Last night I was feeling impatient to know my progress, so performed two basic tests on my mirror. The first test is described by Scientific American’s Amateur Telescope Making as the “Pencil Test”, but has many other names depending on the item of stationery used. This test determines how close the mirror is to a spherical surface by showing visually how close the mirror and tool are to being totally in contact. It’s very easy: I took a permanent marker and drew a grid pattern all over the tool. I then threw in a bit of #120 grit, sprayed it down with soapy water, and proceeded with grinding one ‘wet’. By noting where the markings remain and where the tool is scraped clean, you can immediately see whether your previous grinding has achieved a spherical surface or not. My result: Tool was completely clean. This does NOT mean that I have a perfect sphere yet, though. First of all, I’m still working with quite coarse grit – the surface could deviate from a sphere by at least as much as the width of a single piece of the grit, and secondly I used a lot of grit so the wet lasted a long time. I could probably have achieved a more accurate result by stopping long before the wet ended, before the grinding action had had a chance to clean the entire surface. Nevertheless, I at least know that I’m close to the right shape.
The second test was to determine the current focal length of my mirror. Measuring the sagitta (the depth of the curve) is a fairly reliable method, provided you know the exact radius of the mirror and can measure the depth accurate to about 10 microns. However, the process of bevelling my mirror has led to the radius being reduced by an amount that I can’t easily measure. So instead, I used a very crude optical test described in Amateur Telescope Making as the ‘Spit Test’, and is a quick way to find the focal length. It works like so: I fashioned a stand for the mirror which allowed it to be propped up on its edge at a comfortable height, against the far wall of my garage. I put a mark on the floor coinciding with the front surface of the mirror (You’re supposed to use a plumb-line, I just squinted with one eye and made a best guess). I then wet the mirror surface with a spray bottle and quickly took a small penlight torch, held it next to my eye, and shone it at the mirror. It took a bit of moving around, but eventually I found the point where I could see the light from the torch reflecting back at me. I then bobbed up and down and observed that the light in the mirror moved in the same direction. I repeated this step a few times, moving further and further from the mirror till I reached a point where the image moved in the opposite direction to my head. After a few back-and-forth motions, I found the centre-point, when the reflection does not move at all but just brightens or dims. Carefully holding steady at that point, I let a drop of spit dribble onto the floor. The spit simplyserves as an easy way to mark the position of your head, without taking your eye off the image. Then I took my tape measure and found the distance from the spit to the mark I’d made earlier. That distance equals the radius of curvature of the spherical surface, and came to about 282 centimeters. Basic optics tells us that the focal length of a spherical mirror is exactly half the mirror’s radius of curvature, meaning that my mirror has a focal length of about 141 cm. The focal ratio equals the focal length divided by the diameter of the mirror (15.5 cm), giving me a f/ratio of about 9.1. Since I want my mirror to be f/7, I still have a fair bit of grinding to do to deepen that curve. I have no idea how long this will take.