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They are used for macrophotography. The bellows are used for focusing closer than one can get with just the lens' own movement, or with extension tubes. It allows for reproduction ratios of up to 3:1. Also, the bellows are used for coping transparencies, or creating internegatives, with the transparency copy holder.
I bet the "bellows" is the professional lens hood which fits on the front end of the lens (the cylinder with glass circles at each end [sorry, couldn't resist]). Real bellows go between the camera body and the lens.
If it is the prof lens hood, it is designed to keep unwanted light rays entering the lens and messing up the image. It should clip onto the front of the lens.
If you are shooting portraiture, then you are probably going to find the extension tubes of more value to the kind of shooting you do. The shorter tubes (8 or 16, or the older 10) will allow you to get closer to the subject. The longer ones may get you too close. A short telephoto lens may give you more working distance with the same "crop" while also compressing the perspective. The tubes are cheaper than a new lens, but a second lens adds more flexibility.
Either the old or auto extension bellows will work with your 500C/M. Many prefer the old style to the auto, because the rail extends underneath the camera, instead of towards the subject. The old style requires a double cable release.
The bellows and tubes are complements of each other. Unless you are using the 135mm lens, which requires the bellows or the variable tube, I suspect that what you are looking for is a short tube to get a little closer, or if budget allows, a 120mm, or 150mm lens to get that closer "crop". Unless the subject is inanimate, getting within half a meter gets to be uncomfortable for most living subjects. Now, if you are looking to shoot a subject's eye, then maybe the bellows is what you are looking for.
I don't think that an extension tube will be good for portraiture, unless you want to photograph just an eye or the tip of one's nose. For portraiture what you need is a portrait lens, which would be the 120mm, 150mm 160mm or even the 180mm Zeiss lenses. If you can't spring for one of these lenses, then a Hasselblad teleconverter (also not cheap) will convert your 800mm "normal" lens into a portrait lens.
for your opinion about extension tube for portraiture, I'm not very sure that you will not need it. With the 180mm, because I used this lens, you have 1.50m, and you can't have a small part of one person, if you speak about portraiture.
You can see my picture with the 180mm and the ext. tube 16 : http://www.hasselbladinfo.com/photos/details.php?image_id=252
I think that you can need it.
If you read my post carefully, I was trying to steer Karen towards considering a short telephoto, but since the original question was about the bellows, I was trying to be complete in my answer regarding their use and included the extension tubes, since they seem to be make more sense for the kinds of images Karen studio seems to shoot.
Some photographers actually like using the 250mm with tubes to get those head shots. It gives them plenty of room to work with, but gets close enough to fit the head and shoulders into the field of view. And you get the compressed perspective of the longer lens. The 80mm or shorter lens very close would exaggerate perspective, that is, make the nose look larger, because it is so much closer to the lens.
We should probably let Karen digest this information and ask follow up questions based on these suggestions. It is possible that she may be interested in copying her transparencies/negatives... we can not be sure as of yet.
Thank you everyone.
Taras, my goal is to buy the 120mm/macro lens, which should suit my needs. I asked about the bellows as a temporary fix to my limited 80mm lens. Sometimes, I should like to photograph an eye/cheek bone, focusing primarily on one eyelash, or the curved lip of a cali lilly, or the tiny hand of a small child lying on their mother's swollen, pregnant stomach... hence the bellows question.
I haven't any transparencies.
Laurent, that's a beautiful image.
With the bellows and 80mm lens, the length of subject side ranges from 2.75" to 0.85" (approx.).
With the 55 tube + the 10 tube and 80mm lens, the length of subject side ranges from 2.75" to 2.3" (approx.).
With the 55 tube and 80mm lens, the length of subject side ranges from 3.2" to 2.75" (approx.).
With the 21 tube + the 10 tube and 80mm lens, the length of subject side ranges from 5.8" to 4.25" (approx.).
With the 21 tube and 80mm lens, the length of subject side ranges from 8.5" to 6" (approx.).
With the 10 tube and 80mm lens, the length of subject side ranges from 18" to 9" (approx.).
With the 80mm lens alone, the length of subject side ranges down to 19" (approx.).
The old 10 an 21 tubes can give an inexpensive (relatively) way of getting a subject of down to 7 inches to fill your composition singly, and combined can get you down to a subject of about 4.25". The 55 tube may used alone or with the 10 tube to get the kinds of images you mention in your post. The bellows sounds like overkill for these kinds of images, but you may get creative going smaller. I would recommend one tube to start and see what kinds of images you can create with it, and then go from there.
The numbers above are my approximations from the chart in the old Close-up Photography theme booklets published by Hasselblad in the '70s.
I hope this helps as a rough guide. The above are not distances, but subject size. Plus I mention just the older tubes, because they can be acquired for a lower price than the newer ones. One can extrapolate where the 8, 16, 32, and 56 fit in based on the above guidelines.