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【CK's Theory Related Post】PART II: If the upper portion of the lens is covered, is the formed image the lower portion of the scene?

CK Shene


The photo below was taken at a focal length of 200mm . The real dark shadows have receded out of the frame, leaving only a trace of "something wrong" (shutter problem?):


Finally, the photo below was taken at a focal length of 300mm . Not only the dark shadows, but also the darker areas are gone!


What "truth" do these photos show? Why do black shadows shrink slowly as the focal length increases? Is there a problem with the experiment or the theory? The answer is that the theory is correct, and we need to understand what the shadow is and where it comes from (that is, the control parameters during the experiment), which requires further knowledge.

Basic concept of Compond Lens

The photographic lens uses more than one lens. Traditional Gauss optics can condense the optical system composed of multiple lenses into a virtual lens, and satisfy the formula of single lens. Although Gauss optics only give correct results close to the optical axis, this is good enough.

In the figure below, L is a virtual lens, which represents a photographic lens, and O and I are the subject and its image respectively. There are two extremely important points N 1 and N 2 (Note that N1 and N2 actually have 1 and 2 as subscripts which I don't know how to do it, yet!) on the optical axis of lens L , they are called nodes ( nodal point ), and the plane passing through these two nodes and perpendicular to the optical axis is called nodal plane, on both sides of the node each has a focal point F 1 and F 2 , F 1 is matched with N 1 , and F 2 is matched with N 2 .


Why are nodes and nodal planes important? The ray parallel to the optical axis from the top of O enters the system from the nodal plane of N 1 , leaves at the nodal plane of N 2 , and turns to the focal point F 2 on the right of N 2 . The ray starting from the O vertex and passing through the left focus F 1 of N 1 will intersect the nodal plane of N 1 , thus turning to be parallel to the optical axis, and then leave the system from the nodal plane of N 2 to intersect the previous ray for imaging. The light from the O vertex to N 1 travels on the optical axis after being turned, and leaves the system after reaching N 2 and turns to the I vertex for imaging. As can be seen from the figure above, the single lens theory we learned in high school or university is a special case under N 1 = N 2 ; It became the single lens theory.

three examples

Let's look at three practical examples of camera lenses. The figure below is the optical structure of Nikon 's Nikkor-N 24mm f/2.8 wide-angle lens. The nodes H and H ' are marked in the figure , and the corresponding focal points F and F ' are marked . This is the design of a traditional SLR wide-angle lens. The node on the right and the focal point are at a considerable distance behind the lens, so that the reflective lens will not hit the rearmost lens when it bounces up. Not only that, the left node H and the left focal point F are both inside the lens barrel. Although not every SLR wide-angle lens is designed like this, most of them have H and F inside the lens barrel, and H ' and F ' behind the last lens. This is called a retrofocus design .

  • NIKON - E4500
  • 10.0 mm
  • ƒ/8.1
  • 1/125 sec
  • Pattern
  • Manual exposure
  • ISO 100

Below is the optical structure of Nikkor-S 50mm f/1.4 . Interestingly, the two nodes of H and H ' reciprocate left and right, and the left focal point F is still inside the lens barrel, but very close to the surface of the first lens. Generally speaking, the left focal point of a standard lens will be near the first lens surface, which may be inside or outside the lens barrel, depending on the design.


Please continue with PART III. Sorry.