A Large Pinhole Viewer

The sun subtends an angle of about 0.53 degrees in the sky, which means that its image projected through a pinhole is about 0.00925x the distance from the pinhole to the projection screen (you can do this math yourself with a little trigonometry: if `d` is the distance, `s` is the image size, and `theta` is the angle, then `1/2 s / d = tan(1/2 theta)`, so `s/d = 2 tan (1/2 theta)`). This is why a pinhole viewer with a length of 1m shows an image of about 1cm. This is certainly a visible image, but not very impressive and not large enough for many people to view comfortably.

(Yes, there's an image of the Sun in the shadow on the righthand image: it's quite faint but if you look carefully you'll find it. A darker target area would improve the contrast.)

What if we want an image 30cm (about 1 foot) across? Working backwards, 30cm / 0.00925 = 32.43m, which is a bit over 100ft. That's big. If at this point you're envisioning a 100-foot cardboard tube with a pinhole at the end, supported by a crane so it points at the Sun, read on: there's a better way. Turns out we can skip the tube: all that really matters is that the image winds up projected into a dark place for easy viewing. And we don't even have to put the pinhole directly between the Sun and the viewing location. We can do the same trick with a pinhole mirror, and we can site that at ground level. The large brains at Cambridge did this for the 2004 Venus transit of the sun and got some beautiful imagery.

What we still do need is (1) a dark room, (2) with a nearby open door or window (we'll need to think a bit about letting in the light from the viewer without letting in so much ambient light that we spoil the image), (3) pointing into an open area at least 100 feet long, (4) which will be able to view the sun during the total eclipse on April 8, 2024. Turns out I have relatives who satisfy every one of these conditions. So we're in good shape: just get a mirror, put some electrical tape over most of it, wait seven-plus years, and then reflect the eclipse into the dark room.

Alas, it isn't quite that simple. According to NASA, the eclipse is expected to last 2 hours, 39 minutes and 20.3 seconds, during which time the Sun will cross around 40 degrees of the sky. If we focus the image at the beginning of the eclipse, the image will drift as the Sun moves. The drift rate is around 1 solar diameter every 2 minutes (the math: 360 degrees over 24 hours is 15 degrees/hour or 0.25 degrees/minute, and the Sun is 0.53 degrees wide). We need to have the mirror track the Sun to keep the image centered. With my 1m pinhole viewer I just moved it manually, but this is impractical for a 30m focal length.

Next week, we consider how to build an automated mirror pointer...