This should be a fairly simple problem. I can't explain more about the context but basically I have a camera and in front is a plank of something in which we will cut a window so the camera has an unobscured view.
How big does this window need to be?
So let's be measuring the distance of the wall to the principal plane of the lens, s. The lens has focal length, f. The camera sensor is for simplicity a square of side, d.
So the field of view of the camera setup is given by, a=2 arctan (d/2f)
Similarly, the field of view afforded by the window is given by, a=2 arctan (w/2s). Of course both values of a should be the same, so we can equate.
d/2f = w/2s
=>
w = ds/f
Now if the focal length is 28mm and the standoff is 30mm and the sensor is 25mm across, the window needs to be be 27mm across. Less than 3cm seems so smaller when placed in front of your typical Nikkor lens.
