected. All of these cardinal points lie on the optical axis and allow the system's behavior to be analyzed using paraxial approximations.

1. CARDINAL
POINTS
RABIA AMMER
Optometrist & Orthoptist
(Gold Medalist)

2. LEARNING OUTCOMES
Optical Axis
Optical interface
Paraxial Rays
Cardinal Points
Focal Points & Planes
Principal Points & Planes
Nodal Points
Optical Center

3. OPTICAL AXIS
An optical axis is a line along which there is some degree of rotational symmetry in
an optical system.
The optical axis is an imaginary line that defines the path along which light
propagates through the system.
For a system composed of simple lenses and mirrors, the axis passes through the
center of curvature of each surface, and coincides with the axis of rotational
symmetry.

4. OPTICAL INTERFACE
The boundary separating 2 different optical media.
When light strikes an interface, some is reflected,
some is transmitted through the interface and
some is absorbed.

5. PARAXIAL RAYS
The rays extremely close to the optical axis are called paraxial rays
A refracting surface that is sufficiently close the optical axis treated as flat surface.

6. CARDINAL POINTS
The analysis of an optical system using cardinal points is known as Gaussian optics,
named after C F Gauss
For an optical lens system - characteristics are defined by its "cardinal points”
Cardinal points consist of three pairs of points located on the optical axis of
a rotationally symmetric, focal, optical system.
These are:
1. 2 FOCAL POINTS
2. 2 PRINCIPAL POINTS
3. 2 NODAL POINTS

7. CARDINAL POINTS
For ideal systems, the basic imaging properties such as image size, location,
and orientation are completely determined by the locations of the cardinal
points
 Cardinal points provide a way to analytically simplify a system with many
components, allowing the imaging characteristics of the system to be
approximately determined with simple calculations.
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, in the paraxial approximation

8. FOCAL POINTS & PLANES
The Front Focal Point of an optical system has the property that
any ray that passes through it will emerge from the system
parallel to the optical axis.
The Back Focal Point of the system has the reverse property i.e.
rays that enter the system parallel to the optical axis are focused
such that they pass through the back focal point.
The Front And Back Focal Planes are defined as the planes,
perpendicular to the optic axis, which pass through the front and
back focal points.

10. An object infinitely far from the optical system
forms an image at the back focal plane.
For objects a finite distance away, the image is
formed at a different location, but rays that leave
the object parallel to one another cross at the back
focal plane.

11. PRINCIPAL PLANES & 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.
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, e.g. 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.

13. PRINCIPAL PLANES
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.
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.

15. NODAL POINTS
The front and rear nodal points have the property that a ray aimed at one of them
will be refracted by the lens such that it appears to have come from the other, and
with the same angle with respect to the optical axis.
The nodal points therefore do for angles what the principal planes do for transverse
distance.
Rays pas through them non deviated.
If the 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 points,
respectively.

18. OPTICAL CENTER
The position where the nodal ray crosses the optical axis.
Wavelength independent
Index of refraction independent

22. THANK YOU