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

CK Shene



The following article is an abridged version of an article I published on my Chinese language blog. It was published on December 25, 2007 and later revised on January 22, 2009. This was the first article on basic optics theory.

I used Google Translate to get this English version. Because Google Translate sometime produced very funny translations, I have to proof-read the result. However, I would definitely miss something, and please blame Google Translate if you see something funny. :)


I once saw such an exam question on the web:

If the upper portion of the lens is covered, is the formed image the lower portion of the scene? (True or False)

Because the question itself is somewhat ambiguous in semantics and assumptions, it may cause students to have different interpretations or different opinions, so debates and arguments are inevitable, but the question itself is indeed very interesting and enlightening. So, this article intends to focus on This issue is discussed further and in more detail.

simple statement

First of all, I think the "lens" in the questioner's mind should be a thin convex lens, because the camera lens has to be focused on the sensor; and to cover the lens refers to taking something (such as a piece of black paper) to cover the convex lens . Under this premise, we can use fairly simple optical knowledge to get a FALSE conclusion.

In the figure below , L is the lens, the two Fs are the focal points, O and I are the subject and its image respectively; in addition, the solid line and dotted line of different colors are used to mark the distance from the vertex of O to the vertex of I Imaging light rays. If you use B to cover the upper part of the lens, B will block the light rays formed by the upper part of the lens, but the light rays through the lower part of the lens can still reach image I/ Therefore, the whole object will still be photographed. However, because the incident rays are blocked in half, only half of the original light can reach the sensor.


The Origin of the Controversy

Many people insisted that "images speak for the truth", and they showed their works to disprove the "false" conclusion in the previous paragraph. These works are generally photos taken with a black card (similar to a split ND filter) that used to cover the upper half of the lens to reduce the exposure of the sky. The upper half of the picture is black.

Does this reveal Is the truth? No! Let me also do an experiment. I used a telephoto lens Nikon AFS 70-300mm f/4.5-5.6G ED , and a Nikon D50 . In order to ensure that the position of covering the lens is consistent, I use the Cokin P series filter holder and lens cap, and the lens cap is placed at the position as shown in the image below. In addition, because the photo was taken on a cloudy day with strong winds and showers, the leaves in the photo will sway with the wind and be slightly blurred, but this will not affect the conclusion of this topic.

  • 1/10 sec
  • Center-Weighted Average
  • Manual exposure

The photo below was taken at a focal length of 70mm . The black shadow caused by the lens cap covers about half of the frame, and the upper 1/3 of the potion without shadow is darker than the lower 2/3 :


The photo below was taken at a focal length of 100mm , and the black shadow portion has shrunk upwards to about 2/3 of what it was at 70mm :


The photo below was taken at a focal length of 135mm , and the black shadow portion shrinks upwards to only about 1/3 of that at 100mm :


Sorry. I have to stop here. Please search for PART II.