I want to focus at far distances but close, what lens could I use?

Question

I want to be able to set the focus at far distances, like 500 m, but in a smaller setting, like 5 m. What lens could I use to achieve this?

I have found this lens that achieves it for a FOV of 120 degrees. But it lacks info (e.g. ray tracing, lens info) on how it's done. I work with FOV like 60 and 30 degrees. I have no settings on the lens, just manual screwing in or out.

https://www.imatest.com/product/120-collimator-lens-for-wide-field-of-view/

To be clear, as an example. I was to set the focus for 500 m while inside a room 5 m wide, using lens to give the equivalent focus. So I can go outside later and the focus will be set at 500 m without additional lens.

Answer 1

What you need is a means to create a virtual image 500 meters away in a room-sized setting. If you get a lens with 1 meter focal length and put it 0.998004 meters from an object the thin lens formula says you will have a virtual image 500 meters behind the lens. You can then put your camera in front of this and focus the camera lens on the virtual image. You need to be accurate. A 1 mm shift in the lens-object distance can make the image be 333 meters or 1000 meters away.

Answer 2

It's not practical, to be honest. To map every finite distance into a 5m range, you add a "closeup lens" (I hesitate to even call it that) of 0.2 dioptre strength. Then to focus for 500m, you actually focus with that lens on to 1/((1/500m)+(0.2/m))) which is about 4.95m. See the problem? Large distances like 500m actually correspond to very small changes in optical lens strength.