ello HydroIce,
An extractor fan and ducting straight to the light bulb/globe would be essential....hook that up so the ducting goes into the roof/ceiling.
For the sliding door, i suggest the white reflective plastic (white on one side & Black on the other) so light doesn't escape.....you could use mylar but it still lets light pass threw it.
Good luck and keep us posted.
Peace & Merry Christmas,
Bliss