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Funny Reflection: Newsletter Challenge (11/06/07)

Posted November 04, 2007 5:01 PM
Pathfinder Tags: challenge questions

The question as it appears in the 11/06 edition of Specs & Techs from GlobalSpec:

John bought a brand new house and invited his friend Tom to visit. Tom arrived and took a seat in John's new living room. Directly across from him he noticed a large mirror in the wall. The mirror had a table directly in front of it with two lit candles on it. Tom noticed that in the mirror, one candle was upside down and one was right side up. At first he was confused but then saw his own reflection and understood. What did Tom realize?

(Update: Nov 13, 8:30 AM EST) And the Answer is...

Tom notices that his reflection is upside down in the mirror, notices the candle that is right side up is closer to the mirror than the other candle which appears upside down, and concludes the mirror is concave.

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#1

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/04/2007 7:29 PM

This sounds like a simple beveled mirror. One candle is closer to the wall than the other.

My girlfriend said that John's first mistake was inviting Tom.

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#69
In reply to #1

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 10:12 AM

Is she planning to constrain your social life as well?

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#145
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/14/2007 9:11 AM

First line of your answer may be right. Second? I would not say any thing.

May I add to it by saying that it could be an optical illusion? Or one too many beers?

Regards;

Nadeem

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#2

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/04/2007 10:07 PM

Assuming a rectangular mirror I go along with a concave shaped surface, One would think that maybe John has a warped sense of humour.

Regards JD.

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#4
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/05/2007 6:05 AM

I would go with concave and one candle at the end of the table closest to the mirror and the other at the furthest end (presumably the "rectangular" bit was to explain Tom's confusion) - except that the table is "directly in front of it" and it's hard to see how a large concave mirror could have sufficient curvature throughout its area without this being obvious from the periphery (unless perhaps the mirror is round and John has let the centre into the wall - which would indicate an odd sense of humour). Maybe I have an overblown definition of large - but I'd be assuming something a minimum of 5' high, which would need the table to be exceedingly long)

However, although I can think of myriad other explanations (even a fairground mirror, part vertically concave and part vertically convex would need to have visually obvious edges), there isn't one I would personally place in my own home.

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#5
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/05/2007 7:41 AM

Yes you have raised the same points and more that crossed my mind, I was unsure if a round or oval mirror would reflect every thing upside down? reading your post and thinking that there must be more to it, and your remark about the mirror edges, made me think, maybe when he looked there was no reflection? a mirror set at 45deg with a false table and candles in the next room? an over blown imagination, maybe, I'll wait and see what other opinions there are, should be interesting.

Regards JD.

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#7
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/05/2007 8:11 AM

The concave mirrors you are most likely to find in the home are enlarging shaving and/or make-up mirrors. If you place one object close to the mirror, and the other rather further away (ideally about twice the focal length), and then look from a distance, you will see the closer object appears the right way up, but the further one is inverted (both vertically and laterally). Then look at the distances and the curvature - and remember that the depth of the curve goes as the square of the dimensions. A pair of angled mirrors to invert one candle, together with a non-angled mirror for the other would be rather conspicuous, I fear - as would be a mirror facing another room.

Maybe John has one of those stretched mylar mirrors, and has sucked a suitable section to become concave. That wouldn't create any shadows at the edges to make it visible. Assuming it's not a contrived joke, the more likely cause would be some sort of lens (gold-fish bowl?) between the upside-down candle and the mirror - but that wouldn't really fit the last part of the question.

Re-reading the challenge: perhaps the clue is that the mirror is IN the wall. That would allow a fairground mirror with its edges hidden. That would be a great deal of trouble and expense for a one-off joke.

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#3

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/05/2007 1:11 AM

Tom saw his reflection upside down and knew that he was looking at 45deg at 2 mirrors at right angles to each other, (horizontal placing).

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#34
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 10:08 AM

If that was so, why would one candle appear right-side up?

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#38
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 1:13 PM

The real candle would be upside-up. Tom cannot see himself directly.

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#39
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 1:25 PM

Have you ever tried burning a real candle upside down? It will not stay lit very long. Heated combustion gases from the burning wick (melted wax is the fuel) must go up. If it is a cylindrical or block candle (non-tapered) the gases given off will quickly exclude the oxygen and the candle will extinguish. If a tapered candle, where the gases escape up the side and are replaced by air, so there is no lack of oxygen, the wax melts far too quickly to be consumed and will run down the side and smother the wick.

Try again!

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#54
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 4:57 AM

I haven't tried it, but might a Kompressor arrangement work? (Turbo-charged candles would be even nicer, but I couldn't even envisage a Heath Robinson approach...)

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#63
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 9:54 AM

No, it would have to be an anti-gravity candle!

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#67
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 10:09 AM

How close to vertical do you think we could go with an optimum downdraught? I know from burning candles at both ends that 60-degrees away doesn't give problems (other than messed-up carpet tiles**). Could we get it close enough to vertical that it wouldn't be obvious if the slant was towards the viewer? We need to know

**How naff can John get?

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#154
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/14/2007 7:55 PM

The table has a mirror top. The candle closest to the wall mirror is reflected once. The other candle, and the face, are reflected from the table and the mirror.

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#6

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/05/2007 8:07 AM

I find it a bit curious that the author selected the wording "a large mirror IN the wall". A mirror that is hanging on or mounted to the wall would be referred to as "ON the wall".

My thought is that the mirror or what initially appeared to be a mirror was actually a window and behind the wall were a set of reflecting/refracting devices to create the illusion observed. Why anybody in their right mind would waste valuable building space on this type of setup, is quite beyond me!

This odd set-up could also play tricks such as, there was actually only one candle where the apparent second candle was the reflection from the glass and the apparent reflections where the product of what was behind the glass.

Oh, by the way, is FUNNY used to mean "HA HA" or FUNNY as in unusual?

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#8
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/05/2007 8:21 AM

I've seen an equivalent effect laterally with bow windows where the glass was bent to accommodate the bow. But the distances involved would not really be compatible with both candles being on the same normally-sized table. I haven't ever seen the use of vertically-curved glass like this - but architects being what they are, it's perfectly possible. If it's in a hot area, the high level of reflection from the window might be explained by local regulations to limit heat insolation effects (perhaps that is the relevance of it being a new house?).

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#22
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 7:46 AM

The glass curved in one plane would not cause an image to invert, it would cause the image to look fat or unusually thin maybe.

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#25
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 8:03 AM

That depends on the distances involved. If one candle was close to the mirror, it would be almost unchanged. If the candle that was further from the mirror was spaced twice the vertical focal length from the concave mirror, it would appear vertically inverted and the original size. There would be a great deal of image astigmatism, of course, but this would only make the image appear somewhat out of focus - and there is no sharpness to a candle-flame in any case.

When you next take children to a fairground, try varying your distance from the distorting mirrors, and see how you can get different vertical and horizontal magnifications from different mirrors.

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#9

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/05/2007 1:35 PM

Two additonal thoughts:

The mirror could have a convex surface and a concave back. I have a magnifying glass that I keep on my desk. When I use it, I often see two reflections of the ceiling light. One is inverted.

Another observation is that the images get closer together when I rotate the maginfier to an angle closer to perpenicluar to the angle of incidence.

I'm not sure that this info applies, but I'm sure Fyz or STL will pick up on it. I'm also waiting on the reflections of our squirrely friend. Or is he a devil this week? Or a superhero? Or....

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#28
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 8:58 AM

That all sounds reasonable. A hint at an explanation of the variation with angle of view: there are at least two effects here:

If you had a flat sheet of glass, the images would be separated by about twice the refractive thickness of the plate. You wouldn't notice this when one image is behind the other in the direction you are looking - but it becomes quite obvious when you look somewhat from the side (or off-axis to the plate).

The focusing effect depends on the path-length of the light relative to the off-lens-centre position. When you angle the lens, the same focussing effect will be closer to the central path in one direction, causing the lensing to gain power along that direction. That applies equally to the front and back-face reflections. You are also increasing the differences between the effective paths by looking off-axis - but that effect is proportionately stronger on the front surface than on the back one.

With so much going on, it's hard to be certain which effect is which just by looking.

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#73
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 9:47 PM

...I'm a bit bust with some other stuff, but..

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#74
In reply to #73

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 10:59 PM

I see four candles in that picture. Two are standing correctly, one is standing inverted, and one is diagonally across the floor tiles...

bob

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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 11:33 PM

Maybe Liberace had a tantrum and chucked the whole candelabra and piano.

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#10

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/05/2007 11:08 PM

The candle in its holder was resting on a mirror.

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#11
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/05/2007 11:26 PM

The candle in its holder was resting on a mirror.

Wouldn't he see two candles in that case? The candle itself, and the reflection of the same candle from the mirror it is on... Like looking at the reflection on a lake that has a mountain in the background. You would be looking a the "mountain" itself, and the inverse of the mounain underneath.

Very clever though.

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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 6:48 AM

I was thinking: the candle and the image of same reflected from the tabletop mirror to the wall mirror and then to the guest's eyes. When the guest saw his own reflection, one of the candles did not appear as between his eyes and his image; it was superimposed on his image...by which he realized (1) there was only one actual candle and (2) the upside-side down candle was a virtual image of the actual candle...or something like that. Thanks for the good word.

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#20
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 6:54 AM

Oh, and the wall mirror was a framed mirror hanging by a wire from mounting hooks on the wall. So it hung away from the wall at the top...so that it could pick up incident rays from the table and direct them to house guest's eyes.

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#23
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 7:56 AM

Another possibility here is that the table top mirror creates the inverted image in the wall mirror which is actually a thermopane window. With two panes in the window the candle will appear multiple times as the light reflects between the panes. Actually there would be a infinite number of reflections but after the second reflection the image gets very weak. The image of the already reflected inverted candle would only be recognizable in the first reflection off the window's panes. In fact the table top could be just glass, making the inverted reflection from the window even weaker.

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#12

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 1:47 AM

The top of the table was also a mirror. The reflection in the wall mirror is right side up. The reflection from the table was up side down.

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#13
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 2:27 AM

Yes I can see how one candle can be reflected upside down, assuming left and right, but how will his reflection reveal this?

Regards JD.

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#17
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 3:37 AM

Hi there

Having worked in special effects for film, and if I would have been given the challenge of creating such an effect, I would have used a video screen. Bluff is all. Or at least some times. Mirror Mirror on the wall....

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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 5:08 AM

Magnetic Island nice place, only sailed passed there. A place for special effects, all that candle power to lay on the beach? could have been a video but some how I think not, I will need to reflect on it a bit more.

Regards JD.

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#26
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 8:03 AM

His image would also be upside down.

The mirrors must be at 90 deg to each other and at 45deg to the viewer.

Take some mirrors and try it out.

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#29
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 9:03 AM

You have it Hen, mirror on the ceiling Tom sitting down low, candles one close one afar of the wall mirror. Must be a bachlor pad. Why did he invite Tom an not Mary? UMMMM

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#78
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 11:58 PM

He was sitting down so the mirror may had been above him creating a 45 degree angle and then the mirror if hanging by a nail typically the top is farther from the wall than the bottom creating a downward angle then to the table seeing one candle in the mirror and the reflection off the table of the other candle! It works try it!

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#82
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 4:29 AM

Is this a single mirror whose surface is at 45-degrees to the vertical? And is the surface of the (reflective) table horizontal? If so, all upside-down images will have an associated image (or original) that is the correct way up, and all the inverted images will appear below the top of the table.
If that confuses Tom, we would have to postulate some disturbance to Tom's mental faculties (possibly John is Tom's boss, and Tom took an oversized portion of Dutch courage before visiting?).

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#126
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/11/2007 1:20 AM

Ahh well Ahh yep ok!

single mirror "frame" looking like < Then table __ then tom i

< __ i

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#122
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/10/2007 6:23 AM

His reflection and the "upside-down candle" he sees will always coincide, not matter which direction he move (so long as he sees the "second candle"--i.e., so long as the upside down candle reflection falls on the wall mirror for him to see.

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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/10/2007 9:58 AM
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#124
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/10/2007 1:56 PM

Clever! But many things that are done can be undone.

For reference sake, I didn't "mirror" this as Edgar did. I clipboarded the image into ACAD, stretched it to a larger size, and typed the text into a multiline text object. I clipboarded that into Paint to convert it to a .bmp, then used Photo Plus to crop the image to remove excess whitespace, and to convert to a .gif.

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#127
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/11/2007 2:28 AM

That's a bit long 3Doug- I clipboarded it direct to paint, flipped it, then pasted it back into the editor. Where does Edgar enter all this ?

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#128
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/11/2007 4:08 AM

As I understand, Edgar is genetic for any guest. Maybe it's an allusion to E.A. Poe?

What I did was just look at it.

Cross-eyed Edgar.

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#131
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/11/2007 6:55 AM

generic ?

What I.. Nevermore so.

So it's a bit like Ed Wood then.

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#14

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 3:05 AM

It's obvious - Tom is a complete klutz. When he sat down he knocked one of the candles over, that's why it is upside down.

When Tom looked in the mirror he realised he had wax all over his pants and John's new $8000 suede couch was on fire.

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#24
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 8:00 AM

Ahhhh! The overly creative mind. You should be a screen writer, but then again you would be walking a picket line at the moment being that we are in a writer's strike!

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#59
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 7:15 AM

Rather than striking I'm just on a go-slow; it took me 5 hours to write that entry.

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#15

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 3:23 AM

How about 2 mirrors, one concave catching one candle turning it upside down, and reflecting unto the big mirror?

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#16

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 3:31 AM

How about two mirrors in the room, one concave reflecting one candle and turning it upside down, and the big mirror catching the reflection of the other mirror and the reflection of just one candle right side up?

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#27
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 8:34 AM

I agree 2 mirrors would give this effect and men don't notice mirrors unless they are right in front of them.

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#21

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 6:58 AM

He realized he had had too much to drink.

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#30

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 9:29 AM

I'm going to wager that the upside down candle was in fact upside down. Or possibly it was a vampire candle, so that its initial reflection (in the mirror behind it) would not appear, but it's secondary reflection (of the mirror beneath it) might appear--I've never heard or read about the reflection of a mirror involving a vampire. So watch out for that candle. It wants to suck your blood.

I've noticed that many decorative candles (a plain cylinder of wax usually tinted lavender) would be difficult to orient, particularly at a distance. If an unlit decorative candle without a wick or with only a little nub of a wick were upside down, how could you tell?

Oops. Just noticed that the candles were lit. Hmm. I guess one of them could have been lit on the bottom. The wick generally runs all the way through the candle and can be lit from either end.

Tom might be having a stroke, also, affecting his vision in one eye.

Is John the sort of person who might spike your beer with DMT or LSD or some other perception altering alkaloid?

One end of the mirror was slightly concave and the entire mirror is concave toward the center. The other end of the mirror might be flat or slightly convex. Tom might have noticed that his head had disappeared--that he was just two shoulders--two identical shoulders--in the mirror. But one arm was rotated 180 degrees so it pointed up rather than down. This would require quite a dramatic warping in the mirror, but I can imagine it'd be easy to pull off with a sheet of aluminized mylar. I don't understand why more people don't use mylar wall hangings in the rooms of their homes. It would make the rooms look infinite and not a single ray of infrared light would enter or leave, saving on heating and air conditioning. A slight rippling of the walls would result in massive gyrations of reflections throughout the infinite space of the compound reflections. And as happens ever more frequently in this day and age, if a vampire were to come to a party in your apartment, you would know instantly.

Are there other supernatural beings that don't cast reflections or is it just vampires?

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#31

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 9:39 AM

there can be no ambiguity in a scenario where one man invites another man to his place, lights decorative lavender candles, and has mirrors on the ceiling. Is John's house in Georgetown? Is John a republican senator?

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#32

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 9:40 AM

Lysergic acid diethylamide

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#33

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 10:06 AM

Is the table, a mirrow table placed at front of the mirrow? JorAl.

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#35

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 10:15 AM

The mirror is concave one candle is inside the mirror's focal point the other is outside it's focal point the one outside will appear upside down.

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#129
In reply to #35

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/11/2007 4:24 AM

Omigosh! Please explain: how many candles were there? And how was this made evident by his own reflection? Did he see himself blurred? Or did he see the image of his eyebrows singe-ing--from being inside the focal point?

And how were you able to bait someone to post the second thumb-up? Is this some kind of "virtual" conspiracy? Huh? Reflect on that.

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#36

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 10:40 AM

Although the only answer I have, rightly or wrongly is a concave mirror etc., why would anyone have a concave mirror in the house.....if that is the correct answer, I call foul!!!

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#37

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 11:02 AM

Tom saw the reflection of the candle on the shiny table it was sitting on, right by the mirror.

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#40

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 1:32 PM

hello ladies and gentlemen

As an engineer a tradesman and a photographer the correct answer is the mirror hung on the wall with a coffee table in front of it; the top of the coffee table was made in three sections 2'x2' wood, 2'x2' mirror, and 2'x2' wood. One candle was on the mirrored surface and the other was on the wood portion of the surface. Thus one candle would reflect upside down and the other right side up.. to offset and upset some, use the same scenerio but add a mirror to the ceiling and see what you get.

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#43
In reply to #40

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 3:15 PM

But then wouldn't you see six candles? The one on the wood and its upright reflection in the wall mirror (2), the one on the table mirror and its upright reflection in the wall mirror (2), and the inverted reflection in the table mirror, and ITS inverted reflection in the wall mirror (2), would all be separate and visible "candles", would they not?

This is assuming that a "coffee table" (your description) would naturally be lower than Tom's eyes, allowing a good angle for viewing all reflections. I suppose if you were at just the right angle, 45° from both the table mirror and the wall mirror, that is what you would see, but this would require one to be MUCH closer to the mirror than "directly across from him" in the living room would imply.

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#55
In reply to #43

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 5:02 AM

Part 1 could be satisfied if the horizontal mirror is higher than the table, and the mirror on the wall angled downwards so tom only sees the reflection. But how does this satisfy "Tom saw his own reflection and understood..."?

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#142
In reply to #55

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/14/2007 7:57 AM

His own reflection was his feets!

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#41

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 2:53 PM

As noticed by others, the key may be that the challenge states that the mirror is "in" the wall, not "on" the wall. Of course, that MAY be a typo, since the "i" key and "o" key are adjacent on the standard "QWERTY" keyboard. In any case, I agree that the mirror(s) must be set into the wall for the trick to work, without being noticed immediately.

OK, I see only two possibilities here. IMHO both are equally valid. However, implementation may be what sets them apart. Also as noted by others, a concave mirror will present a virtual image (one appearing behind the glass) as inverted and the same size if the candle is placed in front of (away from) the mirror's principal focal point. The image will appear smaller the further the object gets back from the focal point. The other possibility is that two flat mirrors are used, one at 45° above horizontal and the other at 45° below. Depending on the angle of viewing the object will appear inverted, but with a horizontal line across it where the two mirrors join.

However, because of the nature of glass and the ability of the human brain and eyes to sort out subtle changes, Tom must somehow be fooled into thinking it is a normal mirror. Add to that the desire to have one candle appear "normal" while the other appears inverted. This leads to the necessity of constructing a multi-panel mirror. Since it is not uncommon for large wall mirrors to be constructed from more than a single mirror glass, when viewed straight on it would be difficult to see the transition from flat mirror one side to concave or tilted mirrors on the other side. This is especially true since the brain is expecting to see a normal set of mirrors, and if there are no other visual cues, such as wallpaper or other objects, the brain can be easily tricked to see what it expects to see. I would expect only two panels, one concave and one flat, or four panels, two flat and two angled. Positioning and angle become critical though, otherwise the virtual images may appear smaller or to float higher or lower than the actual candle.

I would expect that the seat taken by Tom was either the only seat available, or that John indicated to Tom that he should take that particular seat. When gazing on the candles, the one in front of the flat mirror section would appear upright in the mirror while the one in front of the "trick" mirror section would appear inverted. Tom's confusion was quickly cleared up when he saw his own image in the trick mirror was also inverted (for either trick mirror) and much smaller than expected (for the concave mirror).

I think that is more likely that the two 45° angled mirrors would be used than the concave mirror simply because the distortion would be much more detectable and the "sweet spot" for viewing much more limited.

The angled corner mirrors are often used to invert images, but usually left to right rather than top to bottom, because in that way one sees himself as if in a photograph, or as others would see them, and not a typical mirror's reflection. For example, hold up a sign in front of you in a typical mirror and the lettering appears backwards. Hold up the same sign in front of you in a corner mirror and you can easily read the words, which appear just as if you were seeing someone else holding the sign. This is important to people who are extremely critical of their images, such as actors, TV personalities, fashion models, savvy politicians, etc.

Concave mirrors are also used for closeup work, such as makeup or other facial observation, because when you place your face CLOSER to the mirror than the focal point, your image will NOT be inverted and WILL be magnified. On the other hand, if you don't really care what you look like, go play with a concave mirror placed further than its focal point initially and move it back and forth through its focal point, noting the crazy distortion as you go from small inverted image to large upright image.

I would also think John was an idiot to spend so much time and money constructing such a lame trick. (That goes double for the writer of this challenge and quadruple for the editors who published it!)

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#56
In reply to #41

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 5:11 AM

Agree with most of this - but the "sweet region" for viewing an inverted image of a candle at twice placed the focal distance from the concave mirror is anywhere that is more than about six times the focal distance from the mirror. However, the image will be in front of the mirror, so the candle (and thus Tom) need to be offset from the axis of the mirror. Also, as Tom moves slightly sideways, he will see that the image is in the same front-to-back plane as the candle - that would not happen with a cylindrical (fairground?) mirror.

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#42

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 3:13 PM

Rough sketch of the setup. 2 mirrors at 90deg with horizontal joint.

Tom would see his image inverted, The one candle direct with a inverted image.

see my posts way up. (#3, #28 and #38)

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#44
In reply to #42

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 3:18 PM

Hen, I agree with your illustration (see my post #41 above), that this would invert the image, except that you appear to enlarge the image as well. I do not believe that any magnification occurs with flat mirrors set at any angle.

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#49
In reply to #44

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 8:30 PM

I agree. My reflection angles is surely not correct.

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#130
In reply to #42

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/11/2007 4:37 AM

This seem just like the correcting vanity mirror set-up, where one sees one's actual, un-reversed self (one's doubly reversed image)--only turned 90 degrees. It also seems essentially the same as the candle on plane mirror guesses. Maybe Tom saw the light when he reclined on the settee and took a second look...and that's when he noticed the "second" candle, seemingly not inverted. BTW, how do you think the blacklight candle is supported?

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#45

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 3:33 PM

There is a parllex happening , don`t mirors show exact opposite of actuals .reflexions from side mirrors were one candle reflects other , possibly and surely it is only one candle , that is exact and other one is reflection seen on the table , refracting towards mirror , something similar to mirrage phenomenon happening in desert , if you observe a rough wall from a particular angle far away from 90deg supposly in heated condition you see your reflections like highly polished ones , that `s how Tom felt when he saw himself upside down with candle plus original of himself upright ,

Initially he must have felt world over him , if looked himself before candle ....oops

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#46

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 4:09 PM

Tom realized that he still had his glasses on, which are the type with the high magnification on the bottom. (inverting the lower candle)


He also realized that he was in the dining room, not the living room, hence the candles on the table... etc.

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#47

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 5:13 PM

There is also a mirror on the wall behind Tom.

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#48

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/06/2007 6:55 PM

Instead of thinking of the complete mirror surface as being distorted, perhaps only a section is. If you look into a shiny spoon every thing is inverted, so if we have a large rectangular mirror with a small round or oval area at the bottom made concave or spooned in, and placed at a height such that a candle place in front of it would be reflected upside down. Having such a small area distorted would then become obvious when viewing ones reflection, the area in question would show up with the gradual light distortion around it's edge?

Regards JD.

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#50

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 2:06 AM

The answer is 103 tiles diagonally in the first case i.e. in rectangle of 81 x 63.

and 558 in a rectangle of 472 x 296

And the formula used is the pythagoras theorom considering the each tile to be 1 x 1 unit size

I welcome ur corrections and comments

Regards

A. M. M.

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#51
In reply to #50

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 3:19 AM

Right answer, wrong Blog?????

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#57
In reply to #51

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 5:15 AM

No, I think that's humour - wrong answer, wrong blog...

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#62
In reply to #50

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 9:49 AM

No, no!!!!! John had instructed Tom to cross the living room along a diagonal line, counting the tiles as he went. On reaching his chair he took out his favorite coin, and having noticed that it was sunny outside, proceeded to flip the coin. Since it came up "heads", he decided to take a piece of chewing gum out of his pocket that had been given to him by his Grandpa who had been on the original survey team in San Juan, Puerto Rico. In his excitement at what he saw on sitting down, he forgot to unwrap the gum and felt an unpleasant tingling in his mouth.

Since John had already put a solar film on the windows, the house remained cool, even though it was a sunny day, so when the Australian Aborigine down the street played his Didgeridoo, through the open window he could hear the native cursing when a leaf fell on the end and stuck to it. That is strange, thought Tom, I thought the weather forecast on my FM car radio said it would be Non-sunny today. I should have checked in on my favorite AM station, he thought, but a tunnel was blocking the signal at the time. Tom had just returned from a Tropical Vacation and was once again enjoying static electricity effects from the carpet in John's new house while shuffling along the diagonal line, when he noticed the two candles on the table in front of the mirror.

One candle's reflection was upright while the other candle's reflection was inverted. This confused Tom at first, because that only happened on Non-sunny days when a cool layer of air descended and trapped a warmer layer (warmed by the candle) on the side nearest the window (where the cold air came in at the top) creating a mirage effect at the boundary of the two layers, mirroring the upright candle and causing an inverted image in the wall mirror. But when he looked at his own reflection and saw John standing behind him, choking with stifled laughter, he knew that John was up to his old tricks and that the "mirror" was actually an HDTV monitor which was set "in" the wall, displaying an image from a hidden HD video camera, only the live video feed had the image reversed to give one the perception of a mirror, with a "green-screen" effect allowing the mixing in of an inverted candle image in front of one of the two candles.

At this point Tom got up, punched John in the nose, and left vowing never to accept another one of John's lame "challenges".

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#64
In reply to #62

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 10:03 AM

Where's Blain?

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#65
In reply to #62

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 10:05 AM

That makes it all clear now. I was way off base. I thought the inverted image was caused by the appearance of duplicate matter caused by the fact that this occurrence was exactly at 2AM on Nov 4.

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#66
In reply to #62

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 10:08 AM

Great writing. Truly we are in the presence of a genius

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#68
In reply to #66

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 10:10 AM

Floored genius if John punches back?

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#52

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 4:50 AM

Ok guys, I think most people are going off on tangents again.

Physicist and Buzz have hit the nail on the head and hung the mirror properly by the way :)

Where in the question is the mention of the word "Rectangular", which so many people are assuming?

The mirror must be a circular concave mirror and at the age of 13 I remember my physics teacher demonstrating to me that if you place an object between a concave mirror and it's focal point (One candle on the table) it will appear in the morror the right way up.

If you place another object (The second candle or "Tom in his seat") outside the focal point, it will be inverted in the mirror.

Tom was no longer confused when he saw that his own reflection was upside down

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#53
In reply to #52

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 4:55 AM

And furthermore, if I can type "Morror" when I actually meant to type "Mirror" then I think the question setter could have easily typed "in the wall" when they really meant to type "on the wall" :))))

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#58
In reply to #53

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 5:30 AM

A mirror of undetermined shape with a suitable small area sucked in, first suggested by Fyz in post #7, would reflect a candle inverted at the correct focal length, and the distortion of the area would be self evident when viewed by Tom. Hope this is back on track.

Regards JD.

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#60
In reply to #58

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 8:06 AM

I find it odd that the puzzler mentioned the fact that this was a "BRAND NEW HOUSE". I take this as possibly meaning that there is something unique about what is done in new housing that leads to the puzzler's answer. My first thought was the thermopane windows, but maybe there is something I am missing. I live in a 60 year old house so ideas are just not popping up. Of course a couple of you folks in Europe are probably living in 300 year old houses so you are at a similar disadvantage.

I don't believe the puzzler was suggesting an art deco answer, because if that is the case you could have a myriad of possibilities.

Let's explore this thread.

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#61
In reply to #60

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 9:05 AM

"300 year old houses": as new as that? And what do you mean, disadvantage? Please bear with me while I go and put on some warmer clothing...

BTW, if this is typical new-build standard, the lintel has sunk onto the thermopane window causing it to bow outwards. Another few mm and it will shatter, but meanwhile it makes a good distorting mirror

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#70

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 10:49 AM

Outside of the focal point, the light reflecting from the top of the object (you), hits the top of the inward curve of a concave mirror and is reflected downwards while the light from the bottom of the object is reflected upwards. The point where the rays of light cross, in front of the mirror, is the focal point and you see an inverted image.
As you move nearer, a point is reached where the light hasn't yet crossed. The image is therefore not inverted

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#71

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 1:39 PM

http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l1a.html

i think the solution lise in high schools! ha ha

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#72

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 1:51 PM

glass tables reflect pretty well

vampires don't reflect at all

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#76

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 11:39 PM

So Simple! One candle is reflecting of of the table and then seen in the mirror!

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#77

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/07/2007 11:42 PM

To Add I feel that John needs a new friend that doesn't find themselves as confused as Tom!

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#79
In reply to #77

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 12:07 AM

A candle reflected off a glass table would reflect laying down, wick towards Tom, plus the reflection of the candle itself, the correct way up. If this is not correct then I suppose you can simply laugh.

Regards JD.

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#125
In reply to #79

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/11/2007 1:13 AM

So Truth! What if the mirror look like = < on the wall and you so both candles in the mirror or like / on the wall and you see both candles in the mirror or perhaps like ( on the wall then you need more in the room?!!! Any way it seems to be such a issue and the wick may just have fallen in his lapp! Ha Ha!

Lets However reflect;

John bought a brand new house and invited his friend Tom to visit. Tom arrived and took a seat in John's new living room. Directly across from him he noticed a large mirror in the wall. The mirror had a table directly in front of it with two lit candles on it. Tom noticed that in the mirror, one candle was upside down and one was right side up. At first he was confused but then saw his own reflection and understood. What did Tom realize?

Ok Tom took a seat!

Large mirror on the wall / directly in front of him! / a table dirctly in front of the mirror

2 candle in it wall = l, table= __, mirror= <, tom= i

Ok now here layed out=== l<__ i

Only possible answer!!!!!!!! Now it is your turn for a laugh or will you?

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#80

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 12:42 AM

There is one candle sitting on a mirrored table top. Tom saw his own image (partial) which was also flipped.

Don

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#81

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 3:51 AM

http://www.glumbert.com/media/mirror It's a bit of a long clip, but could be a partial answer.

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#83
In reply to #81

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 4:38 AM

That must have taken some care with the camera positioning. Nicely done, nonetheless...

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#84
In reply to #83

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 6:08 AM

They probably had to do a double-take.

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Guru

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#85
In reply to #84

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 6:30 AM

Treble, I think - and not boy soprano either. (I.e. three mirrors - one for the "proper" reflection, and two at+/-45-degrees for the shifted one). The camera angle would have to be so that the reflections at the joins were of the plain wall. And I wouldn't be surprised if there had been a bit of retouching - possibly even movement of the non-angled mirror. Either way, I'm sure that the arrangement would have been pretty-much obvious to the participants.

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#86
In reply to #85

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 7:18 AM

Twins

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#90
In reply to #86

Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 8:55 AM

Spoilsport. (Just try that with the candles)

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