I think you might want to check your arithmetic. It seems you've made a very simple mistake; the magnification is related to o/i, not i/o.
The very simplest wide-angle converter is a concave lens. Consider two rays coming from the object, and converging on the image plane. Inserting a concave lens in the path (behind the primary lens) will cause those rays to diverge somewhat, thus moving the image plane backwards (or allowing you to move the primary lens forwards). A concave lens has a magnification factor less than one, and thus will concentrate a wider object field-of-view into a smaller image view; both phenomena which are familiar to the majority of eyeglass wearers. It's the positive-magnification TC that doesn't work as a simple case, which is why teleconverters are fairly complex optical designs; they need at least two optical components, so that the film-to-rear-plane distance can be less than original-image-behind-front-plane distance. Neither the wide-angle-converter nor the teleconverter invert the image. > and I thought I was trying to put it simply! You could in theory make > the upside down one, but it would be huge and never sell. APS format > K-mount wide angle lenses are probably the best bet. > > -Scott > > > > > First consider a regular teleconverter. Just looking at one we can see > > > that the focal length is positive because of the way the elements are > > > curved. For this very crude calculation, we can approximate it as a > > > single thin lens, and use the thin lens equations > > > > > > 1/f = 1/o + 1/i > > > m = -i/o > > > > > > i = image distance > > > o = object distance > > > m = magnification > > > f = focal length > > > > > > for the regular teleconverter, o is negative, because the object for the > > > TC is the image from the regular lens, which is usually formed behind > > > the TC. > > > i must be positive, otherwise there is no real image > > > |i|>|o| because we want a magnification greater than 1 to expand the > > > size of the image. This works fine and the TC refocusses the new image > > > farther away, leaving room to stick a TC housing between the lens and > > > camera body. This also explains why 2x TCs are almost always shorter > > > than similarly designed 1.4x TCs > > > > > > correspondingly, m is positive, so we don't have an upside down image. > > > > > > ************************************** > > > For the so called reverse teleconverter, we would need to have |m|<1, > > > which means |o| > |i| and we have a problem. The wide angle converter > > > moves the real image closer to the back of the lens than the original > > > image, so there is no spaces for a converter. You could make this work > > > if you let o be positive, but then the image would be upside down in the > > > viewfinder. > > > > > > -Scott > > > > >
