In lens formulas it is convenient, called away from a number of points "to measure the main points" to. There are two of them, one for the front of the lens and one for the rear properly as the primary and the secondary principal point principal point. While most expect the formula lens object distance is measured from the front main point, which most are calibrated scale so that the distance from the object to read the film plane. So you can not use, need the distance on your focusing scale in most calculations, if you are only an approximate distance. Another interpretation of the main points is that a (probably virtual) object on the primary principal point of incident light is formed from the front of the back seems to take a (probably virtual) image maintained exactly in the secondary principal point with magnification.
"Nodes" are the two points, so that a light beam is formed in the front of the lens and headed straight to the front hub had gone straight from the rear hub in the exact same angle to the axis of the lens as the input ray. The nodes are identical to the major points where the anterior and posterior media are the same, eg air, so that can be used interchangeably for most practical purposes the article.
Are in simple double-convex lenses, the two most important points somewhere inside the lens (actually 1/n-th the way from the surface in the middle, where n is the refractive index), but in a complex lens they can be almost anywhere, even outside the lens or the rear main point before the front main point. In a lens with elements that are fixed relative to each other, are the main points fixed relative to the glass. The internal focusing lenses or zoom the main points of the rule to move relative to the glass and each other during zooming and focusing.
When a camera lens is focused at infinity, the rear principal point is exactly one focal length before the movie. To find the front main point, take the lens from the camera and let light from a distant object through "backward". Find the point where the image is created, and the measure on the lens a focal length. Some lenses can mainly ultra Wides, do not do this because the image is not formed before the front lens. (All this assumes that knowing the focal length. I suppose you can trust the numbers the manufacturer's enough for educational purposes.)
How to reach the object to the front main point.
Si rear principal point to image distance
Focal length f
Magnification M
1/So 1/Si = 1 / f
M = Si / So
(So-f) * (Si-f) = f ^ 2
M = f / (So-f) = (Si-f) / f
If we interpret f Si as an "extension" of the lens on infinity focus, then we see that this extension is inversely proportional to a similar "extension" of the object.
For the rays near and almost parallel (the axis that we are) as "paraxial" rays can approximately model most lenses with just two planes perpendicular to the optical axis and is located on the main points. "Almost in parallel" means that the angles involved, theta ~ = sin (theta) ~ = tan (theta). Medium ("~=" be approximately equal.) These planes are called principal planes.
The light can be thought of as processes in the foreground main level, then jump up to a point in the rear principal plane to be exactly the same shift of the axis, while breaking even be thought of (curved). The angljavascript:void(0)e of refraction is proportional to the distance from the center where the beam on the plane and inversely proportional to the focal length of the lens. (The "front main level is related to the front of the lens. It could be behind the rear principal plane.)
Terms of the paraxial approximation of the principle of "levels" are not real planes, but turning areas. With a lens that is free of coma aberration is one of the classic (), the principle planes that could be called more properly equivalent to the refracting surfaces are centered spherical sections around and object and image point for which the lens is.
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