DIY Long Throw adapter?

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I have an InFocus X1. I plan to build an anamorphic lens for it using prisms to get a better 16:9 image.

The 1st problem I need to solve is reducing the height of the image on the screen from 60in to 48in.

Is it possible to construct a throw lens to put in front of the existing lens to allow me to get a smaller image on the screen?

How would I go about this?

I would then project into my prisms to do the horizontal stretch.

I do not want to move the projector as it is mounted in another room and projected through a hole in the wall into the viewing room.
 
There's no need to, because the anamorphic prisms work to compress the image as well as expand it by just flipping the assembly.

Be aware, it's a nice project to tinker with, but the final image may be no brighter than before, with uncoated prisms, and you'll definitely introduce colour abberations. They're not too observable with movies from the regular watching distances though.
This is probably much worth if you have a 4:3 projector and watch 2.35:1 movies than with modern 16:9 projector.

You can obtain the anamorphic expansion by projecting at an angle and dekeystoning too, particularly with longer throw projectors.
 
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