Re: diameter of reflected sun image

[John Carmichael]

Hi Chris (& others)

What a nice easy to use formula! I was wondering why you used a rectangular
mirror instead of a circular or square one?

I've noticed that the eliptical sun spot, of course, has its major long axis
oriented in a north south direction on the ceiling at apparent noon. Do you
think that it would be possible to make the spot more circular by using a
rectangular mirror who's long side is oriented in an east west direction?
Shouldn't this compensate for some of the north/south stretch?

(I must go purchase a larger mirror and experiment with masking tape to test
this!  I will also test your idea of two close mirrors.  Also, I'm thinking
the fuzzy region on the circumference might be sharpened a little if there
was a thin frame around the mirror because the glass edge of the mirror
might be throwing light rays off in several durections.)

What do you think

John

John L. Carmichael Jr.
Sundial Sculptures
925 E. Foothills Dr.
Tucson Arizona 85718
USA

Tel: 520-696-1709
Email: [EMAIL PROTECTED]
Website: 
- Original Message -
From: "Chris Lusby Taylor" <[EMAIL PROTECTED]>
To: "Dave Bell" <[EMAIL PROTECTED]>
Cc: "John Carmichael" <[EMAIL PROTECTED]>;

Sent: Tuesday, August 14, 2001 10:04 AM
Subject: Re: diameter of reflected sun image


> Dave Bell wrote:
>
> > On Mon, 13 Aug 2001, John Carmichael wrote:
> >
> > > Knowing the apparent diameter of the sun, the size of the mirror, and
> > > the distance from the mirror to the ceiling, how could I calculate the
> > > diameter of the sun spot?
> >
> > Take the limiting case, of a (nearly) zero-diameter mirror. This is
> > exactly the same as a pinhole "lens", which casts an image no smaller
than
> > the angular diameter of the Sun, or 8.7 milliradians. (*Much* easier to
> > work in than degrees!) If the spot on the ceiling is an average of 10
> > feet, or 120 inches from the mirror, the spot will be at least 1.04 inch
> > diameter. Diffraction from the edges of the mirror will make the spot
> > larger (and fuzzier), and a larger mirror will cast a larger image.
> > Without modelling it (or thinking too hard), I'd also guess that the
image
> > spot would be the diameter of the mirror, PLUS the above figure derived
> > from the 8.7 milliradian cone angle. So, a 1 inch mirror should make a 2
> > inch spot at 10 feet...
> > 
>
> Funnily enough, my brother was just asking why the spots produced by my
mirror
> dial are apparently round when the mirrors are 1cm x 5cm. As Dave Bell
says,
> the truth is that the spots are rounded-cornered rectangles with overall
> dimensions of (1cm + 0.0087 x Distance) x (5cm + 0.0087 x Distance) and
corner
> radius of 0.0044 x Distance. When mirror-to-screen distance is 10M, this
gives
> 9.7 x 13.7 cm, which looks near enough circular.
>
> The optimum thickness of a string gnomon is such that the umbra has zero
> width. If you use a mirror of equivalent width (0.0087 x Distance) only
the
> very centre of the spot is fully illuminated, but to the human eye this
isn't
> obvious, and in my experience a narrower mirror is better as the spot is
quite
> bright enough. Judging the centre of the spot is harder than judging the
> edges. Maybe the ultimate would be two or more mirrors spaced so that
their
> spots just touch. Masking a large enough mirror to leave two small circles
> would be worth trying.
>
> Chris Lusby Taylor
> Newbury, Engalnd
> 51.4N 1.3W
>
>

Re: diameter of reflected sun image

[Chris Lusby Taylor]

Dave Bell wrote:

> On Mon, 13 Aug 2001, John Carmichael wrote:
>
> > Knowing the apparent diameter of the sun, the size of the mirror, and
> > the distance from the mirror to the ceiling, how could I calculate the
> > diameter of the sun spot?
>
> Take the limiting case, of a (nearly) zero-diameter mirror. This is
> exactly the same as a pinhole "lens", which casts an image no smaller than
> the angular diameter of the Sun, or 8.7 milliradians. (*Much* easier to
> work in than degrees!) If the spot on the ceiling is an average of 10
> feet, or 120 inches from the mirror, the spot will be at least 1.04 inch
> diameter. Diffraction from the edges of the mirror will make the spot
> larger (and fuzzier), and a larger mirror will cast a larger image.
> Without modelling it (or thinking too hard), I'd also guess that the image
> spot would be the diameter of the mirror, PLUS the above figure derived
> from the 8.7 milliradian cone angle. So, a 1 inch mirror should make a 2
> inch spot at 10 feet...
> 

Funnily enough, my brother was just asking why the spots produced by my mirror
dial are apparently round when the mirrors are 1cm x 5cm. As Dave Bell says,
the truth is that the spots are rounded-cornered rectangles with overall
dimensions of (1cm + 0.0087 x Distance) x (5cm + 0.0087 x Distance) and corner
radius of 0.0044 x Distance. When mirror-to-screen distance is 10M, this gives
9.7 x 13.7 cm, which looks near enough circular.

The optimum thickness of a string gnomon is such that the umbra has zero
width. If you use a mirror of equivalent width (0.0087 x Distance) only the
very centre of the spot is fully illuminated, but to the human eye this isn't
obvious, and in my experience a narrower mirror is better as the spot is quite
bright enough. Judging the centre of the spot is harder than judging the
edges. Maybe the ultimate would be two or more mirrors spaced so that their
spots just touch. Masking a large enough mirror to leave two small circles
would be worth trying.

Chris Lusby Taylor
Newbury, Engalnd
51.4N 1.3W

AW: diameter of reflected sun image

[Arthur Carlson]

The 
classical experiment using a mirror to detect minute rotations is not by 
Michelson and Morley, who used an interferometer, but by Cavendish, who measured 
the universal gravitaional constant in the lab.  But the technique has been 
used often.
 
--Art 
Carlson

  -Ursprüngliche Nachricht-Von: 
  [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]Im 
  Auftrag von John CarmichaelGesendet: Tuesday, August 14, 2001 
  4:15 PMAn: [EMAIL PROTECTED]Cc: 
  sundial@rrz.uni-koeln.deBetreff: Re: diameter of reflected sun 
  image
  Hi Fritz
   
  Good to hear from you!  What an interesting 
  story.  I seem to remember an experiment by Michaelson-Morley at the turn 
  of the last century where they used mirrors to amplify the small movements in 
  light.  (I think they were trying to prove the the old theory that 
  Einstein later disproved that light traveled through an "either" and that 
  its speed changed).

Re: diameter of reflected sun image

[John Carmichael]

Hi Fritz
 
Good to hear from you!  What an interesting 
story.  I seem to remember an experiment by Michaelson-Morley at the turn 
of the last century where they used mirrors to amplify the small movements in 
light.  (I think they were trying to prove the the old theory that Einstein 
later disproved that light traveled through an "either" and that its speed 
changed).
 
John
 
John L. Carmichael Jr.Sundial Sculptures925 E. Foothills 
Dr.Tucson Arizona 85718USA
 
Tel: 520-696-1709Email: [EMAIL PROTECTED]Website: 


  - Original Message - 
  From: 
  Fritz Stumpges 
  To: John Carmichael 
  Sent: Tuesday, August 14, 2001 6:10 
  AM
  Subject: RE: diameter of reflected sun 
  image
  
  Hi 
  John,
   
  Back 
  in High School, about 1963, my neighbor and friend Rick Kidder made and 
  interesting  radio for his science project.  (Mine generated 
  hydrogen and oxygen, combined them in a strong pipe at the 2x1 ratio and used 
  a glow plug to make the explosion and water!)  His project used a mono 
  radio with the cone removed from the central magnet of the speaker.  He 
  mounted a wire straight off it to the top of a small mirror, which could 
  pivot.  He then used a small light source which reflected off of the 
  mirror to a photo/electric cell to create a signal for another radio which 
  produced the final sound.  The light source reflected off of the 
  vibrating mirror and so attenuated the light intensity at the photo cell just 
  perfectly to duplicate the original sound!  You could place your hand in 
  front of the light and stop the sound or block some and make it fade 
  etc.  It was fun!  He has since been a JR High School science 
  teacher and I, a mechanical Engr.; fun beginnings!  

Re: Sundial at Montegufoni, Tuscany

[fer j. de vries]

Steve,

This dial shows Italian hours.
The numbers should read 101319 and then it is correct.
The diagonal line across the dial is the equinox line.
The 12 hourline, the equinox line and the horizon line intersect into one
point which is correct.

Best wishes, Fer.

Fer J. de Vries
[EMAIL PROTECTED]
http://www.iae.nl/users/ferdv/
Eindhoven, Netherlands
lat.  51:30 N  long.  5:30 E

- Original Message -
From: Steve Lelievre <[EMAIL PROTECTED]>
To: Sundial mailing list 
Sent: Tuesday, August 14, 2001 1:41 AM
Subject: Sundial at Montegufoni, Tuscany


> Hi,
>
> A friend has sent me a couple of pictures of a sundial at Montegufoni in
> Tuscany, and has asked me how it works. I can't figure it out fully.
>
> On the face of it, we seem to have a fairly ordinary vertical decliner
using
> a nodus, but we don't understand the hour numbering. They don't seem to be
> modern, and I can't make sense of them as Italian Hours either. The
pictures
> were taken at 8 am (during daylight saving time). Note that they go
> 16...13...19.
>
> Also, what is the diagonal line cutting across the first picture?
>
> Thanks, Steve
>
>
http://www3.ns.sympatico.ca/dave.chapman/Sundials/European%20Sundials/image/
> 1.jpg
>
http://www3.ns.sympatico.ca/dave.chapman/Sundials/European%20Sundials/image/
> 2.jpg
>
>
>
>
>

Re: Request for help - analemmatic dial

[Willy Leenders]

A specialist in analemmatic sundials is Frans Maes.
You can find his 'analemmatic extra info' on
http://www.biol.rug.nl/maes/zonnewijzers/welcome-e.htm

Willy Leenders

Robert Terwilliger wrote:

> Hi Dialists,
>
> Can anybody in the Philadelphia area help this lady?
>
> Hi Bob -
>
> I work for the Pennsylvania Horticultural Society and we have a
> community project where we are hoping to create an analemmatic dial. We
> would like the child's shadow to show the time.  Could you be of any
> assistance in helping me find someone to lay this out?  We are located
> in Philadelphia.
>
> Any help would be appreciated.
>
> Chris Howse
> 215-988-8875
> [EMAIL PROTECTED]

Re: diameter of reflected sun image

[Dave Bell]

On Mon, 13 Aug 2001, John Carmichael wrote:

> Knowing the apparent diameter of the sun, the size of the mirror, and
> the distance from the mirror to the ceiling, how could I calculate the
> diameter of the sun spot?

Take the limiting case, of a (nearly) zero-diameter mirror. This is
exactly the same as a pinhole "lens", which casts an image no smaller than
the angular diameter of the Sun, or 8.7 milliradians. (*Much* easier to
work in than degrees!) If the spot on the ceiling is an average of 10
feet, or 120 inches from the mirror, the spot will be at least 1.04 inch
diameter. Diffraction from the edges of the mirror will make the spot
larger (and fuzzier), and a larger mirror will cast a larger image.
Without modelling it (or thinking too hard), I'd also guess that the image
spot would be the diameter of the mirror, PLUS the above figure derived
from the 8.7 milliradian cone angle. So, a 1 inch mirror should make a 2
inch spot at 10 feet...
 
> p.s. Something very interesting also happens to the reflected sun
> spot.  It is extremely sensitive to the slightest vibrations. I put
> the mirror on my workbench next to the window and had the stereo
> playing soft music, and the sunspot danced vibrated with the music in
> perfect sinc with the sound level meter on the stereo!  It also
> shimmers when I walk across the floor.  Who would have that a sundial
> could be a siesmometer?

An effect long taken advantage of in making precise measurements! A tiny
torsion movement on a mirror will move a light spot (laser, today) a long
way, on a scale across a lab. I'd suggest experimenting with vibration
damping mounts, for your friend's reflection dial!

Dave

Re: diameter of reflected sun image

[Brooke Clarke]

Hello John:
A friend who does optical design pointed out that a pin hole can act
as a lens.
At one time there was an "F100" school of photography.
The idea is that a hole, flat piece of glass or a mirror operated at
f # 100 or higher acts as a lens.
The f# = (diameter of the optic) / (distance from the optic to the
object).
A fast camera lens like f 1.2 means that the lens is almost as big
as it's focal length.
A stopped down lens like f22 is in focus almost everywhere.
In my case it was a piece of aluminum with a hole of about 5/8" placed
at the bottom of a skylight up about 20 feet.
By using a watch that was set by WWV and a template with a number of
ellipses made on white paper I tracked the ellipse until the noon alarm
went off then drove a brass tack into the wood floor.  It took a few
years but the result was a very accurate noon mark.
Have Fun,
Brooke Clarke
http://www.pacificsites.com/~brooke/Sundial.shtml
John Carmichael wrote:

Hello
all, A friend of mine
wants a reflected ceiling sundial and asked me to build it.  We've
been discussing how large the reflected spot of sunlight should be so that
it both artisticly pleasing, easily visible and precise.  A large
spot is easily visible but lacks precision. A small spot is precise , but
hard to see. At the
NASS Hartford meeting, Fred gave us all a little one centimeter square
mirror to play around with.  At the time, I thought that this was
awfully small and that its reflected sun spot would be too small to be
seen easily on a big ceiling. But after experimenting, I noticed that the
spot spreads out and gets bigger with greater distances between the mirror
and the ceiling. (This, of course, must be due to the apparent diameter
of the sun's disk in the sky).  Also, while the reflected sun spot
is shaped like the square mirror at close range, it transforms into an
elipse at larger distances. Knowing
the apparent diameter of the sun, the size of the mirror, and the distance
from the mirror to the ceiling, how could I calculate the diameter of the
sun spot? (I realize
that since the reflected sun spot is an elipse, that it would have two
diameters: the major & minor axis who's length would also depend on
the reflected angle, so to make this problem easier so that we are dealing
with a circle instead of an elipse, let's assume that the mirror is almost
perpendicular to the suns rays and that it reflects a circular sunspot
back towards a projection screen located right next to the sun.) Thanks
mucho John p.s.
Something very interesting also happens to the reflected sun spot. 
It is extremely sensitive to the slightest vibrations. I put the mirror
on my workbench next to the window and had the stereo playing soft music,
and the sunspot danced vibrated with the music in perfect sinc with the
sound level meter on the stereo!  It also shimmers when I walk across
the floor.  Who would have that a sundial could be a siesmometer? John
L. Carmichael Jr.
Sundial Sculptures
925 E. Foothills Dr.
Tucson Arizona 85718
USA Tel:
520-696-1709
Email: [EMAIL PROTECTED]
Website: