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Old 2007-09-14, 15:13   #1
mfgoode
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Question Projected Pictures.



When a screen is placed 10 feet from a projector, the picture occupies 10 sq.ft.

How large will the picture be when the projector is 15 feet from the screen?

Mally
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Old 2007-09-14, 15:32   #2
Wacky
 
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How about

"10 sq ft" because that is the size of the screen.

or

There will be no picture at all because the power cord isn't long enough to reach the mains.


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Old 2007-09-14, 15:45   #3
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15ft :)
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Old 2007-09-14, 17:16   #4
Mr. P-1
 
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22.5 sq. feet.
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Old 2007-09-14, 23:12   #5
Orgasmic Troll
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Quote:
Originally Posted by Mr. P-1 View Post
22.5 sq. feet.
ditto
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Old 2007-09-15, 04:09   #6
retina
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2.0903184 m^2
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Old 2007-09-15, 07:22   #7
mfgoode
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Thumbs up Tricky solutions.

Quote:
Originally Posted by victor View Post
15ft :)


Well Victor, the others were right including Wacky with his lateral thinking.

Retina gave a tricky conversion from sq. ft to sq. metres.

Mr. P-1 and OT were on the dot too.

To be honest I was bowled over too !

You see, you cannot compare linear feet with square feet.

One has to square the linear feet into square feet.

Thus 10^2 = 100 sq.ft.

15^2 =225 sq.ft.

Then set up the proportion

10 : 100 = x : 225

Thus x = 22.5 sq.ft.

Hence the picture will have an area of 22.5 sq.ft. when the projector is 15 ft
from the screen.

Mally
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Old 2007-09-15, 07:57   #8
retina
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Quote:
Originally Posted by mfgoode
To be honest I was bowled over too !
I am amazed how this simple algebra would bowl you over and yet you say you managed to solve Beals conjecture! &
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Old 2007-09-15, 08:18   #9
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Note that "10 sq.ft." <> "10 ft square"
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Old 2007-09-15, 08:33   #10
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Treat the projector as a simple convex lens,
and take the distance of the screen to be measured from the
optical centre of this lens.
If we assume the images are accurately focussed, then we
find that the object slide/film is closer to the lens for an
image distance of 15 feet. So the angle subtended is larger
in the second case giving a larger image than you have
all been assuming.

David

Last fiddled with by davieddy on 2007-09-15 at 08:38
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Old 2007-09-15, 10:40   #11
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Quote:
Originally Posted by davieddy View Post
Note that "10 sq.ft." <> "10 ft square"
Haha, now I see why my answer was incorrect!

I thought the image was fitting a 10 ft square screen :)

Thank you David!

If 10ft away from the beamer the image occupies 10ft x 10ft, 15ft away the image is 15ft x 15ft big.
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