Photographing a solar eclipse is not difficult, but you must be careful because the sun can quickly cause eye-injury and damage to your equipment. Even if only a small slice of the sun is showing, a correct solar filter in front of the lens or a projection methods must be used. The only time that the sun can be safely viewed without protection is during "totality"; even the ring of an annular eclipse can be unsafe.
The sun and moon are each about one half degree in apparent diameter so their images are very small with a normal 50mm SLR lens or a "point and shoot" camera. Filling the small dimension of a 35mm slide requires a focal length of almost 3000mm. Short-tube refractors with their focal ratios of f5 to f7 and fixed focal lengths of 400 to 500mm are very good for full-sphere shots, and to get more detail their focal lengths can be increased using a teleconverter (TC). For example, with a refractor acting as a 500mm f5 lens, a 1.4x TC will make it 700mm f7.1, a 2x TC will make it 1000mm f10, etc. The exposure is controlled by varying the shutter speed. To reduce vibrations, the telescope and camera should be mounted on a solid tripod with the weight centred as much as possible. A cable release should be used, the camera mirror may be locked up and under really bad conditions anti-vibration pads can be placed under the tripod feet. Finally, unless a tracking mount is used, the exposure cannot be long. For example, about one second is the maximum exposure length for a focal length of 800mm because any longer will result in image trailing.
Lunar eclipses and the partial phases of solar eclipses are easy to photograph because they take place over hours, but totality lasts for only minutes so organization is needed.

So many things can be photographed in such a very short time! There are "Bailey's beads" and "diamond rings" at 2nd and 3rd contacts and the chromosphere, prominences and the corona during totality. At the same time, many other interesting things are happening such as temperature changes, shadow bands, approaching and departing shadows, reactions of local wildlife and other people, and the feeling of awe that can leave you just standing and looking, or laughing, or cheering. The most important thing is to observe and experience totality. Photography should be only a small part of it and every effort should be to limit the time spent fiddling with a camera.
The following example is a fairly ambitious shooting schedule, like the one used to take the eclipse pictures seen in these pages, with ISO 400 film, a manual focus SLR, a 400mm short-tube refractor (without the finder scope) and a 2x TC to give a final focal length of 800mm. Photograph the partial phases using a solar filter or a projection method. If necessary, change the film so that it doesn't run out during totality. At second contact, having recently focussed, remove the filter and, without looking through the camera's finder, shoot Bailey's beads and the diamond ring. If the partial phases were shot through a solar filter, such as mylar which gives a blue image, refocus on the red prominences. Now, shoot the chromosphere and prominences, and a corona series within about a minute. The corona series, running from your fastest shutter speed down to one second, can be manipulated and combined digitally at a later date. Finally, after presetting the camera speed for the 3rd contact diamond ring, "look and experience" until it is time to release the shutter for that gem of a shot!

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