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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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#96
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 10:19 AM

Spoilsport. (Just try that with the candles)

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#87
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 7:52 AM

I am surprised that that trick would fool people. Looking into another room will appear quite different than looking into a mirror. For instance the twin's reflection would not be directly infront of the others if reflected, it would be offset as with the position of the room.

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#89
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 8:51 AM

I am surprised that that trick would fool people.

You are forgetting that the power of suggestion can have a very strong effect on one's mind. In the video, the people being fooled were expecting a normal restroom mirror. The presence of another person who acted as if nothing was wrong confirmed it. For those who do not speak German (I speak a little), the young lady was asked by the person being fooled if she could see them, and she replied that she could. That would be enough for one to doubt one's own sanity at that point, I would think!

Obviously, they knew something was amiss, which is why one woman kept taking off and putting on her glass and why they almost all asked the young lady to change places or move over, so they could see if it was a trick mirror, being normal where the young lady was standing, but not on their side. Also, the twins were standing so close to the mirror, the difference in angle or position would not be that noticeable.

Perhaps part of my alternative explanation of the "challenge" which I gave in #62 is not so far-fetched after all:

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.

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#103
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 7:44 AM

I could not hear the dialog, the sound quality was quite poor, but I thought the language was French! Also, unless the one participant was a very unattractive woman, they were inferring the toilet was co-ed which surprised me, even for Germany.

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

11/09/2007 8:17 AM

That co-ed toilet scenario is a little bit odd, but the gag was funny and well done. It also illustrates a point of visual deception. Many times I've seen women using the mens facilities (and OK,I admit vice versa). Even if it was contrived for camera, it could happen. How about the mirror shelf illusions as another possibility of perception over knowledge. eg ;

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#106
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 9:33 AM

OK guys, I went back and revisited the clip. At the very beginning, as you enter the room, the sign on the door clearly says "WC -Damen/Herren". The WC part is clearly understood by international travelers, "Water Closet", meaning restroom, toilet, etc., although Germans usually say "toiletten", "Wasser Closet" has the same meaning) and "Damen/Herren" is German for "Ladies/Gentlemen" or "Women/Men" if you prefer. And the language was clearly German, though it would be hard to say if it was actually in Germany, Austria, or Switzerland (the German-speaking part, anyway). Perhaps a native German speaker who can differentiate accents would review the clip and let us know (if anyone really cares!).

The same sign is posted on the wall inside, but this time with an arrow pointing to another door, so presumably the first room is an anteroom and is indeed co-ed, with separate facilities for "private functions" available past the second door. Actually, a novel, nice, space-saving and efficient design, just what one would expect from the Germans.

By the way, I once had dinner in a fine 5-star restaurant in Germany with some US customers, including a young engineer from Indiana (who had probably never even left his own state before). The young man excused himself to find the restroom, and came back a few minutes later, very red-faced. When quizzed about his consternation, he said he was confused by the signs on the restroom doors. He saw "her-en" (as he pronounced it) and figured that was the Ladies room (Her room), so went into the one marked "da-men", thinking that was German for "The Men". He was surprised to find ladies inside "Da-Men's Room"!

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#107
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 10:06 AM

Given that there was clearly a wash-room on the other side of the "mirror", I took it that the single washroom would have been a temporary arrangement until works were complete. The toilets themselves may or may not have been separated (other than the urinals, there would seem to be even less purpose in segregating the toilets than the wash-rooms). Maybe (?) I'm over-analysing

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#108
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 11:06 AM

This may seem irrelevant but hold with me. It's only anecdotal (alarm bells sound). When making the latest film Titanic ( the de Caprio/Winslet one), they couldn't afford a full scale mock-up of the ship. One side of a 'Titanic' was made, and the film inverted when a view from the other side required. Things like Insignia on crew hats were written in mirror image to make it work on film. Urban myth or not ? I have no idea. ( and just to annoy all , its sister ship The Olympic* was not sunk in real life as part of some big conspiracy)

* http://www.snopes.com/history/titanic/gigantic.asp

http://praveenzone.blogspot.com/2007/08/goofs-in-titanic-movie-intersting.html

http://www.titanic-titanic.com/titanic_conspiracy_theory.shtml

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#109
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 12:18 PM

A pair of well-placed cameras and merging the shots would have worked fine for this if they had used actors. Or they could have used a genuine mirror and added the victim from a different shot. Then the actions, speech and lips could have synchronised perfectly.

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#111
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 12:53 PM

"A Night To Remember" was much better anyway. My stiff upper lip is almost quivering

< I said 'almost'>

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#110
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 12:53 PM

"Maybe (?) I'm over-analysing"

MAYBE?

Maybe the sun will rise in the east tomorrow. Maybe tides will rise and fall. Maybe ER will entertain us with more poetry or prose.

But there is no "Maybe" here. It's a SURE THING!

ROFL!

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#112
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 12:55 PM

Hold on - you just analyzed the post by Fyz ! What is this, some kind of place to argue ?

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#132
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/12/2007 8:44 AM

What is this, some kind of place to argue ?

No, it isn't!

< ROFL with reference to Monty Python >

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

11/12/2007 1:05 PM

I'm going to reflect on that, otherwise it could go on foreverreverofforeverreverof.......

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#91
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 9:04 AM

There's no reason you can't place the twin in the correct location in the "mirrored" room, and if you get the lighting correct, there need be no visual clues - apart from the intended one that you appear to have turned into a vampire. However, I'd be surprised if any of the participants didn't actually know what was going on - for example, the answers would need to be rehearsed for there to be adequate synchrony between the speech of the local twin and the lips of the other. Even with the clips they selected, and on the very small scale we can see, there are enough mismatches to show the deception (even if you ignore the camera angles from behind the 'mirror').

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#94
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 9:37 AM

So you think the "participants" knew what was going on and pretended to be fooled, and were just hired actors who "played along", pretending to be random restroom customers?

I think there are enough simple-minded people out there who could be fooled by such a set-up. Obviously, the producers did not show the dozens and dozens of "participants" who were not fooled, as you were not, and immediately saw through the trick. What would be the fun of that? Yes, the lips were not synchronized. Yes, the motions of the twins did not EXACTLY mimic the other. But unless the "participant" was suspicious of the young lady (the twin on his/her side of the mirror), they had no reason to watch her that closely, being more concerned about their own image, or lack thereof, since the young lady had verified that she COULD see the "participants" image. Besides, don't identical twins often finish each other's sentences, know pretty well what the other is going to say? How hard a stretch would it be then for the one "in the mirror" to quietly lip-synch to her identical twin's predictable (and possibly re-hearsed) responses? A good example of this is how the young lady asks "Is anything wrong?" as the "participant" is backing off or about to leave, drawing them back in. Obviously, some of her lines WERE scripted and rehearsed, but I doubt that the others' lines were!

I have seen enough "hidden camera" shows (starting with the original US "Candid Camera" to know there are plenty of gullible people out there who see what they want to see, or what they think they see (or don't see in this case), to believe that this clip was genuine and not played by all actors.

Of course I could be wrong, but what entertainment value could a show such as this provide if the TV audience knows it (the show) is NOT trying to fool anyone but the TV viewer? If faked, these things have a way of getting out, and the show and its producers would lose all credibility with the public. The TV viewer wants to be in on the joke, not the victim of it!

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#95
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 10:18 AM

I'm not saying I would immediately know which technique was being used - but the length of time the "victims" were there was long enough. But I hadn't really thought of this as a 'professional' production and subject to those constraints - which I now realise I should, given the expected cost of tidying up the rooms before the final partitions were placed.

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#114
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 2:34 PM

the glass is just glass no mirror -- the room on the other side of the "window" is identical to the one they are in the lighting is all indirect and exactly the same in both

the real mirrors on the back walls are angled down as not to reflect into each other

the twin does not have to do the exact same motion because the person watching can never really see both at the same time -- if you watch very closely they are stage to be in constant contact with the counters maintaining their distance and reference perspective

-and at times are "off" when they move laterally

these were most likely the "best" victims and i am sure there are others where they messed up sneezed coughed etc....

excellent trick! thanks for the post

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#116
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 3:27 PM

As you say, visual-to-visual cues would not be that easy to pick up - though you'd have a reasonable chance when looking from the side. But lip synchronisation during speech is really hard to maintain (and didn't appear to be achieved).

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

11/08/2007 10:24 AM

And lets not forget it's hard to look at both person at exactly the same point and time*. Like you say, it's people expecting something to be a certain way that lets them get taken in.

*Anyone with independent eyes like a Chameleon excepted.

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#88

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

11/08/2007 8:41 AM

... and Tom asks: "Do you think I may have had one too many?"

Says John: "Well... one way of checking is to look at those two candles on the table. When you see there are four of them it's time to stop."

"But there is only one candle there!"

"Aah... you see what I mean?"

(Adapted from an old joke about a youngster asking his dad's advice about the limits of social drinking as they exit the taverna, with candles in place of lamp posts. Clearly not applicable in an era when daddy is deemed dumb by default)

And now if I may be permitted to stray into (or on to?) the challenge topic, here's a contrived solution.

Main assumptions are that the candles are standing directly on the table without candle-holders (John doesn't mind the wax dripping), and there are no bright objects above or behind Tom to indicate the reflective nature of the tabletop.

Consider an ordinary mirror fixed on the wall with its top edge somewhere midway between the level of Tom's eye and the tabletop. Actual level will depend on table length and Tom's distance from it. If one candle is close to the near end and the other right next to the mirror, then Tom will see only the single reflection of the far candle in the mirror and the inverted second reflection of the near candle via the shiny tabletop, besides of course part of his decapitated torso also inverted. The direct reflection of the near candle gets chopped off by the upper limit of the mirror. A bit of lateral offset may be necessary for the two images not to clash or appear as one candle with both ends lighted!

Now when the gotcha guy says: what about the inverted reflection of the far candle from the tabletop itself, I would reply that there was a book lying right in front of it!

This is obviously not the 'correct' answer, as the mirror is stated to be 'large', but it may set someone on to a solution without postulating krazy kurved mirrors. Could it be that Tom didn't take off his cap and the rim cut off the direct reflection of the near candle in the 'large' mirror? No end to contrived solutions based on convenient assumptions. If the mirror is tilted down ever so slightly, the inverted image of the near candle may even appear to be at the same level as the real table, though it appears unlikely that Tom would have examined the image closely after he achieved 'realisation'.

I did make a pencil sketch on square-ruled paper of what I have tried to describe, and it looked convincing enough, but I have no idea how to get an image into a CR4 post, being almost computer-illiterate. I manage to peep in here maybe once a week, and actually made some belated contributions to the 'boxes and coins' thread, where my verbose explanations sans sketches must have been truly exasperating, and remained mostly unread!

=TeeSquare=

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#92
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 9:17 AM

"I did make a pencil sketch on square-ruled paper of what I have tried to describe, and it looked convincing enough, but I have no idea how to get an image into a CR4 post, being almost computer-illiterate."

T2 (my short version of your name),

If you have a digital camera or webcam you could get a crude image. If you have a page scanner or an "all-in-one" printer that has a scanner mode you should be able to scan in a better image. Just save the image as a .jpg file (the standard digital photo format). If you have any CAD at all you should be able to convert it to a bitmap (.bmp) file. If you have no CAD, try using the MS Paint utility that come with Windows. You can save those images as .bmp or .jpg (as well as others, but I do not know if the others will upload to CR4). It is fun to play with and can be used to make crude line drawings. You should then save the file in a location you can get back to and remember or note the name you gave it. I think that CR4 may automatically resize images that are too large.

To attach an illustration to a CR4 posting use the green camera icon in the toolbar above the message box. Click on "Browse" and you can navigate your PC to the spot where you saved your file, usually in "My Documents" directly, or on "My Computer", then "Local Disk (C:)", then "Documents and Setting", to a folder with your name, and then "My Documents" folder.

I hope this helps.

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#119
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 7:16 PM

Thanks STL, for the detailed instructions. The first-fruits of my labour should be visible below. I have some practice in dealing with jpg and bmp files in 'Paint', but never tried a webcam or scanner. I've often used the 'draw' commands in MSWord97 for making figures to go with text. It is easier and avoids having to import/embed files which may change their folder locations or names. My signature below is a Word diagram.

Though I am an engineer, I'm too old-fashioned to put up with the breed of Autocad-wallahs who can't think beyond the limitations of the built-in icons. I gave up on it when I was told that you can't draw a helix without 'writing a programme'. I can think far more clearly with a pencil on paper. No doubt a CAD package is useful for repetitive work, or editing/scaling, but it would be too cumbersome for my limited purposes.

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#121
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 7:53 PM

I have a slight confession TeeSquare. Having asked in a thread about 'drawing' , the responce was fabulous. Every kind of advice possible was offered. Best software, how to do it etc etc. Ya know what, I still reach for the nearest back of an envelope or something. They all probably think I'm an ungrateful git, but old habits die hard. Still, some may have got benefit from that particular thread. Oh. I suppose I could, but whats wrong with trad methods. Nothing when it comes to concept ideas or scanning summat into a pooter.

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

11/08/2007 9:25 AM

I think that's clear enough without illustration - certainly easier (for me) to follow than the various "how to" descriptions for posting illustrations into CR4. (STL's here being about as simple as it gets)

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#98
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 10:29 AM

I guess we can allow some on-topic. What does the question try to suggest by saying it's a "brand new house" ? The fact that the morror is "in the wall" also suggests some trickery beyond a mirror on it's own (?).

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#99
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 6:38 PM

I was reading through my emails from CR4 website and came across the original email that posed the problem. On the email the mirror was "on" the wall and not "in" the wall as it states above.

I really do think this is simply a "typo".

And now we have solutions involving high defintion plasma monitors and books in front of candles and all sorts of contrived scenarios.

Come on guys...really...Let's get real here.

The mirror is a CONCAVE mirror or else I'll eat my hat and drown it down with several pints of Guinness :)))

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#101
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/08/2007 8:19 PM

That's an excellent contingency plan (apart from the hat - those on a building site are sort of 'crunchy')). Just make sure the pints are not upside down ( It must be a problem in NZ ). Oh hang on, if you're upside down too it won't matter !

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#105
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/09/2007 9:08 AM

Hey, MPM! I once saw a guy on television eating motorcycle parts, so I guess you should be able to eat a simple hat! (Straw would likely be the most digestible, high fiber, too!) Speaking of television you said:

"And now we have solutions involving high defintion plasma monitors and books in front of candles and all sorts of contrived scenarios."

OF COURSE THE HDTV SOLUTION WAS A CONTRIVED SCENARIO!

Have you never heard of "tongue-in-cheek"? That was part of a larger scenario involving elements from the last couple of months of "challenge" questions.

"Come on guys...really...Let's get real here."

Sheesh! No one appreciates good fiction anymore!

Since we know from previous "Answers", that the official solution is often lacking or assumes too much, you may be right yet still have a different answer from the one that gets posted on Monday!

"The mirror is a CONCAVE mirror or else I'll eat my hat and drown it down with several pints of Guinness :))) "

Does a corner mirror count as "CONCAVE"? I don't think so. We'll have to wait and see if you need a little headgear seasoning. Of course, you won't really have any taste buds left by the time you down a few pints of Guinness, so I guess it won't really matter! <ROFL>

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#139
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/14/2007 7:13 AM

...books in front of candles...

Has anyone spotted the bell yet? And for whom does it toll?

Shucks, I don't think I was supposed to ask that second question...

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#140
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Re: Funny Reflection: Newsletter Challenge (11/06/07)

11/14/2007 7:20 AM

< I'll get yer sack-cloth>

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#100

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

11/08/2007 8:07 PM

A mirrored (or highly polished) table top would cause one candle near the wall mirror to be seen upright while the second candle away from the wall would reflect in the table top first and then the wall showing itself upside down to the viewer. Am I the only one here with mirror topped coffee and end tables in my living room?

-Sully.

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#102
In reply to #100

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

11/08/2007 9:44 PM

In the scenario you describe, Tom would see the second candle and it's reflection in the mirror but the problem clearly states he only sees 2 candles in the mirror:-

"Tom noticed that in the mirror, one candle was upside down and one was right side up. "

Furthermore, how does this scenario explain why :-

At first he was confused but then saw his own reflection and understood. What did Tom realize?

Don't you surely agree that if the table was a mirrored or polished table, Tom would see at least one image of one of the candles upside down on the table and thus he would not be so confused to see upside down images in the wall mirror?

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#113

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

11/09/2007 2:30 PM

Several points here:

My instructor in German 1 in community college was native German. She said that public restrooms there are co-ed. Rooms are numbered, and restrooms are all numbered 00, or Nul-Nul. So if you need to relieve yourself and you're having trouble locating a restroom, all you have to say is "Nul-Nul?".

I forget which show it was, but on a talk show someone who was a twin said that identical twins aren't really indentical, they are mirror images of each other. One will be right-handed and the other will be left handed.

The trick pulled in the video might have been based on a scene from an old Marx Brothers movie. Groucho was passing in front of a wide doorway and someone on the other side made up to look like him mirrored all his movements. I don't remember which movie it was. Later, Lucille Ball and Harpo Marx recreated the scene in an "I Love Lucy" episode. I wouldn't be surprised if one or both of these scenes is on youtube.

The profile of the mirrors in Hendrick's illustration is very similar to the profile of a concave mirror.

As far as eating inedible objects, I heard of a man that ate a Blackberry. The problem is that it wasn't his. When he was accused of eating it, he denied ever doing so. But his bluetooth gave him away! ;-)

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#115
In reply to #113

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

11/09/2007 3:22 PM

"that identical twins are mirror images of each other". Pure mythology.

Most identical twins, like the rest of us, have their hearts on the left. Handedness is a function of brain development, which is influenced by hormonal timing. Identical twins, sharing the same genetics and environmental factors, are more likely to share the same intrinsic handedness than pairs of people selected at random.

On the other hand, they are certainly not identical, though most people would find it hard to see the visual difference between a pair of identical twins if both came through in perfect health. As ever, Wikipedia gives interesting detail.

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#117
In reply to #115

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

11/09/2007 4:18 PM

Excellent point, and very well sated Fyz. 'Identical' is a much misused term in relation to twins. No offence intended to your co-loquator ( which is probably the wrong word/spelling, but you know what I mean). Kudos to both of you for raising the matter*.

* note :I even resisted the possibility to use the word 'issue' because I thought the post was A+ good.

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#118
In reply to #113

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

11/09/2007 4:43 PM

Are single sex female restrooms numbered 000?

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#120

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

11/09/2007 7:20 PM

Since we are assured that it is a LARGE mirror ON the wall, and supposedly a curved one at that (post 99), I would first presume it to be spherical or cylindrical, perhaps even corrected for off-axis aberrations. The focal point or line would have to be somewhere mid-table with the candles at the extreme near and far ends for the images to be reasonably 'life-size'. Tom no doubt saw himself as some kind of inverted pygmy.

[In this scenario would anyone like to speculate on the fate of an object (say a third candle) at the centre of the table?]

However, since the mirror would have to curve forward over the candle at the far end, it would have got blackened with soot long before Tom got to see anything through that portion of it. Or was the question-setter imagining some kind of imitation candle with electric bulb?

Should we presume that the whole point of this elaborate arrangement is to fool Tom into thinking the mirror is flat (which backfired anyway the moment he saw his own reflection)? Any overhead lights or bright objects, not to mention a reflective tabletop, would have alerted Tom that something was amiss even before he seated himself. If the 'correct' answer is indeed on these lines, I must say the whole situation will need to be very carefully contrived with regard to illumination and avoiding any objects on or near the table which can give the game away. Alternative solutions will probably call for an even more convoluted mirror!

=TeeSquare=

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#135
In reply to #120

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

11/13/2007 9:50 PM

One must understand that the word, concave, is being used very loosely, and not according to strict definition. In fact, the official reply is essentially the same in that plane mirrors set at angles could be thought of as being "concave" as a unit.

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#143
In reply to #135

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

11/14/2007 8:58 AM

The official reply meant spherical concave. But would a "large mirror" be sufficiently concave (or is it a very deep table)?

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#134

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

11/13/2007 9:44 PM

So? Why didn't he observe that his image was reversed as well?

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#136
In reply to #134

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

11/13/2007 11:08 PM

His image is upside down and reversed ( I.E. if he moves his head to the right the upside down image of his head will move to the left from his perspective.

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#137
In reply to #136

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

11/14/2007 1:34 AM

Thanks, man.

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#138
In reply to #136

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

11/14/2007 1:37 AM

So, it looked like one question has been overlooked: which candle was upside down? Or, can an inverted candle burn from the bottom?

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#141
In reply to #138

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

11/14/2007 7:30 AM

Or, can an inverted candle burn from the bottom?

Fyz answered this very early on in the thread...and the answer is no, based on the same physics that prevent a candle burning in zero gravity. (Where No means it doesn't behave in the nice way candles do)

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#144
In reply to #141

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

11/14/2007 9:01 AM

I though STL answered that bit. I'm still not completely certain we couldn't create a candle that would burn upside-down in a suitable down-draft

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#146
In reply to #144

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

11/14/2007 9:30 AM

Right, Fyz. In #39 I said:

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.

And I am sure you are correct. With suitable down draft, or even side draft, it could be possible to feed in ample oxygen and blow away the products of combustion. The remaining problem would be melty wax wicking down (no pun intended) and smothering the flame. However, a side-draft might cause a melt cavity on one side only whereby the liquid wax would have an alternate path and drip down away from the wick, creating a stalactite-like formation.

A zero-gravity environment would also be problematic for candle-burning (what DO those lady astronauts on the space station do when it is time for their relaxing bath? Oh, yeah, baths are a problem also!) but a suitable air feed could eliminate the problem, and zero-gravity would prevent or diminish unwanted wicking of melted wax, unless it just blobbed up faster than the wick could burn it. A moot point, as I am sure that intentional combustion is not allowed due to safety and air quality issues (Hmmm, birthday cakes rigged with LED "candles" and a very sensitive air pressure transducer to trigger the "off" switch?)

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#147

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

11/14/2007 9:39 AM

There is one thing that bothers me about the "concave mirror" solution given in "And the Answer is..."

From what I have read, a right-side up virtual (directly viewable in the glass) image would be created by a candle placed inside the focal point of the mirror, however, the inverted image that is claimed for a candle placed outside the focal point would actually be a "real" image, that is, a projection of light, and would only be viewable if there was some media for the light to focus on, like a frosted glass screen, water vapor mist/fog, or a cloud of smoke or dust particles. Nothing of the sort was mentioned in either the question or the "Answer".

Am I wrong about this?

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#148
In reply to #147

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

11/14/2007 11:36 AM

Agreed. It wouldn't matter if Tom was blind in one eye and sat still - the brightest bit (flame) of the candle is quite blurred anyway. That was why I posed a cylindrical mirror - the astigmatic image would appear behind the mirror laterally, so eye separation and wobbling in your seat wouldn't reveal the problem.

Fyz

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#149
In reply to #147

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

11/14/2007 3:15 PM

Real images are visible without a screen if you can see its rays directly.

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#150
In reply to #149

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

11/14/2007 3:39 PM

Real images are visible without a screen if you can see its rays directly.

Oh, really? How can you see rays of light "directly"? Have you never done this experiment: In a dark room, turn on a flashlight and shine it on the wall. You can see the reflection of the light off the wall, but you cannot see the "beam" carrying it there. Now clap two "dirty" chalk erasers together, scattering tiny particles of chalk dust floating through the air. At once the beam becomes visible, at least as it extends through the cloud of dust which is reflecting and scattering the light.

Unlike a beam, a real image will have a spatial point of convergence where it is in focus. Unless you have some semi-transparent media (allowing light in and out) for that image to project onto you would be unable to see the image clearly. If your eye were perfectly lined up with the "beam" of that image, just as if looking directly into the beam of a flashlight, you might see light from its source, but not a clear image, especially not one that could be recognized as an upside down burning candle!

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#152
In reply to #150

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

11/14/2007 4:14 PM

Have you never looked at an upside-down image through a lens - or at your own upside down image in a convex mirror. Or used prismatic binoculars? Or a high-quality refractive telescope. Those are all real images - images projected into real space between the lens (or mirror) and yourself. You can see them directly, so long as the image lies directly between your eye and the surface of the lens (or mirror) that is producing it.

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#159
In reply to #152

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

11/15/2007 11:39 AM

"...so long as the image lies directly between your eye and the surface of the lens (or mirror) that is producing it."

Yes, exactly, and you are using an objective lens (eyepiece) to focus on that image. This is not the case in the challenge question or the example which I gave. How can you view the candle image directly and without any other device unless you are at the same point as the object (like when you view your own inverted image)?

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#161
In reply to #159

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

11/15/2007 1:26 PM

Borrow a ******* mirror and try it. Place an object about twice the focal length away from the mirror. Stand about three feet further away from the mirror than the object, placing yourself so that you would see the reflection in the mirror if the mirror was flat. Then come back and tell me it doesn't work.

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#151
In reply to #149

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

11/14/2007 4:08 PM

Agreed. So long as you can see the mirror in line with the image, the image real image will remain visible. That is just the same as for a virtual image. But this can be perceived differently than for the virtual image - because you expect a virtual image to vanish behind the frame/surround of the mirror, whereas it can come as a bit of a shock when the real image (in front of the mirror) vanishes when the frame/surround appears behind it.

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#153

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

11/14/2007 4:25 PM

.... was it concave or hollow parabolic......

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#155

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

11/15/2007 12:11 AM

The situation shown below has been commented on at length in post 120, and hence remained unnoticed perhaps. Thanks to STL Engineer's instructions in post 92, if Tom is able to see anything at all in the soot-blackened mirror surface he can reflect on what the images represent (one too many?).

Whether the mirror surface is spherical or cylindrical is immaterial in the elevation view shown.

I think that ALL images seen as REFLECTIONS in any mirror have to be VIRTUAL (by definition?).

I still think the plane mirror solution suggested in post 88 is better than the official one. Someone complained about the missing bell. The missing book must be under it.

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#156
In reply to #155

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

11/15/2007 1:11 AM

ROFL !

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#157
In reply to #155

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

11/15/2007 4:45 AM

Sorry, but that is not what happens at all.

To obtain the positions of the reflections, you could trace pairs of rays of light from points on the object as they reflect from the mirror, and see where a pair of rays cross. If they actually cross after reflection, you have a real image, which you could (if you wish) reflect off a screen, or place a sensitive emulsion to provide a photographic record. Just because you can do this does not mean that you cannot also see this directly - you just have to place your eye in the path of the light and far enough away from the mirror that the focussed image lies between your eye and the mirror (and far enough for you to be able to focus on a real object in the same position).

In order to do this for multiple objects, it is almost certainly simpler to apply the schoolboys' equation, 1/u+1/v=1/f, with f (the focal length) being twice the mirror's radius of curvature. Positive results are behind the mirror (virtual images - light originating at any point on the object is diverging as it leaves he mirror), negative results are in front (light from any point is converging to a focal point as it leaves the mirror). To obtain the sizes, reflect lines off a fixed point (the "centre" of the mirror) to where they meet the plane of the image.

The real images do have some interesting properties - if examined carefully, it can be seen that they are inside out (i.e. the image of the point nearest the mirror is nearest the mirror); but you usually need to be looking for that to notice.

If the explanation doesn't convince, get yourself a magnifying mirror and try it. (But remember that objects that are just a little further away from the mirror than the focus will create real images that are behind your head - and your eyes are only structured to refocus images that are in front of you). The existence of such images is probably the cause of all this confuscucation.

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#158
In reply to #157

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

11/15/2007 9:06 AM

Won't the wick of the candle be on the outside?

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#160
In reply to #158

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

11/15/2007 1:20 PM

Nice thought (ha-ha he-he ho-ho). The front of the flame will be at the back and vice versa - and because flames are transparent you really won't see any difference. The effect is really most visible with solid objects.

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#162
In reply to #157

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

11/16/2007 7:09 PM

"Sorry, but that is not what happens at all....".

Must admit I got taken in by your confident assertions. Finally I had to check the calendar to see whether we are anywhere near the beginning of April. But read on ....

"... Just because you can do this does not mean that you cannot also see this directly - you just have to place your eye in the path of the light and far enough away ..."

I actually got hold of a ******* mirror and rigged up the whole show. For the benefit of all the other suckers out there, here's a report of the proceedings:

The mirror was about 8 cm dia, and I guessed the focal length to be about 80 cm, because that's where the reflection of my eye zooOOMed out and everything got inverted beyond that. I take it the radius of curvature would be about 160 cm.

On lining up assorted objects along or near the axis from 100 to 200 cm, the only IMAGES I could see from about 300 cm away were their inverted reflections BEHIND the mirror, either magnified or shrunk as expected. In the picture shown in post 155, another bell near the first candle would have its image magnified but inverted. (It would also have an 'invisible' real image between the table and Tom!)

This is exactly what I concluded from a ray-tracing procedure, for which I don't have the time or patience to create an illustration here (also because the process of transferring an image from MSWord to MSPaint to CR4 makes it very blurred !).

Part II of the experiment was done with the room darkened, and a candle flame as the 'real' object of interest. It was placed slightly off-axis about 140 cm from the mirror with a shield behind it, and a translucent paper screen in the darkness beyond caught the focused image at around 180 cm. This PROJECTED image could be seen from anywhere in the room, but it vanished when the screen was removed, even when my eye was behind the location. The virtual image of the flame BEHIND the mirror could be viewed from anywhere near the axis.

Adjusting the positions and heights of the mirror, sundry objects and candle was done using an assortment of books, including Old Possum.

I hope my description has been reasonably clear. If anyone repeats it and achieves different results we can discuss why.

I am still of the opinion that we can SEE only VIRTUAL images BEHIND a mirror. Whether images seen THROUGH a lens are virtual or real can form the subject of another controversy! When I look at an object through a magnifying glass, I SEE a VIRTUAL object behind the lens, but it actually produces a REAL image which may even be behind my head, but I can't see it!

"... with f (the focal length) being twice the mirror's radius of curvature ..."

I think you meant to say 'half'. I never got the hang of those 1/v and 1/u formulae because different authors used conflicting sign conventions. Ray tracing made more sense. But I'm out of practice for decades now.

"... Have you never looked at ... your own upside down image in a convex mirror...."

(ref to post 152) No, I haven't! I've only noticed the image shrinking as I got further away.

"... The existence of such images is probably the cause of all this confuscucation."

To that I can only quote:

'Well, of all . . . Things . . . Can it be . . . really! . . . No! . . . Yes! . . .

Ho! Hi!

Oh, my eye!

My sight's unreliable, but I can guess

That the cause of the trouble is Old Deuteronomy!'

=Tee Square=

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#163
In reply to #162

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

11/16/2007 7:39 PM

Would you summarise for the more simple minded of us ? Thank you.

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#164
In reply to #163

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

11/16/2007 7:48 PM

..IF YOU CAN - YOU PATRONISING SO AND SO .Who says I can't be nice at times. If you really want to play hard-ball and discuss this - go for it ............ (you might wan't ot consult my book first). Never mind, lets hear it.......

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#165
In reply to #164

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

11/16/2007 7:55 PM

TeeSquare ? I wouldn't let you loose with a set square ! Bring it on babe ! Neutrino mine. Bring it on you orthoganal.

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#171
In reply to #163

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

11/19/2007 7:13 PM

Hi Kris,

I too have a confession to make (of a rather different sort than the one in post 121). I'm rather hopeless at 'summarising' things as you requested. I always end up making long-winded explanations, but it's not a captive audience so the reader can always exercise the option of ignoring them, and perhaps s/he does most of the time.

It is also a fact that there is a huge gulf of continental magnitude between me and the CR4 'regulars'. Not to mention the cultural divide, and the time warp I inhabit, which should be evident from the archaic expressions strewn around whatever I write. Since I have little contact with the young or computer-savvy generation, I find much of the modern idiom unintelligible.

I have observed that there is a cosy community within CR4 which exchanges a lot of banter and sometimes obscure humour, but I guess that's what keeps the interest alive. Occasional visitors (guests, to which category I belong temperamentally, despite having registered) are liable to find a lot of the off-topic stuff rather disconcerting. (I did see the separate thread about guests posting on CR4, which also went off-topic.)

I won't pretend I understood all the expressions in your posts 164 and 165, but it doesn't matter I guess. However I can't take your phrase "... for the more simple minded of us ..." at face value. I'm pretty certain that all of us who are capable of engaging in this discussion the way it has gone, are anything but simple-minded. Which is not the same as saying we are immune from committing mistakes or holding contrary or even 'wrong' opinions. CR4 is a useful forum precisely for airing these differences, and I'm sure most of us do get some benefit out of the new insights which are thrown up in each thread. For instance I have to admit my ignorance about the nature of real and virtual images in mirrors.

With regard to post 121, the point you made regarding reaching for the back of an envelope, or using traditional methods, touches on a much larger issue which I cannot help but be concerned about. It has to do with taking our increasing dependence on technological conveniences for granted, and being rendered helpless when something doesn't 'work' as expected. But that's a huge subject of a metaphysical sort, very far off-topic and even off-forum. I try to be conscious of the problem, by way of making free-hand sketches for instance, or keeping my slide rule handy, though I seldom use it now.

=TeeSquare=

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#172
In reply to #171

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

11/20/2007 6:05 AM

Hi TeeSquare. Many thanks for the detail. I'm one of those who's typing ability is somewhat poor, hence I post briefly. Also, a lot of my stuff is just gibberish. If somewhat vainer I'd have thought they devised the 'off-topic' button just for me.

Your quite right in that all the idiom, and seemingly 'knowing' jokes that appear are confusing. Usually confusing to the people that make them ! Good old scroll button.

Like yourself I'm much in favour of the 'back of an envelope' design method. One day when there is a power cut, all the computer geeks will be left stranded.

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#166
In reply to #162

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

11/18/2007 6:06 AM

Hi Tee-square
No, it is not April-1st in the UK; and as Chennai is still in the Northern hemisphere, there seems no reason to imagine you would have a different solar tradition. In any case, the topic has caused enough confusion without wilfully adding to it. Additionally, although I would at one time have enjoyed puncturing pomposity, now that I have myself matured(?) into a pompous old *&^%$, the fun in such things has somewhat evaporated.

Now to look at your comments:
First, when looking at your own eye, you will see the image from your eye throughout the mirror surface when the light is reflected straight back at your eye. That means that what you call the zooOOM-out position for your eye is the centre of curvature, not the focus. So your observation suggests 80-cm as the radius of curvature. The focus is where light originating at a very distant point would refocus - or 40-cm.

Now, assuming that this observation is as described, and that all your objects were more than 80-cm from the mirror, we would expect all the images to be be inverted and between the objects themselves and the mirror. And they will be smaller than the original. That leaves me thinking two versions of rather uncharitable thoughts – i.e. that either:
a) you were so certain of yourself that you have not actually performed the experiment as you state, but relied on calculation; or
b) you somehow swapped mirrors for another of twice the focal length, and succumbed to your inbuilt belief that the images were located behind the mirror.
. In case of the second possibility, a good experimental way to check the location of an image is to use a vertical thin rod as the object, and place another vertical thin rod to coincide with the image. If the second rod actually is coincident with the image, the two will remain coincident when you move your eye from side to side. (The reason for choosing thin rods is that it allows you to check images that are behind the mirror as well as those in front – the ends of the visible part of the image will lead into the ends of the unobscured parts of the second rod).

Finally, a link to a some simple ray-tracing diagrams.
(Regarding the descriptions in that link: I wouldn't myself consider the image of an object at the focus to be "non-existent" - but I can see why someone might might choose to describe it in that way).

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#167
In reply to #166

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

11/18/2007 7:21 PM

Hi Fyz,

I do admit to getting rather confused. I did genuinely think your post was a hoax, because I did not manage to view any real image except for the projected one on the translucent screen. Actually I left all my optics behind in school and college ages ago, and even imagined that spherical mirrors was 'simple' schoolboy stuff.

Anyway I was able to find out (from a book) why I failed. The trick of making flowers appear in a seemingly empty vase was described quite convincingly, but it required the object to be well illuminated by a source which is shielded both from the mirror and the observer's eye. I have not tried to reconstruct that.

So I'm now prepared to believe that a real visible image can be made to appear in thin air if the proper procedure is followed. It is possible that my inability to see real images is due to my spectacles which did cause some confusion, and I had to indulge in some donning and doffing or keeping one eye closed.

I still maintain that the distance at which my eye zoomed out was the focus and not the centre of curvature. At C I see a life-size image of my face, albeit inverted, whereas near F the centre of the eye gets magnified indefinitely.

The measurements mentioned were estimated by eye and not measured precisely, but I couldn't be VERY wrong. Particularly with the candle etc. balanced on books on rickety tables, and me stumbling about in near darkness, I got results to my satisfaction, without setting the whole place ablaze. I could find a position for the candle (very roughly 1.5 m distance) such that its image could be captured about a foot further away, but only if the screen was shielded from direct candle illumination.

My post was a fairly honest description of what I tried, and I would appreciate it if anyone else does something on similar lines and reports the results. I don't think I was just imagining I saw only what I expected to see.

I've concluded that we are talking about different things altogether. While you are referring to the real images in front of the mirror (which I failed to see due to certain practical limitations), my images are the ones seen IN the mirror, which is presumably what Tom saw as well. Or would you say that Tom saw images of the candles and himself only in FRONT of the mirror?

This discussion has so far not resolved, at least for me, the issue of HOW MANY IMAGES are formed by a mirror for a single object. Maybe it is a matter of semantics. I can see myself in a convex mirror -- always upright (!) but reduced in size -- but is that an image in the mirror or only on my retina? In a concave mirror I may see myself as upright or inverted, enlarged or reduced, depending on my position, but the book says I form a real image in front of the mirror according to the 1/u 1/v formula. So what the hell is that damned thing staring at me from behind it? Or from a plane mirror for that matter? An optical illusion perhaps, or just semantic 'confuscucation'? Perhaps that's where the bell and the candle enter the picture.

I am STILL seeking enlightenment. So far I have been groping around in dim candle-light. =TeeSquare=

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#168
In reply to #167

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

11/18/2007 9:56 PM

Hi Tee-square,

I agree with most of what you have said.

However, my understanding is as follows:

There is only one image. If the object is between the mirror and the focal point then the image is virtual and formed behind the mirror.

If the object is outside the focal point then the image is always real, inverted and is formed in front of the mirror.

In fact the experimental way of finding the centre of curvature of a concave mirror is to place an object such as a sewing needle stuck into a cork and position it until the inverted image is equal in size and aligning your eye so that the real needle and it's image line up ( I.E. the real needle is pointing up and the inverted image is pointing down. Now you move your eye from left to right and if the needle is positioned at the centre of curvature the image will be formed exactly at the same position as the real needle and you will get as Fyz pointed out what is called "No Parallax". If the two needle points offset from each other as you move your eye from left to right then you are not quite at the centre of curvature and you may need to move the needle either closer or further away to get this point of no parallax. The upshot off this is that although you think the inverted image is virtual and behind the mirror, it is in fact real and formed in front of the mirror. The "No Parallax" is proof of this.

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#169
In reply to #168

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

11/19/2007 4:51 AM

A further thought hit me later today:-

If the object is placed at the centre of curvature, then you should be able to focus on the object and the image simultaneously as they will both be at the same point. I have never tried this and I do stand to be corrected here but you will not be able to do this with a flat or a convex mirror, where the image is formed behind the mirror.

Try it and see...

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Guru

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#170
In reply to #169

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

11/19/2007 6:59 AM

Hi TeeSquare, Maths Physics Maniac

I agree everything that MPM says in postings #168 & #169.

However, he doesn't address the zoom-out position. I think your logic is that an infinite-size image placed at infinity (the image of an object placed at the focus) will always look infinite in size. On that basis, the image of an object placed at the focus will appear zoomed-out wherever you place your eye, and objects at other positions will never appear zoomed-out.

However, a very crude experiment will show that this is not the case. I'm going to work with what I believe to be the mirror you have described. Place your eye at the zoom-out position. Now place a small object 10-cm closer to the mirror than your eye. Now move your eye further from the mirror until the image of that object zooms out. You don't expect this to happen - but it will. For the figures you have provided, that will be when your eye has moved back about 13-cm from its original position.

The reason is that the zoom-out position corresponds to the situation where all the light from a single point on the object arrives at your pupil - you are not focussing an image at all, so it is irrelevant to consider the situation in terms of image size.

Good luck

Fyz

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#173
In reply to #170

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

11/20/2007 6:10 AM

Hi MPM & Fyz,

Thanks for the inputs. A little bit of the fog has cleared, but confusion persists.

First of all I stand corrected regarding the focus and centre of curvature, because I checked the mirror and found that a distant light got focused at about 40 cm. The figure in my earlier post 155 needs substantial correction.

But I'm truly puzzled about what I see when my eye is near the centre. There is obviously a world of difference between the images formed by well-established rules of optics and what the eye or human brain "perceives".

The virtual image in the first figure is as it should be, and I have no problems with that.

When my eye is near the focus I see a right-sized upright image at about the same distance behind the mirror (not illustrated). Should it be at infinity?

When I move away towards the centre of curvature things get really crazy. Prof Optikus would have me believe that a real image (as shown in blue in the second figure) is formed behind my head, or even behind an opaque screen. I am prepared to swallow that as well, because although I am blocking the axis, if the mirror were large enough and suitably corrected for aberrations, the image can indeed be formed and I may be able to view it if I possessed spider-vision. But what I actually "see" is the magnified image shown in red (location indeterminate, but roughly as shown). Up-down or left-right movements are repeated in the same sense by the image.

At the centre of curvature (which I had previously thought was the focus) everything zooms out, though this is where I would have expected a 1:1 inverted image!

Beyond the centre when the images start re-forming, what I "see" is still enlarged but inverted as in the third figure, and the movement directions are reversed. I simply don't see any real image in front of my nose, as I supposedly should. The image I see becomes life-size when my distance is around twice the radius, and gets smaller as I move further away.

There is yet another twist to all this. When I move my head aside, I notice that an entirely different field of view opens up, and I see the inverted reflections of far away objects facing the mirror through an open window. This is true even when I see my self upright as in the second figure! Objects within the room appear quite hazy and difficult to view unless I'm quite far from the mirror.

All this is quite bewildering, and the explanation may have to do with the mechanics/physiology of human (or animal) vision, which is obviously not dealt with in textbooks on optics. I don't dispute the explanation by Fyz, but I'm not quite able to relate it to all the observations as recorded above.

Or am I simply SEEING things? I think there's a shrink down the road, and maybe I need a check-up. But will someone PLEASE bring this thread back on topic and tell us about the candles that Tom saw and where they were located?

=TeeSquare=

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#174
In reply to #173

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

11/20/2007 9:27 AM

Hi TeeSquare

I think we should start by understanding one of the things that is relatively straightforward - why are the (inverted) images of things that are outside the room easy to see, and those that are inside difficult. In this case you are simply looking at an image as if it was an object. The images of things outside the room are close to the focus of the mirror, whereas those inside are significantly in front of the mirror. So the main reason you can se the images from outside clearly is that they are simply far enough away from you to focus.

Next, figure 1. This is incorrect for what is actually happening, although I would not argue with your perception (for which I suggest you look at the next paragraph). The larger image has to be further from the mirror than the object. The magnification of an image depends only on the relative distances of the object and the image from the mirror: writing as an equation, magnification=HimageI/Hobject = Dimage/Dobject, where H represents size, and D represents Distance. If you measure D as distance in front of the mirror for the object, and behind the mirror for the image, a positive sign will represent an erect image and a negative sign an inverted image.

Regarding the perceptions of distance: when you are looking at a face, your brain is trying to sort out conflicting data; this is because faces are very familiar objects, and you know just how far away they need to be to apear a given size. That deeply ingrained knowledge will tend to override the information you are receiving from the focussing action of your eye - particularly if only one of your eyes is able to see the image (stereoscopic effect are more significant in estimating distance than the focussing requirement). Different people will be differently affected in this regard - some people will have a stronger at which the effects of size, focussing and stereoscopy swap dominance. And of course there is no experientia reason for your brain to be able to perceive that an image is behind you.
Hopefully, when you take this into account, that will give reasonable correlation to where you think the objects are located.

Now, to the apparent movement of images: if an image is behind the mirror, when you move your head both image and mirror will be "left behind" the movement of your head, with the mirror falling further behind. Similarly, if ane image is between your eye and the mirror, both will be left behind, but the image will be left further behind. If the image is behind your head, your perception (as you don't know it is behind but only know which direction you lok to see it) is that it will actually overtake your movement.

I think that more or less explains what you have described, except that the perceived image in 2 should be upside down?

Regards

Fyz

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#175
In reply to #174

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

11/21/2007 4:42 AM

Hi Fyz and TeeSquare,

I think I now understand what is happening:-

When you are looking at your own image in a concave mirror, the zoom out point is the centre of curvature, which explains why TeeSquare sees what he sees and his Fig 2 is correct from his own perspective. However, if he is to move back a few metres and look at a candle or other object he will see this object zoom out at the focal point which is half of the centre of curvature. This stands to reason as the focal point is where parallel light rays coming from an object infinitely far away will converge or inversely where a small point will become infinitely large to a viewer at infinity ( Or several metres away should give an approximation of infinity in this case). when you move your own eye in closer to the mirror you are effectively closing in those parallel ray diagrams and again it stands to reason that your own Iris and retina represent a single point source that when placed at the centre of curvature will see all rays of light emanating from that point source strike the concave mirror at all points on it's surface and bounce right back to you retina. Remember basic geometry, all lines drawn from the centre of a circle hit the circle at right angles.

So now, finally to explain what Tom saw:-

TeeSquare's concave mirror was 8cm in diameter with a focal point of 40cm. It is not unreasonable to believe that this concave mirror hung on a wall is maybe a half metre in diameter with a focal point of let's say 1 metre and a centre of curvature of 2 metres. The table is close to the mirror but not close enough that the closer candle has to "blacken it". The closer candle to the mirror might be a half metre away and it's image to Tom who is sitting several metres away appears upright. The second candle is sitting at perhaps the centre of curvature or thereabouts and is inverted. Tom is puzzled to see the closer candle's image right way up and the further away candle's image upside down. He moves ever so slightly to align himself up with the mirror and sees that his own image is also upside down (Because he is further away than the centre of curvature of 2 metres). He is a good student of Physics, remembering everything his teachers taught him and concludes he is looking at a concave mirror :)

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#176
In reply to #174

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

11/21/2007 7:08 PM

Hi Fyz,

Thanks for elaborating on the psychology of vision. I had suspected that something of the sort was at play. So I suspect that in the challenge question what Tom perceived and interpreted could have been rather different from the inferences drawn by Dick or Harry based on their individual prior conditioning.

Maybe we mostly imagine what we see, because we are not aware that the brain is making some convenient background interpretations match the visual clues with past experience. I guess it would take some scientific training plus training and intellectual effort to 'correctly' interpret the significance of inverted or distorted reflections, or contrary movements seen in a mirror. I don't think I'm quite up to it! But you have made a significant contribution to my understanding by stating that an image whose movement "overtakes" that of my head is actually behind me. I faced some difficulty in viewing the images because of confusion created by my spectacle lenses with regard to image distance and sharpness.

Regarding your last sentence (which you have terminated with a tentative question mark), I have again verified that the image I see is right-side-up in Fig. 2. But do I agree that in Fig. 1 it should have been drawn further away. However, as I move my head back through the 40 cm point (which I concede is the focus) the image of my eye keeps enlarging seamlessly until it reaches ZOOM. Only after that does my face get inverted. I hope my brain is not doing a sudden image inversion as I transit the focus! I would have expected 'something' to happen at that point. The apparently life-size image occurs when I am at twice the radius. Like wise in the candle experiment, it would have been near that point, and its projected image a little further away (what I reported as 140 cm and 180 cm in post 162). You may have a good explanation for this.

Anyway it's high time I bowed out of this discussion, as I've spent far too much time on it and even neglected some important work. However it has not been a waste. I'll just look in again to see if there are some fresh insights to be digested, but I don't want it to go the way of boxes and coins. I'll probably show up in some other thread in due course.

Thanks to you and MPM and Kris and others for all the excitement. I would have said the original question was rather carelessly chosen, but it has generated a stimulating discussion!

[PS - The above was composed off-line. Have just seen MPM's subsequent message and will read it later.]

Regards, =TeeSquare=

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#177
In reply to #176

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

11/22/2007 5:38 AM

Thank you - I've now checked this one properly, and I was indeed mistaken .

Rough explanation: as you would expect, upside-down vs right-way-up will depend on the image at the retina - your brain isn't going to do anything strange to this, as this part of the information is self-consistent. Usually, objects that that are the right way up will produce an upside-down image on your retina. With the image behind your head, the lens in your eye produces a real image in front of the retina that remains inverted (not reinverted as would be the case if the original mirror image was in front of you). So what lands on your retina is a blurred inverted image - which is what your brain interprets as the "right way up".

Regards

Fyz

BTW, Tom can see the real image of the inverted candle in front of him. That means that he is far enough away from the mirror for the confusing effects you have been observing to be largely irrelevant - with the possible exception of the the apparent distance and magnification of the reduced-size inverted image of his own head.

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