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I have recently noticed that when two objects with blurry shadows cast by the same light source are brought close to each other, their shadows appear to merge in a way where one shadow appears to "bulge" and meet the other even though the two objects are not in contact. I noticed this in my bathroom while I was brushing my teeth. Here is a gif of the same:

Blurry shadows merging

I thought that this might have to do with diffraction (although diffraction is a phenomenon that only occurs when light meets objects that are of size comparable to its wavelength, which is not the case here) or the umbrae and penumbrae of the blurry shadows but I'm not sure.

I am aware of this question that seems to ask about a similar phenomenon, but have decided to post mine anyway because:

  1. It is related to the shadows cast by the Sun while in my case it is just a bathroom light
  2. The answer to it, although a fantastic one, concludes that this effect is captured by the camera due to the limitations of its sensor even though I was able to capture it on my phone with high resolution and the video is indistinguishable from what I saw with my own eyes.
  3. Moreover, my bathroom is not brightly lit at all, which is what the answer suggests is required for this effect to be seen or captured by the camera.

Hence, I am inclined to believe that there is something more to it.

I was also able to easily recreate this effect using my table lamp, and found that the object that is further from the light source seems to be the one whose shadow "bulges" outward towards the shadow of the object closer to the source of light. This agrees with the gif above as my finger in it is closer to the bathroom light than the faucet, which is the one whose shadow appears to bulge towards the shadow of my finger. It also seems that the blurrier the shadow (i.e. the closer the object is to the light source), the greater is the "bulging" effect although I have not thoroughly tested this.

Does anyone have a clear explanation for this phenomenon?

Edit

While searching about this phenomenon on the web, I came across this Wikipedia page that describes it as the "Shadow blister effect". Although the page is pretty barebones and lacks citations, it seems to agree with my observations about the positions of objects with respect to the light source and each other, and suggests that:

The effect takes place when two objects are located at varying distances between a non-point light source and a backdrop upon which their shadows are cast. As the two objects move transversely such that their shadows approach each other, the object nearest the light source will begin blocking light from reaching the inside of the other object's penumbra, thereby expanding its umbra. This expansion of the further object's umbra will continue until the umbras of both objects meet. This effect can be demonstrated and understood using ray theory.

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    $\begingroup$ Related (possibly duplicate): physics.stackexchange.com/q/94235/123208 $\endgroup$
    – PM 2Ring
    Commented Mar 4, 2021 at 19:55
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    $\begingroup$ @Ruslan Did you not read the entirety of my question? I have mentioned that question and also mentioned that I found the answer given there to be unsatisfactory. Also, there it is the Sun that is casting the shadow which is so far away from the Earth that it can be considered a point source, while here my bathroom light is an extended source, so the two phenomenon may be unrelated $\endgroup$ Commented Mar 5, 2021 at 5:47
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    $\begingroup$ @TheLastAirbender it's frustrating when mods close these questions when the referenced answer is very poor. That answer PM 2 ring linked is incredibly poor quality and does not even accurately answer the question. $\endgroup$
    – Mdev
    Commented Sep 3, 2022 at 23:56
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    $\begingroup$ "the sun can be considered a point source" have you looked at the sky ever? does that bright circle look like a point to you? $\endgroup$
    – amara
    Commented Sep 6, 2022 at 21:02
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    $\begingroup$ It actually is a duplicate question in the sense that they are asking about the same phenomenon. However, all of the answers to the other question are either wrong or overly complicated. $\endgroup$
    – Rich006
    Commented May 26, 2023 at 13:06

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The shadow blister effect does not depend on diffraction or nonlinearity. It only requires two shadow-casting objects at different distances from a light source that is larger than a point. The wiki you linked to has a nice video that shows how it works, and also a reference to an Applied Optics paper by James A. Lock. From the paper's introduction:

Consider the shadows on a viewing screen of two objects α and β illuminated by the Sun or some other extended light source. Because of the angular extent of the source, each shadow has both umbra and penumbra regions. If α is closer to the viewing screen than β is, its penumbra is narrower than that of β If one of the objects is moved so that the penumbras of the two shadows overlap, the umbra of α appears to bulge out toward the umbra of β, giving a blisterlike appearance to the umbra of α. This is the shadow blister effect.

This phenomenon may be easily observed with illumination by the Sun. For example, consider sunlight entering a room through a window when the Sun is relatively low in the sky. If a person stands in the middle of the room and moves his or her head until the shadow of the head on the wall opposite the window almost touches the edge of the shadow of the window frame, the shadow of the person’s head appears to bulge toward the shadow of the window frame.

The paper continues with equations and diagrams.

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When I was a kid and would read about eclipses, all the talk of umbras and penumbras made my eyes glaze over a little bit, but it's a concept you really need to have if you want to understand why this works.

When something has a blurry shadow, the blurry part is called the penumbra, and it's there because the light source is larger than a point. If you're in the penumbra, you can see part of the light source peeking out from behind the shadow caster. The fully dark part is the umbra. In the umbra, you can't see the light source at all.

If you think about it, the larger the light source, the smaller the umbra (the dark part) is. That's because some of the light from the part of the light source that sticks out the farthest angles back inward and illuminates area that would otherwise be in full shadow (i.e., in the umbra). If you shrink the light source, the umbra gets bigger.

So think about what happens when an object close to the light source moves so that its shadow overlaps the shadow of a farther object. From the point of view of the surface on which the shadow is cast, the moving object (the one closer to the light source) is effectively making the light source smaller. So the umbra (again, that's the dark part) of the object farther from the light source gets bigger just where the moving object's shadow is.

I should say that I learned this explanation just now by watching the animation in the linked Wikipedia article, but I thought it would help to put it into words.

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If all intensity can be detected and displayed, then I don't have an explanation. If there is a minimum detectable intensity, then this following thought comes to mind.

As the objects get close, then the light blocked from the extended source to the effectively point receptor increases in the area between the shadows. The amount visible between the shadows reaches the minimum detectable intensity before the individual shadows actually meet.

A way to test this is to increase the brightness of the light source. With a brighter source, the intensity would not move below the detectable limit nearly so soon. The effect would not exist until the shadows were much closer together.

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