We produce projected slides (RGB) and printed posters (CMYK) that sometimes appear adjacent to each other. We find that the same graphics looks very different in the two mediums. How can we adjust the RGB values to match or come close to the CMYK appearance?
You need to calibrate your printer and your projector using specialized hardware like Colormunki photo.
One primitive way to do it is to use your graphics card's software and tweak it a bit to get closer to the print.
You also need to use some standardized lights to view the print. In modern led lights there is a unit called CRI (Color rendition index), the closer the number to 100 the better.
Fluorescent lamps have a CRI very low, so normal office lamps will do a bad job.
You will have to create similar viewing conditions for both of the images if not industry standard ones.
The colour matching is the subject of "Colour Management." Within that is what is called "Standard Viewing Conditions." It involves characterizing and calibrating your "display monitors" to match. The degree to which they match is an issue
To begin, the slide and the print should have the same "White Point" and be illuminated at sufficient intensity that the "whites" in both appear to match. This alone is going to get you very close to your goal without modifying the file to compensate for display differences.
In normal press-check situations, a calibrated RGB monitor displays the correct "slide" physically located beside the "print" inside a viewing booth with the correctly illumination inside——all this in a consistently lit neutrally coloured room.