Chart for Home Brew Spherical Planetarium

Posted by: Ken Miller Jul 31 2007, 08:49 AM
I went back to basic optics 101 (searched the internet), and discovered that a plano-convex lens does basically the same thing if you flip it around, BUT the focal length will be different. The focal length will be longer if you present the flat surface to the light source. The difference in focal lengths increases as the thickness of the lens increases, and it increases as the power of the lens increases. As I think about it, I remember observing this effect before with plano convex lenses. If I had observed more closely, I would have noticed that the focal length had changed when I did my experiment, but it was not shifted by a lot.

Posted by: Ken Miller Jul 31 2007, 11:17 AM
QUOTE(Ron Walker @ Jul 31 2007, 11:04 AM) *
The filters are for star color and can be used with a lens because they don't really effect the optics much. A filter over a pin hole would be a different story and could very easily shift the position of a star kind of like how a fish swimming under water is not really where we see it but is diffracted by the water itself.
Wow! I didn't know that about pinholes and filters. I have another fact to store in my "wish I could remember" memory.

The filters that I looked at seemed to be neutral density filters (shades of grey). It looks like the star brightness is being determined both by aperture and neutral density filtering.

Posted by: Ron Walker Jul 31 2007, 01:11 PM
QUOTE(Ken Miller @ Jul 31 2007, 11:17 AM) *
Wow! I didn't know that about pinholes and filters. I have another fact to store in my "wish I could remember" memory.

The filters that I looked at seemed to be neutral density filters (shades of grey). It looks like the star brightness is being determined both by aperture and neutral density filtering.

It is interesting that they would use both ND filter as well as aperture to control star brightness. Perhaps this is because they are using a focusing lens. But in that case the aperture would control how bright the image was and you would not need the ND filter, huh.gif

The only reason for both is if they only made a couple of aperture sizes, like for1st and 2nd magnitude. Then they would use ND to get the variations within each of the magnitudes.

In the later A3P globe there are many different size holes as well as apparent lens designs. Some are even numbered but the number doesn't appear to have any correlation with the star's magnitude. Like there are several with a 5.5 nomenclature for an obvious 2nd magnitude star.

Someplace in the Spitz archives this information must exists, it's just getting to it.

QUOTE(Ron Walker @ Jul 31 2007, 01:11 PM) *
Someplace in the Spitz archives this information must exists, it's just getting to it.
Boy would that be great if we could get our hands on it.

Posted by: Ron Walker Aug 1 2007, 11:55 AM
QUOTE(Ken Miller @ Jul 31 2007, 02:09 PM) *
from www.nfos.org/degree/opt12/Geometric_Optics_files/thick_lens_ray_tracing.html

The formulas for the power of the lens are:


where: F1=front surface power.
F2=back surface power.
t = thickness at the vertex in meters.
n = index of the material of the lens.


This is for "thick lenses", for which the Model A lenses probably qualify. The curvature of the lens is very small compared to the lens thickness. And my previous testing on these lenses did show a difference in focal length depending on orientation. I can't remember exactly how much, but I think it was a few inches (definitely inches and not feet).

This is interesting though I must say things are getting a bit over my head.

Looking at the diagrams they show parallel light beams (from infinity) entering the lens and then being focused to a point at the obvious focal length of the lens. What if the direction of light was reversed. If we placed a point source of light at the focal length of the lens, I would assume then that the light leaving the lens would then be a "shaft" or light beam the exact diameter of the lens. This would lend me to believe that this beam would be the same diameter at any distance from the lens. Placing an iris over the lens would then limit the diameter of the projected beam or size of the star projected.

With a pin hole we know the light beam emerging from the globe continues to expand in diameter the further out the projection goes. Thus a limit is placed on the size of hole to limit the diameter of the projected star. If indeed the lens works as outlined above the a hole one inch in diameter would remain one inch in diameter no matter how far from the projector the dome was. That projection would however contain all of the light projected from the one inch hole and thus look much brighter then a pin hole that would diverge to a spot one inch in diameter on that size dome.

Now we all understand this and it should work, but we still get actual focused images of the light source on the screen. Why??? Is it because the light source is not an exact point source but a filament that has a dimension?

I think it obvious that all the Spitz projector lenses are set up with the focal length of the lens the exact distance to the light source. This would (if we think of a camera in reverse and the light source as the film) project a focused image of the light source at infinity. The closer to the lens the fuzzier the image would become. This goes totally against the experiments you have made as you get a focus at around six feet. Why?? It doesn't make sense in my mind.

There is another diagram in that source you quoted that shows what appears to be an optical flat. Note the divergence from a point source on the left transitions into a parallel light beam out the other side. This does not compute in my mind as an optical flat would offset an image or point but not change what it looks like.

When an early A3P star ball is converted to an arc lamp, it is said that all of the star lenses have to be replaced with new ones. Why? The light source is at exactly the same point, why should it matter? It the existing lenses project out a focused image of the filament, the arc point should make for some great looking stars as they would be sharp points. Why change the lenses???

From experimentation, the smaller the light source (placing the Spitz wide angle lens over the stinger bulb for instance) the better the projection of all the stars. Progressing to the arc lamp makes for even better stars.

Now I have only had the actually arc bulb on once just to make sure it was all working properly and I must admit that I was so overwhelmed by the star field that I really did not scrutinize the projections from either the pin holes or the lenses. The beauty of it just blew my inquisitive nature away. I do need to make a more intelligent report on the differences of the star projector light sources.

Hopefully that will come soon as I will have a dome of some sort up and running as well as the support structure for the A3P which I have been told will be arriving in a week and a half.

I must admit, I feel like a five year old the week before Christmas.

Posted by: Ron Walker Aug 1 2007, 02:59 PM
QUOTE(Ken Miller @ Aug 1 2007, 01:42 PM) *
Is the dome going to be ready that soon? Is this a temporary dome -- the one that you were making out of fabric? I'm pretty sure your permanent dome is not going to be up in the immediate future. It does sound, as you say, like Christmas. I wish I could be there to see it.

That lens and ray tracing stuff has my head spinning as well. The light source in my projectors is not at the focal point, or it wouldn't focus an image at a non-infinite distance (by the way, the image focuses at about 3 or 4 ft on the Model A). The magnification of the size of light source also increases as light approachs the focal point. I think the light source is actually about an inch or two outside the focal point.

One lens ray tracing tool I like to play with is at: webphysics.davidson.edu/Course_Material/Py230L/optics/lenses.htm

Yes this is the dome. It will probably be a very long while before I can make a permanent one. I just want to be able to actually use some of this stuff and be able to get useful information out of the experiments. The walls of the room are not cutting it any more for me.

That tool is fun and I can get the output of the lens to be a shaft of light. Just not at all sure whet it means as I don't see any information about focal length etc..

I don't understand why Spitz would place the lenses so far from the focal point but I'm sure they had a good reason. Sometimes I think were trying to reinvent the wheel, but it's the only way to really understand how these lenses work.

Gare, on your copper cylinder, how do the stars look projected through both the pin holes and the lenses. Please be extremely detailed in your descriptions as to the size and appearance of the stars. I'm particularly curious as if you can see any resemblance of the filament of the bulb projected onto the dome.