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I was watching this video on the YouTube channel Veritasium. In this episode, the host shows people paper containing holes of different shapes in the middle. So there is a paper which has a hole in the shape of a triangle, another one containing a square, a circle and so on.

Every time you place a cardboard against the sun and observe the shadow, a circle is obtained,at the centre of the shadow, regardless of the shape of the hole. The host explains that this is the image of the sun that we are seeing on the shadow.

I find this difficult to comprehend.

My question is: Aren't 'lenses' required to converge the rays to make an image? How can a hole in the centre of a cardboard form 'images'. When the rays from the sun reach the cardboard they are going to be parallel. How can a hole in the center of a paper form an image from parallel rays? Is the host correct? Is this caused due to diffraction, where in the light bends around the hole, blurring the edges and hence forming a circle regardless of the shape of the hole?

PS: I am sorry, I couldn't summarise the question into a nice title.

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It's a pinhole camera image of the sun - as DJohnM's comment said.

My question is: Aren't 'lenses' required to converge the rays to make an image? How can a hole in the centre of a cardboard form 'images'.

No - all that is required is an aperture (hole) to restrict the range of rays that reach the screen to form an image. All a lens does is allow a wider bundle of rays to be used to make the image = more light. In terms of making the image it is the hole formed by the center of the lens that is important.

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Actually, both the other answer and Veritasium himself are wrong. The shape shown is not due to the pinhole effect (the holes are way too large for that). In fact, the resulting image isn't even a circle!

If the sun were a point source - an infinitesimally small source of light - the triangle hole would indeed result in a triangular image.

Point source
(Projection of a triangle from a point-source. Source)

The reason the image is not a triangle is that the sun is not a point-source, but a circular-source. We can model that by treating the sun as many different point sources, equally spaced throughout a circle.

Each point source will contribute one triangle to the resulting image. Each triangle will overlap heavily with its neighbors, but be slightly offset from them. The final image will be the sum of many different overlapping triangles whose centers are equally spaced around a circle (or an ellipse, depending on the angle between the sun and the wall). The edges will be faded because only a few point-sources contribute there, while the center will be bright because many point-sources contribute there.

Simulation - few point sources
A simulation of a triangular hole + a few point-sources arranged in a circle

Simulation - many point sources
A simulation of a triangular hole + many point-sources arranged in a circle

Shape of the image
The ultimate shape of the image with edge-fading removed

So as you can see, the shape is circular, but it's not a circle.


Interestingly, while researching this topic, I found a video by someone who accidentally created an experiment for this. They shined a rectangular LED spotlight through a small triangular hole. LED spotlights are unusual because they consist of an array of very bright LEDs (basically point-sources) that are equally spaced, with empty space between them. Essentially, it's a real-life point-source approximation of a rectangular light!

As expected, they found a result similar to the "few point sources" image above, but with the triangles arranged in a rectangle rather than a circle.

Triangle experiment

(They attributed the effect to diffraction, but that's actually incorrect. The hole would need to be on the scale of a few micrometers before diffraction would be noticable)

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  • $\begingroup$ You simulations are great, but your text is wrong: what you’re showing here is how the pinhole-camera effect arises. $\endgroup$
    – rob
    Jun 14 at 11:30
  • $\begingroup$ @rob: Perhaps that's a matter of definition, but from my understanding, one of the key features of the pinhole effect is that a recognizable image of the source forms. That does not happen with holes this large. For example, if the sun had writing on it, or was multicolored, or had a small donut hole, you would not see that (recognizably) in the projected image. $\endgroup$ Jun 14 at 19:38
  • $\begingroup$ All that matters is that the angular size of the hole is small, when viewed from the image plane. Consider that during a partial eclipse, all of the normally-round dappled spots under the shade of a tree turn into images of the crescent sun — even though, if you look through a tree's leaves for patches of blue sky, the patches are almost never very good circles. (I've observed sunspots with a setup like this one, non-round aperture and all.) $\endgroup$
    – rob
    Jun 14 at 19:53
  • $\begingroup$ @rob: True, but in order for the pinhole effect to be significant in that case, the angular size of the hole (from the image plane) must be significantly smaller than the angular size of the sun, so that a small portion of the sun maps to a small (relative to the overall image size) part of the image. The angular size of the sun is ~32', so to be even 1/100th of that, the hole should be ~19", which for a 1 inch (2.5cm) hole means it would need to be held $\frac{60*60*360}{2\pi*19}$ inches ≈ 900 feet (275m) away $\endgroup$ Jun 15 at 6:53
  • $\begingroup$ You overestimate both the size of these pinholes and the size of the safety factor you need. Here’s the calculation I used when I did this years ago. With a quarter-inch pinhole, you can resolve sub-arcminute sunspots at 20 or 30 meters. The gross feature that the image of the sun is round, regardless of the shape of the pinhole, is clear much sooner. I suggest you find some cardboard and a knife and give it a try. $\endgroup$
    – rob
    Jun 15 at 11:51

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