Camera Focal Length vs Projector Throw Distance

[Patrick Bienvenu]

Challenging question. Can the mathematical relationship in size be defined by the relationship between the focal length and the projector throw distance. Assume shooting a lifelike image of a person in HD and projecting it on to a wall using a projector with 1280 x 800 max resolution. In order to keep the projected image the actual size of the person, how far should the camera be from the subject and how does zoom impact the distance the projector would need to be from the wall to maintain the persons actual size? The goal is to have the projector as close as possible to the wall while maintaing the actual (real) size of the person - like a short-throw projector. Is there truth to "the shorter the subject" the shorter the projector throw distance. Shooting in Portrait and projecting in Portrait for max resolution.

[Shaun Roemich]

Not challenging at all - you are approaching the problem incorrectly.

Step 1:
Use an appropriate focal length lens to shoot the subject full frame at the distance you need to be from the subject. The two interconnected variables are distance from subject and focal length of lens.

Step 2:
Use an appropriate combination of distance to projection surface and lens on projector to get the size you need.

In other words, there is <i> no direct and constant correlation </i> between the two focal lengths.

[Patrick Bienvenu]

Thanks for your reply. The problem is we need the shortest possible throw distance, while maintaing the actual (real) size of the subject. We can control step 1, but step 2 needs to be as close as possible and we have no control over the type of projector lens. We can only adjust the projector zoom. In step 1 - we believe the focal length impacts the throw distance. In simple terms the question would be, to achieve the shortest possible projector throw distance - is it best to be as close as possible to the subject (and then what impact does zoom have on throw distance), or is it better to be back further and zoom in to fill the frame? What results in the shortest throw distance? Appreciate your response.

[Shaun Roemich]

Again, the issue is you are assuming there is a correlation. There isn't. This is merely a (frustrating) issue with projection. It's going to be a matter of trial and error, moving the projector back and forth and zooming the image (which on projectors is QUITE limited... usually no more than 1.5x) until you get the right portrait/person size.

No more complicated than that, although much more frustrating than a mathematical quick fix.