What are the physics of an optical snoot & gobo?

TheAthenA714 wrote:

Thank you very much, I'm gonna experiment with all that and do some calculations.

Quick follow up questions:

For the image of the gobo to be projected at infinity, the lens should be focussed at infinity and the distance between the gobo and the lens should be exactly the same as the distance between the camera sensor and the lens.

If I'm understanding this correctly I should look up the flange distance of the specific lens mount I'm using and use that as the space between the lens and the gobo right?

Yes.

The 55mm lens I'm using now is an M42 lens, but that means if I were to switch it to an EF lens or something else, I would have to change the spacing right?

Yes.

• You can find the infinity focus position for the gobo by trial and error using the far wall of a very large room (which will be near enough to infinity) to focus the image on.

Sounds simple enough to do, but just out of curiosity is there a formula to calculate that? What would be the variables that impact that value?

There are various formula according to whether you measure the distance from the principal points or the pupils of the lens, but the problem with these is in determining exactly where the principal points of the lens are, or where the pupils are.  These positions can be determined, but it is not trivial to do.

Have a look at Bill Claff's Optics Primer if you want to go into more detail.

The simplest thing is to find the sensor to flange distance for your lens, as you suggest, and use that to determine the position of the infinity focus (usually just called the focal point of the lens).