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There are quite a few questions about blurry shadows and diffraction on this site, though, none of them specifically answer my question about why shadows blurriness is distance dependent, that is, why shadows are sharper near the object and blurrier farther.

Just to clarify, the other question is specifically about a case, where an object is being moved relative to a surface (where the shadow is cast upon). The answers state "diffraction", but do not go into any kind of detail as to how diffraction actually causes a blurred edge with the varying traveling distance of the photon (or classical light), somehow causing a magnification of the change in angle of the photons/light (as it interacts with the edges). I am specifically asking about this quantum or classical explanation as to why this scattering at the edges (and more specifically the change in the angle of photons/light) causes them to become more spread over a surface that is farther.

I have read this question:

Why are shadows more defined the closer you move the object to the surface the shadow forms on?

But it does not answer my question specifically.

enter image description here

If you look at the picture, you can see that the shadow is very sharp close to the object, but farther the shadow becomes more blurry.

Diffraction simply as a word that is often used does not explain as to why the distance matters in this specific way.

Question:

  1. Why are shadows sharp close to the object, but blurry farther?
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  • $\begingroup$ You can think of the ground in your image as a bunch of smaller surfaces, each at a roughly constant distance from the object. Quantization (photons) doesn't affect the shadow noticeably, and diffraction doesn't affect it much. It's essentially a matter of geometric optics and the nonzero size of the light source. $\endgroup$
    – benrg
    Commented Jan 26, 2022 at 5:45

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Given the image in your question, I think the answer has nothing to do with diffraction and is related to the light source not being point-like.

The discussion in this answer will be entirely based on geometric optics where all optical phenomena are described by light as a ray.

I will base my discussion on the image below (from Wikipedia). The image is in the context of the Earth's shadow, but the description applies to any scenario with a light source and a shadow casting object.

Umbra, penumbra and antumbra of Earth and images that could be seen at some points in these areas

For an extended light source (non-point-like), such as the sun, the light does not originate from a single direction and results in three shadow regions:

  • Umbra - In this region of the shadow the complete light source is blocked by the shadowing object. The shadow is maximally dark and uniform over the region.
  • Penumbra - Within the penumbra region only a portion of the light source is block so the shadow here is not as dark. The depth of the shadow is in proportion to the area of the light source blocked by the shadowing object. This region results in a gradual transition from the dark umbra to the shadowed region. As you move farther away from the light source the relative angular size of the shadowing object decreases faster than that of the light source so the penumbra region becomes larger while the umbra shrinks.
  • Antumbra - The final region, the antumbra occurs when you move far enough away from the obscuring object that it no longer completely cover the light source. Here the shawdows are not a deep as in the umbra and gradually transition from the full umbra so unshadowed, once again making the edges of the shadow less deep.

When you are closer to the shadowing object, relative to the light source, the umbra region is greater and the penumbra is thin. As you move farther away, the umbra region shrinks and the penumbra grows. This causes the effect asked about in the question.

The above discussion applies when the size of the obscuring object is smaller than the light source. For example a lamp post and the sun. When the shadowing object is bigger the situation is somewhat different and there is no antumbra.

For a point-like source, or an extended source that is far enough away to be considered point like the only region that remains is the umbra as seen from the shadow, the light route is either visible or completely blocked, leading to sharp shadow boundaries.

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  • $\begingroup$ Thank you so much! $\endgroup$ Commented Jan 30, 2022 at 18:39
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I believe it has something to do with an angular "spread" around the edges. This angular "spread" will translate into a larger and larger edge as you go away from the source of the angle, which is at the edge of the object. See my drawing.enter image description here

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This is a geometric-optics fact, and is due to the source not being point-like. An ant sitting at the shadow does not see the sun- it is hidden by the pole. If the ant moves to the edge- it can see parts of the sun- the parts which are not hidden by the pole (the sun has a finite size). This is called partial shadow, because some of the sun's light reaches the floor, and some is blocked.

Geometrically, the width of the partial-shadow region grows with the distance between the object and the floor.

Imagine an object close to the floor. If the ant moves a tiny amount, then the object no longer hides the sun. If an object is held far away from the floor, the ant can move the same amount as before, but this displacement causes only a slight difference in angles, so the object still hides some of the sun.

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I think it is a matter of type of source: point-like and huge/extended sources. In the case of the sun, experimentally if you get the object away from the screen its shadow gets blurry and if you get the object closer to the screen its shadow gets sharp showing a dependence on the source

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What dreadful answers. Not one mentions the fact that the sun's disc subtends an angle of 0.5 degrees. Over 10 metres that leads to a spread of 87mm for the light rays. That's 10000mm multiplied by sine of 0.5 degrees. Hence shadow edges cannot remain sharp.

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  • $\begingroup$ Welcome to PSE! Please stay factual in your answers. You can leave comments under the other answers, when you have gained a reputation of 50. $\endgroup$ Commented Jan 19, 2023 at 12:04

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