What is the relationship between object distance and image distance?
It is a perfectly inversely proportional relationship. As the distance increases, the image appears to decrease in size. If you double the distance, the images appears to half in size. This is for a straight projection. Anything other than a flat mirror will alter this and will depend on the depth and extent of the concave shape. The less the depth, the less the distortion. You need to work out your angles of incidence before you can calculate where to position everything.
