Is there a correspondence between Tilt-Angle and the angle of the Focus-Plane?

Question

Tilt lenses have their tilt-range specified in degrees, typically around ±8°. It seems that this number corresponds to how much a lens physically tilts along one axis. The effect is to tilt the plane of focus by some angle.

Can one calculate the focus plane angle from the tilt-angle of the lens?

Can we compute the lens tilt needed to tilt the focus plane to a desired angle?

Answer 1

Yes. The answer is given by the Scheimpflug principle: The focal plane, lens plane, and subject plane all intersect at a common line:

Thus the angle of the subject plane depends not only on the lens tilt, but the distance of the subject. As the Wikipedia article states, the angle of tilt of the subject plane, ψ, is given by:

tan(ψ) = (u'/f) sin (θ)

Where u′ is the distance along the line of sight from the center of the lens to the plane of focus, f is the focal length, and θ is the lens tilt.