Shifted Reciprocal
A hyperbola with a vertical asymptote at x = xₒ and a horizontal one at y = C. Use it for inverse relationships with offsets, such as a thin lens’s image distance against object distance.
Parameters
- Scale factor, in the units of y times x.
- Position of the vertical asymptote.
- The level y approaches far from xₒ.
Tips
- The model is undefined at x = xₒ; keep all your data on one side of it.
- For a thin lens obeying 1/x + 1/y = 1/f, with object distance x and image distance y, A = f², xₒ = f and C = f, where f is the focal length.
- With xₒ fixed at 0, this is Inverse.