Principal planes and points. Big encyclopedia of oil and gas

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 thin lens.  

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.

Building an image in a thick lens. Thin lens - a lens whose thickness is much less than its radius of curvature. If the lens cannot be considered thin, then each of the two spherical surfaces of the lens can be considered as a separate thin lens. The approach for constructing images is to introduce the concept of principal planes of a centered optical system, a special case of which can be a thick lens. Centered optical system, which may also consist of a large number lenses, fully characterized by two focal and two main planes. Fully characterized in the sense that knowing the position of these four planes is sufficient for imaging. All four planes are perpendicular to the optical axis, therefore the properties of the optical system are completely determined by the four points of intersection of the four planes with the optical axis. These points are called the cardinal points of the system. For a thin lens, both principal planes coincide with the position of the lens itself. For more complex optical systems, there are formulas for calculating the position of cardinal points through the radii of curvature of the lens surfaces and their refractive indices. To construct an image of a point source, it suffices to consider the passage of two convenient rays through the optical system and find the point of their intersection after the axis. Two conjugate planes P1 and P2, reflecting each other with transverse magnification V=+1, are called the main planes, and the points H1 and H2 are called the main points of the system. The distances from the main points to the foci are called focal lengths: f1 = H1F1; f2 = H2F2. Any segment in front main plane depicted as an equal and equally spaced segment in the posterior principal plane. It follows from here that the beams entering and leaving the optical system intersect the main planes at equal heights h = h. Thus, the action of all refractive surfaces of an optical system for rays coming from infinity can be reduced to the action of a plane perpendicular to the optical axis, which contains the intersection point of the rays entering and leaving this system. For rays traveling from left to right, this will be the back main plane, and for rays going from right to left, this will be the front main plane. The position of the foci and the main planes is determined by calculating or graphical construction of the path of rays parallel to the optical axis, in the forward and reverse directions. When constructing images in an optical system, it can be assumed that between the main planes the rays go parallel to the optical one. This figure shows the path of the rays from the object h to the image h "through the lens. Point F", located on the axis of the optical system (lens), at which the rays converge , which were parallel to the axis before passing through the lens, is called the focus of the lens. The distance from the point F" to the main point P" is called the focal length of the lens. For a lens having a thickness of CT, the focal length is calculated by the formula: where R1 and R2 are the radii of the lens surfaces, n is the refractive index of the lens material. For a thin lens, the thickness CT is taken zero, the main planes P and P" coincide. The formula for a thin lens is: Back focal length, BFL - the distance from the top of the last surface of the lens to the back focal plane is calculated by the formula: The formula for calculating the linear magnification V is as follows: The deflection arrow of the lens surface is calculated from formula: Exercise 1. Determining the focal length of the lens To determine the focal length f, we use the expression for linear magnification β = y′/y (Fig. 1), where y′ is the linear magnitude of the image, y is the linear magnitude of the object. 1. triangles on the left and right side of the drawing, we can write y ′ a′ f z′ β= = = = , y a z f′ z′ = a′ − f ′, a′ = s′ + d ′. Hence z′ s′+ d′−f′ β= = (1) f′ f′ In this formula, all quantities are measurable except d ′ This quantity can be defined as follows: 9 s′ + d β = a′ = ′ a s+d or : d ′ = sβ + βd − s′ The product βd can be neglected due to the smallness of both quantities. Then: d ′ = sβ − s′ . Substituting this expression into (1), we obtain: βs = f′ β+1. (2)

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. Focuses of the 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 surfaces that bound 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.

Principal planes of the lens

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 refractive surfaces can be reduced to the action of these conditional planes, containing the points of intersection of rays, as if entering and exiting the system. This assumption allows us to replace the actual path of light rays in real lenses with conditional lines, which greatly simplifies all geometric constructions .

There are anterior and posterior principal 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

Notes

Literature

• Begunov B. N. Geometric Optics, MSU Publishing House, 1966.
• Volosov D.S. Photographic optics. M., "Art", 1971.
• Yashtold-Govorko V. A. Photography and processing. Shooting, formulas, terms, recipes. Ed. 4th, abbr. M., "Art", 1977.

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MAIN PLANES OF THE OPTICAL SYSTEM

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