Zoom lenses were development of the telephoto lens. It was designed so that the focal length of the lens system could be varied by moving some individual lenses.
Since magnification depends on the focal length then we can get various image sizes.
This is an example of a zoom lenses and it's transfer matrices.
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Example zoom lenses system we going to use it:
These are the value we use to get the postscript pictures below (from book "Lens Design"
zoom2 20.84mm
zoom3 3.75mm
zoom4 15.79mm
R1 -14.3416mm
R2 -24.109mm
R3 26.025mm
R4 -18.543mm
R5 -27.285mm
R6 245.74mm
d1 5.157mm
d2 9.74mm
d3 0.7mm
s1 0.1mm