Cardinal points

Cardinal pointsPrepared byLoknath GoswamiB.Sc. Optom 2nd yearRidley College of Optometry, Jorhat

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

Light travels in a straight lineIn vacuum, light travels with a speed of 3x108 m/sWhen 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

Rules for refractionAny 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.

Refraction by a Convex lens

Refraction by a Concave lens

Introduction The analysis of an optical system using cardinal points is known as Gaussian optics, named after Carl Friedrich GaussFor an optical lens system Characteristics are defined by its cardinal pointsBy knowing the location of the cardinal points we can find out the image produced by an object passing through optical lens

The cardinal points lie on theoptical axis of the optical systemEach point is defined by the effect the optical system has onraysthat pass through that point

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 are2 principal foci2 principal points2 nodal pointsAll situated on the principal axis of the system

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

Cardinal data of the Gullstrands schematic eyePrincipal foci F1 and F2 lie 15.7 mm in front of and 24.4 mm behind the cornea, respectivelyPrincipal points P1 and P2 lie in the anterior chamber 1.35mm and 1.60 mm behind the anterior surface of cornea, respectivelyNodal 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

Gullstrand schematic eye

The reduced eyeThe Gullstrands model of schematic eye had definitely enhanced the understanding of the optics of eye, but the calculations were still cumbersomeListing simplified the data by choosing single principal point and single nodal point lying midway between two principal points and two nodal points, respectively

The reduced eye

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Comparison

Classification Every optical system has 6 cardinal points Focal points primary & secondary Principle points primary & secondaryNodal points primary & secondary

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.

Focal points

Principal pointsThe 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 lensThis means that the lens can be treated as if all of the refraction happened at the principal planesThe 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

If the medium surrounding the optical system has arefractive index of 1 (e.g., air orvacuum), then the distance from the principal planes to their corresponding focal points is just thefocal lengthof 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 athin lens in air, the principal planes both lie at the location of the lens.

The point where they cross the optical axis is sometimes misleadingly called theoptical 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.

Location of Principal points in different form of lenses

Principal and Focal points

Nodal pointsThe 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.

Nodal points

Nodal points

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.

Inanatomy, the surface vertices of the eye'slensare called the anterior and posteriorpoles of the lens.

ReferencesEugene Hecht, Optics, 4th edition, chapter 6Theory and practice of optics and refractionhttps://youtu.be/Wq0eMr_Lib0https://youtu.be/2EUzr8fP0TAhttp://www.physicsclassroom.com/Class/refrnwww.dictionary.com/browse/lighthttps://en.wikipedia.org/wiki/Cardinal_point_(optics)