Thin Lens Image Distance
Image distance, magnification and conjugate ratio of a thin lens, from the object distance or from the magnification, for real and virtual images.
Results
The distances run from the lens (its principal planes, for a thick lens). A microscope objective's working distance, from its front lens to the sample, is set by its mechanics and is shorter than o.
Image distance vs object distance
Model
1/o + 1/i = 1/f, i = f·o/(o − f), M = −i/o
From M: o = f(1 − 1/M), i = f(1 − M)
Newtonian: x·x′ = f², x = o − f, x′ = i − f
Paraxial thin lens in air, real-is-positive signs: o > 0 for a real object in front of the lens, i > 0 for a real image behind it, f > 0 for a converging lens. An object inside the focal length of a converging lens gives a virtual, upright, enlarged image (a magnifier); a diverging lens always gives a virtual, upright, reduced one. The real object-to-image distance is shortest, 4f, at M = −1.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Paraxial thin lens in air with real-is-positive signs. Distances are from the lens's principal planes, so an objective's working distance, from its front lens, is shorter than the object distance.
- Greivenkamp J. E. (2004). Field Guide to Geometrical Optics. SPIE Press. Gaussian imaging equation, transverse magnification and Newtonian equations. doi:10.1117/3.547461