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Author Topic: What determines the shapes of shadows on the wall?  (Read 4404 times)

Offline John Chapman

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If the sun shines through a window it might cast a window shaped square of light onto an adjacent wall. However, the strange thing I have noticed is that the shape on the wall is actually neither window shaped nor square. I understand that you may get perspective as the two walls involved run from the corner and away from each other. I can also see that you might get some sort of parallax if the walls aren't square.

But can anybody explain this? It doesn't matter what angle the sun is shining from, the top and bottom of the light square are always slanted but the sides never are, remaining vertical.
« Last Edit: 14/02/2009 11:20:25 by chris »


 

Offline Chemistry4me

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Re: What determines the shapes of shadows on the wall?
« Reply #1 on: 14/02/2009 01:15:28 »
I don't undersatnd what you mean...???
Are you good at drawing diagrams? :)
 

Offline John Chapman

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Re: What determines the shapes of shadows on the wall?
« Reply #2 on: 14/02/2009 01:31:47 »
Hi Chem4me

Think of the sun shining through a window casting an image of that window on the adjacent wall. The sides of that image will never be slanted but the top and bottom always will be. This was pointed out to me by an artist who was telling me how to draw light and shadows. I can see that he is right but I can't tell why? Is that any clearer? ???

Unfortunately I don't have time (or possibly the ability) to draw a diagram as it is 1.30am here and my long suffering wife is telling me she's a computer widow and I'm a computer whore! I might have a go tomorrow if it doesn't become clearer by then.
 

Offline Chemistry4me

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Re: What determines the shapes of shadows on the wall?
« Reply #3 on: 14/02/2009 01:36:01 »
Hahaha :D Okay mate, you'd better hit the sack then!
 

Offline JnA

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Re: What determines the shapes of shadows on the wall?
« Reply #4 on: 14/02/2009 02:18:20 »
If the sun shone directly through the window at a 90degree angle (to the window) it would cast a square shape.. but suns and windows rarely line up at 90 degrees..
 

Offline John Chapman

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Re: What determines the shapes of shadows on the wall?
« Reply #5 on: 14/02/2009 10:11:00 »
Yes, that's right (but not on an adjacent wall). But the point is that as the sun moves and the shape changes the sides will always remain perfectly vertical. Only the top and bottom edges change their angle.

But even when the sun shines through at 90 degrees the rule (which I have now dubbed 'Chapman's Rule'!!! in an effort to become immortalised) still applies. In that instance the shape cast will not fall on an adjacent wall, only an opposite and parallel one. Anything else and the top and bottom distort - but not the sides.

It's like there's some sort of mathematical quirk that keeps the sides of the shape vertical no matter what! I just can't think why that should be.
 

Offline DrN

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What determines the shapes of shadows on the wall?
« Reply #6 on: 14/02/2009 21:53:31 »
Could be refraction - where the light is distorted when it passes through an object. Think of how light is distorted when passing through water; even a apparently pure sheet of glass with cause some degree of refraction. I expect the greater teh distance from the window to the wall, the greater degree of distortion.
 

lyner

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What determines the shapes of shadows on the wall?
« Reply #7 on: 14/02/2009 23:14:12 »
The amount by which the shadow image is stretched depends on how far it is from the window. (The light beams spread out)
I think the verticals are all vertical because the wall is vertical  and so is the window so the distances are the same between the vertical of the window and the vertical of its shadow.   The window and the wall that it is projected on may be at right angles to each other, however which changes the 'throw' of the image from side to side and, hence, the lengths of the images are different.
 If you see the window projected onto a floor, the 'sides' are splayed out on the floor and are not parallel but the top and bottom will be. Same sort of reason.
 

Offline John Chapman

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What determines the shapes of shadows on the wall?
« Reply #8 on: 15/02/2009 00:58:21 »
Hi sophiecentaur

I've had trouble articulating this question to everyone. The main problem is that, without a pencil and paper, it has been very difficult to communicate exactly what I mean. But you seem to have understood perfectly and your answer seems spot on. And you're right - I hadn't thought about it before, but when the light shines on the floor the distortion is the other way round.

The word your answer needed is 'perpendicular'. The sides of the window are perpendicular with the walls but the top and bottom of the window are perpendicular with the floor. It makes sense now. Thank you very much.
 

lyner

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What determines the shapes of shadows on the wall?
« Reply #9 on: 15/02/2009 22:19:16 »
An interesting puzzle. Things would be different if we all lived in teepees!
 

Offline RD

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What determines the shapes of shadows on the wall?
« Reply #10 on: 16/02/2009 00:13:38 »
I think the shape being described is a trapezoid...




http://en.wikipedia.org/wiki/Trapezoid
« Last Edit: 16/02/2009 00:18:23 by RD »
 

Offline John Chapman

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What determines the shapes of shadows on the wall?
« Reply #11 on: 16/02/2009 00:35:55 »
I wondered that when I rather inarticulately asked the original question and the reason I didn't use that word is because I had an idea that the two slanted sides of a trapezium by definition have to be converging. A bit like a what's left if you cut the top of a triangle. But I'm not sure. Certainly the wiki trapezium has converging sides. However, the shape of the window cast on the wall or floor is a skewed square. I'm not sure if that is still a trapezium - I think it may be a parallelogram.
 

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What determines the shapes of shadows on the wall?
« Reply #11 on: 16/02/2009 00:35:55 »

 

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