What are the physics of an optical snoot & gobo?

TheAthenA714 wrote:

Hey everyone!

So since I've heard about optical snoots and gobos I've been wanting to try and build one on my own. I have an old 55mm/f1.4 M42 manual lens, a few adapters and extensions tubes and a basic Godox non-optical snoot with a bowens mount for my light.

From my basic testing I think I understand the following :

• I need to place the gobo in between the light and the lens
• The smaller the distance between the gobo and the light, the bigger the projected image will be
• The closer the lens is to the light, the further away the projected image will be focused
• I can fine-tuning the focusing with the focusing ring on the lens, but it only allows very minor adjustements. So if I want to move the focus plane a few inches I need to actually move the lens closer/further away
• I don't know if changing the focal length (swaping the 55mm for an 85 or a 35mm) would affect the result

So assuming I'm correct in my understanding, I'm now trying to build a DIY optical snoot that would allow me to place a gobo at the end of my godox snoot (or maybe even inside the snoot itself to bring the gobo closer to the light), and then have a tube of easily adjustable length between the snoot and the lens.

The big question is: how long should that tube be? And that's where I'd like to know the physics so I can calculate some rough estimation of where the focal plane would be based on that length. Basically what I want to know is:

• If I place the gobo at X cm from the light and the lens at Y cm from the light, where will the projected image be focused?

Is there a formula to calculate that? Any other advices/resources to explore that concept?

The projected image will be focussed at a distance that depends on the lens and on the distance between the gobo and the lens.  The light needs to be sufficiently far from the gobo so that the lens is not just projecting an image of the light itself.

Imagine that the gobo is the sensor of your camera and the lens on the camera is projecting light from the gobo. 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.

There are various formulae that describe how to calculate the image distance and it can get very complicated if you want to do it to high accuracy.  However, provided you are happy with getting a good estimate of the distance, an easy formula to use is this one:

image distance from lens = f^2 / distance of the gobo from the infinity focus position, where f is the focal length of the lens.

So, if your lens is 55mm (i.e 5.5cm), then f^2 = 5.5 x 5.5 = 30.

To get the image distance in cm, you need to divide 30 by the distance in cm that you move the gobo from its infinity focus position.

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.

So, moving the gobo just 1 cm from its infinity focus position will mean the image now focuses only 30 cm from the lens (approximately). Make sure that you don't change the focus scale on the lens itself (which will mess up these calculations).

Alternatively, it may be easier to leave the gobo fixed and focus use the focus adjustment on the lens itself.