Solar OBSERVATORY
How I fashioned a low-tech setup to record the sun’s movement.
Originally, I just wanted to make a fancy sundial. My idea was that instead of projecting a shadow on the dial face, I would set up a lens and project a bright circular image of the sun instead. Also, I wanted the dial face to be big, so the lens had to have a long focal length. I wanted to follow the sun during the winter months when its path tracks lowest and closest to the horizon, and to have enough accuracy to see the daily change in its altitude as the days got shorter, then longer again starting around December 22.
My house has a south-facing deck, and the roof there is supported by a post, which made for a convenient place to mount the lens. I calculated that a 4-meter focal length would focus the image against the south wall of my house, and its size would be 37 millimeters. Perfect! All I needed was an objective lens with a focal length of 4 meters. Here was problem number one. I invite you to price a 4-meter lens at Newport or Melles Griot; they can cost hundreds of dollars, if you can even find one. The focal length is the problem.
To the rescue came my optometrist, who offered to order me a couple of ophthalmic lens blanks. These are a terrific resource for affordable optics! They are pre-formed to the right focal length, and the optometrist then grinds each one to fit your eyeglass frames. Polycarbonate single-vision lenses are readily available in 70-millimeter diameter and a wide range of focal lengths, and are cheap as dirt.
Ophthalmic lenses are measured in diopters instead of focal length. The rule is:
F (in meters) = 1/D (in diopters) So a 4-meter lens would be 0.25 diopter.
In the catalog, the smallest positive lens was 1 diopter and the smallest negative was –0.75 diopter. Lenses can be combined, and the simple rule is to add the diopters:
D = D1 + D2
F = 1/D = 4 meters
So using these two lenses produced a combined lens with a focal length matching what I needed.
For a lens mount, an ABS plastic electrical conduit fitting turned out to be just right (Figure A). I glued the first lens in place and made a thin spacer to hold the two lenses apart. If you want a different focal length, you could fine-tune this by spacing the lenses a little further. See the Combining Lenses sidebar for that equation.
With the lenses in their mount, I had a rugged unit I could mount on the beam above my deck (Figure B). This only works when the sun is within about 15° of where the lens is pointing. I aimed the lens at the point in the sky where the sun was at high noon, on November 10. This gave me about an hour on each side of noon where the sun’s image would be visible against the wall.
Each day I would go out at noon and record with a pencil mark where the sun was. On some days I recorded its position every 15 minutes as long as it was visible. The pencil marks made a permanent record on the side of my house (sacrifices must be made in the interest of science). This way I could follow its passage as it dipped lower toward the southern horizon and finally, around December 22, began its slow climb back.
There was also an interesting movement of the spot from left to right as the moment of high noon (by the clock) shifted. Solar noon is not always at clock noon, and you can watch this movement as the season progresses. Astronomers have calculated the yearly variation and refer to it as the equation of time.
Not only did my experiments lead to some interesting astronomy, the equation of time, and a better understanding of the Earth’s movement in the solar system, but it was also reassuring to see definite signs that the sun was a little higher each day. When friends came over one sunny day in December, I showed them the pencil marks, and could assure them we won’t have an infinite winter — spring will definitely return. (At this point my friends started referring to “Craig-Henge.”)
Recently we had a chance to observe a rare solar eclipse. It was time to take down the assembly anyway, so it served wonderfully as a solar eclipse viewer. We simply projected the image against my friend’s garage door.
Several people told me that the focused rays would set the house on fire. Not so. The lens has a diameter of 70 millimeters and focal length of 4,000 millimeters. Thus its so-called f-number is 4,000/70 = 57. Photographers will recognize that the f-number determines how bright an image is cast at the focal plane. High numbers mean the image brightness is quite a bit reduced. I found I could comfortably hold my hand at the focal point and feel only mild warmth.
But “dim” is a relative thing. It’s still too bright to look at the image without very dark glasses. And looking through the lens at the sun will definitely burn your eyes! Bad idea: it’s a telescope, for Pete’s sake! 
Image Size
The sun as viewed from planet Earth measures approximately 32 minutes of arc, or 32/60 of a degree. It’s effectively at infinity as far as our lenses are concerned, so rays coming from the sun are focused right at the focal length of the lens, F. The size of the image is given by the equation:
H = F × tan Θ
For Θ = 32/60°, F = 4,000mm, H = 37mm.
Combining Lenses
Combining 2 lenses with diopters D1 and D2, and spaced a distance (d) apart gives a combined effect of a lens of D diopters where:
D = D1 + D2 — D1D2d
Or if you prefer focal lengths:
Optical Quality
The lens we have constructed here is good enough to image a bright spot, but it’s not of optical quality. You can’t see sunspots. Each lens introduces its own distortion, and they’re additive.
If you want a really good image, for a telescope you'd use an achromatic objective lens made with two elements of different types of glass. In a good objective lens the curvatures of the four surfaces are chosen:
1. To minimize distortion
2. To minimize spherical and coma aberrations
3. To make all wavelengths focus at the same place (reduce chromatic aberrations)
A top-quality 70mm achromatic lens like this would be difficult to make and cost well into hundreds of dollars. A 160mm lens for astronomy would be in the thousands! That’s one reason most amateur telescope makers choose to build reflectors instead of refractor telescopes.
Craig Van Horn was a mechanical engineer doing propulsion R&D right when people started using the phrase “it’s not rocket science” — and for him, it was rocket science.