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I am struggling with a real-life optics problem. At work, I have a projector that makes an image too big for the screen. I think I can reduce the image to the required size by mounting a simple lens in front of the projector lens. However, I haven't been able to determine what lens I need, nor the distance at which I have to mount it.

My questions:

  • Am I correct, at least in principle, that it should be possible to correct the image by mounting a simple lens?

  • What measurements do I need to collect, and how do I calculate the required lens and mounting distance?

I'm rather frustrated that I can't solve this myself. The problem is that I don't have a clear mental model of the optical system. When I've tried to research the optics of a projector/camera, I find much explanation of how focusing occurs, but very little explanation of how magnification occurs in a lens system.

Here are some details:

  • The projector is mounted 360 inches from the screen.

  • The projector has a zoom lens assembly which, at 360 inches, projects an image which is 84.7 to 154.1 inches tall.

  • The screen is 60-inches tall.

  • The image is height-constrained, so the widths of the image and screen don't matter.

  • The projector specifications say that the lens focal length is 24.0mm to 43.2mm.

All advice is appreciated.

By the way, I've labeled this question "camera" because my understanding is that a projector works just like a camera in reverse, so a camera expert should be able to figure this out. Let me know if I'm wrong about that.

Edit:

I've done some research and I think I can partially answer my question. I now think that the image size cannot be corrected with a simple lens. If the image were out of focus, I might be able to correct that with a simple lens, but changing the size of the image requires more complicated optics.

On the other hand, I've learned that those complicated optics are exactly what happens inside a camera "conversion lens". So, now I'm pursuing the same solution, but I'm looking for a conversion lens assembly with the right specs, rather than a simple lens. I'm don't yet know how to determine the right specs, but I'm working on it.

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