Arriving at 1:1 with 3X

Q1: Can anyone tell me how, what calculations are made to arrive at the statement: If you stick a 55mm in front of a 3X Tele-C you get 1:1.

Does this then become a true Macro???

Q2: What is the effect of placing a zoom lense on a bellows? Would the results be different than placing a 55mm lense on bellows? And, what's the difference in reversing the 55mm when compared to all the above.

Sometimes my mind wonders because of the lack of experience and hope that some of you can put things in perspective in simple terms and in one place.

Thanks

The simple answer is this:
to get 1:1 the image on the sensor/film has to be equal in size to the real life object you are photographing.
The math in photographic terms is too hard for a person like me to explain, I'll leave that to others, but suffice it to say that 50mm + 3x ext is too general...the min focus on various 50mm lenses could vary greatly, and that would be a factor in reproducing size ratios.
the optical results of lens and converter combos can oft be disapointing.
many reasons for that including flatness of feild and loss of sharpness. (enlarger lenses are optimin for flatness of feild)
not to mention dark viewfinders.
don't let thah stop you from trying though..experimentation is fun and you never know...every tried and true tecnique I use was once somebodies experiment...
Zooms are a blast...you get three ways to focus...focus ring, zoom ring, and moving camera back and forth (bellows extension)....
the math is complicated, but the 1:1 result is not the only goal...there's image quality, and useability, to factor into the equation.

You can use 50mm lenses with close up devices, bellows, etc., and get away with it because they are computed in a way that tolerates a considerable amount of abuse. The f2 and f1.7 versions are best for this.

Try the same on a zoom and you will likely be disappointed, because the comnpromises in the zoom design will soon begin to show in terms of image quality.

However, it is true that any 50mm lens is a 50mm lens, and a zoom set at 50mm will have the same field of view, etc. as any other 50mm lens.

50mm lenses and especially zooms are computed to be best at longer distances, for general photography. Macro lenses are computed to be optimised at very close distances, and also to have a flat field so that if you were to photograph a document it would all be in focus. Try a zoom and curvature of field would mean you couldn't get the centre and edge of the document in focus at the same time.

For a good overview of lenses, try The Lens Book by Roger Hicks and Frances Schultz (David & Charles, ISBN 0 7153 0149 7) It's very readable, very entertaining and will give you a good grounding in the subject. After that, follow it up with books on Optics if you want to.

Thank you