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both diagrams are wrong, but the middle one is somewhat closer to reality.
look at the bundle rays coming from the right (i.e. from the sun). They appear to be parallel. so those are all coming from one direction (i.e. a single point on the sun.). They eventually come to a focus at point 32, just before the so-labelled "field lens". Other bundles of rays coming from different points on the sun are not shown. the sun is half a degree angular diameter when seen from earth, so those bundles of rays can be up to half a degree different in direction. when those other bundles reach point 32, they will be at a different point to the focus shown. so at the plane of point 32, there will be a real image of the sun. its size depends on the focal length of the objective lens 22, with an image diameter d = sin (0.5 deg) * focal length. Say focal length is about 1000mm (assuming the triangle side length is about 300mm), that would be an image size of 8.8mm.
the so called field lens then projects that little image down onto the screen. the image gets magnified by the ratio (distance from lens34 to screen 36)/(distance from point 32 to lens34) .
But the ray drawing from lens 34 to screen 36 is not really correct. as drawn it is showing the rays which diverged from 32, arrived at 34, then went through a focal point and spread out to a huge out of focus circle. this is wrong. It should really be the rays coming from 34 to arrive at a point focus at screen 36. ray bundles from other points on the suns disc would arrive at focus on other areas of the screen, making a nice big sharply focused image of the sun.
One interesting modification of the design might be to replace some or all of the (fragile surface) first surface mirrors with prisms providing total internal reflection, since they can be more easily cleaned and never need recoating. But that would mean making the folded path into a squarish path with 90 degree folds rather than the 120 degrees, since 120 degrees isn't possible by a single total internal reflection, whereas 90 degree prisms are standard. Depending on the objective lens diameter, the first prism might be too large to be practical, so perhaps keep it as first surface mirror. Perhaps the second and/or third reflections can be achieved with reasonable size prisms. for example, porro prisms salvaged from defunct binoculars.
What is the focal length of your failed folded refractor project?
Hope my comment has been useful. Cheers,
Hamish
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