Thick lenses. Principal points and planes. Calculation. Formulas. Principal planes and points

Principal planes- these are planes perpendicular to the optical axis and passing through the points H and H ", called the main points. The peculiarity of the main planes is that the rays between them go parallel to the optical axis, or as they say, the linear increase in these main planes is +1. Others In other words, if you combine the main planes together, then they will serve as the only conditional refractive surface.

Let's implement a complex optical system by placing several lenses one after the other so that their main optical axes coincide (Fig. 224). This common main axis of the entire system passes through the centers of all surfaces that bound individual lenses. Let us direct a beam of parallel rays onto the system, observing, as in § 88, the condition that the diameter of this beam be sufficiently small. We will find that, after exiting the system, the beam is collected at one point F"", which, just as in the case of a thin lens, we will call the back focus of the system. By directing a parallel beam at the system from the opposite side, we find the front focus of the system F. However, when answering the question, what is the focal length of the system under consideration, we encounter difficulty, because it is not known to what point in the system this distance should be counted from points F and F. "Points , analogous to the optical center of a thin lens, in the optical system, generally speaking, there is no, and there is no reason to give preference to any of the many surfaces that make up the system; in particular, the distance from F Rice. 224. Tricks optical system and F" to the corresponding outer surfaces of the system are not the same. These difficulties are resolved as follows. In the case of a thin lens, all constructions can be done without considering the path of rays in the lens and restricting ourselves to the image of the lens in the form of the main plane (see § 97). Investigation of properties complex optical systems shows that in this case we can not consider the actual path of the rays in the system.However, to replace a complex optical system, it is necessary to use not one main plane, but a set of two main planes perpendicular to the optical axis of the system and intersecting it in two ways. called principal points (H and H"). Having marked the position of the main foci on the axis, we will have a complete characteristic of the optical system (Fig. 225). In this case, the image of the outlines of the outer surfaces that limit the system (in the form of thick arcs in Fig. 225) is redundant. The two main planes of the system replace the single main plane of a thin lens: the transition from the system to a thin lens means the approach of the two main planes to the merger, so that the main points H and H "approach and coincide with the optical center of the lens. Thus, the main planes of the system are as This circumstance is in accordance with their main property: the beam entering the system intersects the first main plane at the same height h, at which the beam leaving the system crosses the second main plane (see Fig. 225) We will not give proof that such a pair of planes really exists in any optical system, although the proof does not present any particular difficulties, we will restrict ourselves to indicating the method of using these characteristics of the system to construct an image.The principal planes and principal points can lie both inside and outside the system, completely asymmetrical with respect to the surface those limiting the system, for example, even on one side of it. With the help of the main planes, the issue of the focal lengths of the system is also solved. The focal lengths of an optical system are the distances from the principal points to their respective foci. Thus, if we designate F and H - front focus and front main point, F" and H" - back focus and back main point; then f "=H"F" is the rear focal length of the system, f=HF is its front focal length. If the same medium (for example, air) is located on both sides of the system, so that the front and rear foci are located in it, then (100.1) as for a thin lens.

The principal planes are located closer to surfaces with greater curvature, i.e. smaller radius.

Principal planes and principal points allow the construction of rays passing through the system without taking into account their actual refraction on the surfaces of lenses or reflection from mirrors.

The main planes are located symmetrically to the real refractive surfaces only for single biconvex or biconcave symmetrical lenses. In real systems, the front and rear refractive surfaces are at different distances from the corresponding front and rear principal points. Therefore, in addition to the focal lengths, it is necessary to determine the segments between the main focus and the corresponding front or rear refractive (reflecting) surface of the system. They are called the vertex focal lengths or, respectively, the front SF and rear SF segments. The value of the rear segment is a design parameter that determines the distance from the rear focal plane to the last lens of the system.

Main plane - a plane passing through the beam axis and one of the main central axes of inertia of the section.

Principal planes and principal points can lie both inside and outside the system asymmetrically with respect to the surfaces that bound the system. If the size of the system in the direction of the main optical axis is much less than the focal length, then the beam, passing through the system, is slightly displaced. Therefore, the points BI and Ci, B2 and C2 (see Fig. 5.1) practically coincide, and the main planes PI and P2 coincide with each other and are located in the middle of the system. Such a system is called a thin lens. Formulas (1) - (4) remain valid for a thin lens as well.

The main planes in this interval of Q change are crossed. With a further decrease in Q, the focal length becomes negative, and the main planes are arranged in direct sequence.

The main plane is a plane perpendicular to the optical axis and passing through the intersection point of a beam parallel to the optical axis and a beam that is a continuation of its last refracted segment. In some cases, the overall dimensions of the OS can be 3 - 4 times less than its focal length.

The main planes and main points can lie both inside and outside the system, completely asymmetrical with respect to the surfaces that bound the system, for example, even on one side of it.

From Wikipedia, the free encyclopedia

Principal planes of the lens- a pair of conditional conjugate planes located perpendicular to the optical axis , for which the linear increase is equal to one. That is, the linear object in this case is equal in size to its image and is equally directed with it relative to the optical axis.

The action of all refracting surfaces can be reduced to the action of these conditional planes, containing the points of intersection of the rays, as if entering the system and leaving it. This assumption allows us to replace the actual path of light rays in real lenses with conditional lines, which greatly simplifies the calculations of the optical system.

Distinguish front $H$ and back $H"$ main planes. In the rear main plane of the lens, the action of the optical system is concentrated when light passes in the forward direction (from the subject to the photographic material). The position of the main planes depends on the shape of the lens and the type of photographic lens: they can lie inside the optical system, in front of it and behind it.

see also

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Notes

Literature

• E. A. Iofis. Photographic technology / I. Yu. Shebalin. - M.,: "Soviet Encyclopedia", 1981. - S. 63. - 447 p.

• D. S. Volosov. Photographic optics. - 2nd ed. - M.: "Art", 1978. - S. 123-131. - 543 p.

• Begunov B. N. Geometric Optics, MSU Publishing House, 1966.

• Yashtold-Govorko V. A. Photography and processing. Shooting, formulas, terms, recipes. Ed. 4th, abbr. M., "Art", 1977.

An excerpt characterizing the main planes of the lens

Two conditional planes H and H ", from which the main focal lengths f and f" and conjugate focal lengths a and b are counted, related by the formula:

The position of the main planes in the lens depends on the shape of the lens and its thickness. AT complex lenses the position of the principal planes depends on optical powers individual lenses and their position in the system.

Rice. The position of the main planes in the lenses different shapes

In symmetrical lenses, the main planes are usually located inside the system, relatively close to the aperture plane. In telephoto lenses, the main planes are far forward and located outside the lens.

Rice. The position of the rear main plane in lenses of various types: a - in a symmetrical lens, the rear segment is shorter than the focal length; b - in a telephoto lens, the rear segment is much shorter than the focal length; c - in a lens with an elongated segment, the rear segment is greater than the focal length

When it is necessary to have a large distance between the lens and the photosensitive layer (for example, in SLR cameras), the main planes are moved back, and such a lens is called a lens with an extended back segment.

The introduction of the main planes facilitates the graphic construction of the image, since, knowing the position of the main planes, one can completely ignore the actual refraction of rays on numerous surfaces of the system and assume that the entire refractive effect of the optical system is concentrated in its main planes.

Rice. Construction of principal planes

The figure shows the construction of principal planes in a biconvex lens. Beam AB, running parallel to the main optical axis OO", is refracted on the first surface, deviates towards the axis and goes in the lens along the line BC, then, refracted on the second surface, goes along the line CF "crossing the main axis at point F".

If we continue on one side the beam A By and on the other - draw the beam CF "in reverse side before they intersect at point h ", then the two actual refractions at points B and C can be replaced by one fictitious refraction at point h ". Of course, the same would take place in a complex system with many refractive surfaces, i.e., several refractions can be replaced by one refraction completely equivalent to them at the point h ". The plane drawn through the point h" perpendicular to the main optical axis is called the back main plane H".

Table

POSITION OF THE MAIN PLANES IN THE MOST COMMON SOVIET LENSES

The minus sign indicates that the distance HH "should not be added to the sum of distances a + b, but subtracted from it, i.e. the expression L = a + b + HH" takes the form: L = a + b - HH ".

Rice. The position of the principal planes in Soviet lenses

If the beam ab enters the lens from the right and, having refracted twice at points b and c, crosses the axis at the front main focus, then the front main plane H can also be found.

The table and figure show the position of the main planes of the most common Soviet lenses. The presence of this data allows you to accurately calculate the relative position of the subject and its image relative to the lens to obtain a given shooting scale, which is especially important when shooting at close distances.

MAIN PLANES OF THE OPTICAL SYSTEM

Physical encyclopedic Dictionary. - M.: Soviet Encyclopedia. Chief Editor A. M. Prokhorov. 1983 .

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