The optical system commonly used in optical instruments generally consists of the * * axis of a spherical system such as Dan Toujing or cemented lens. For a spherical system composed of thin lenses, the positions of objects and images can be determined by Gaussian formula.

( 1)

Sure, where f' is the image focal length of the system, s' is the image distance, s is the object distance, the object distance is the distance from the first principal plane to the object, the image distance is the distance from the second principal plane to the image, and the image focal length of the system is the distance from the second principal plane to the focus of the image. The sign of each quantity is positive when measured from the starting point of measurement, and negative when measured along the ray.

Moreover, the position of objects and images in the * * * axis sphere system can also be expressed by Newton's formula, that is

xx'=ff' ( f=-f') (2)

Where x is the distance from the object focus to the object measured from the object focus, and x' is the distance from the image focus to the image measured from the image focus. The object focus f and the image focus f' are the distances from the first and second main surfaces to the object focus and the image focus, respectively. The symbol is the same as above.

* * * Axis spherical system base point and base surface have the following characteristics:

Main points and main surfaces:

If the object is placed at the first point H perpendicular to the optical axis of the system, an upright image with the same size as the object at the second principal point H' will be formed, that is, the principal point is a pair of * * * yoke points with lateral magnification =+ 1. The planes perpendicular to the optical axis are called the first and second principal planes respectively (MH, MH' in figure 1).

4. Nodes and node planes:

Nodes are a pair of * * * yoke points with angular magnification =+ 1. When the incident light (or its extension line) passes through the first node N, the outgoing light (or its extension line) must pass through the second node N' and be parallel to the incident light of N (Figure 1). The planes passing through the nodes perpendicular to the optical axis are called first and second node planes, respectively.

When the * * * axis spherical system is in the same medium, the two principal points coincide with the two nodes respectively.

3. Focus and focal plane:

The parallel beam parallel to the main axis of the system, the image focus after refraction by the system and the main axis focus F' are called image focus; The plane perpendicular to the principal axis and passing through f' is called the image focal plane. The distance from the second principal point H' to the image focal plane F' is called the image focal length F' of the system. A point f on the principal axis is refracted to form a parallel beam parallel to the principal axis, which is called the object focal plane, and the plane perpendicular to the principal axis passing through f is called the object focal plane.

Obviously, the two principal points of the thin lens coincide with the optical center of the lens, and the positions of the two principal points of the * * * axis spherical system will change with the spatial characteristics of the focal length system of each combined lens or refractive surface. The combination of two thin lenses is discussed as an example. Let the image focal lengths of the two thin lenses be f 1' and F2' respectively, and the distance between the two lenses be d, then the image focal length f' of the lens group can be obtained by the following formula.

Location of two main points:

4. Principle of 4.nodal detector: A beam of parallel light is incident on an optical group composed of two thin lenses, and the optical group and the parallel light are * * * axes. After passing through the optical group, the light will converge on the Q point on the white screen (as shown in Figure 2), which is the image focus F' of the optical group. This is based on a certain direction perpendicular to the parallel light, and the optical group can rotate by a small angle in the following two cases:

A. the rotation axis just passes through the second node N' of the optical group.

Because the light incident on the first node N must emerge from the second node N', and the emergent light is parallel to the incident light, now N' has not moved and the direction of the incident light has not changed. Therefore, the light beam passing through the optical group still converges to the Q point on the plane (as shown in Figure 3(a)), but at this time the image focus F' of the optical group has left the Q point. Strictly speaking, the definition of the rotated image is slightly poor.

B. the rotation axis does not pass through the second node N' of the optical group.

Because the second node N' is not on the rotating shaft, after the optical group rotates, N' moves, but the light emitted by N' is still parallel to the incident light, so the light emitted by N' will shift compared with the previous case, and the convergence point of the light beam will move from Q point to Q' (as shown in Figure 3(b)).

The pitch measuring device is a horizontal chute R which can rotate around the vertical axis OO'. The optical system Ls (shafting composed of thin lens) of the measured base point can be placed on the chute, and its position can be adjusted. The scale on the chute indicates the position of Ls (as shown in Figure 4). When measuring, gently rotate the chute, observe whether the image on the white screen P' moves, and refer to the complaint analysis to judge whether N' is in OO'.