Cardinal Points

Understanding the system of mirrors and lenses.

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: 2 FOCAL POINTS 2 PRINCIPAL POINTS 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. 

9. 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.

10. 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. L ens 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.

11. 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. F or 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.

12. 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.

13. Optical Center The position where the nodal ray crosses the optical axis. Wavelength independent Index of refraction independent 

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