Image plane
The plane where a lens forms a sharp image of an object plane; the two are conjugate. For a thin lens it lies at s′ = 1/(1/f − 1/s): a 50 mm lens images an object 250 mm away onto a plane 62.5 mm behind it, at magnification −0.25. Only for an object at infinity does it coincide with the focal plane.
Every point of an object in front of a lens sends out a cone of rays, and a good lens brings each cone back together at a single point behind it. The surface where those points lie is the image plane, and the object plane and image plane are called conjugate: move the object and the image plane moves with it. A detector, a fiber end or a pinhole placed in the image plane receives a sharp image; placed elsewhere, it receives a blurred one.
For a thin lens of focal length in air, an object at distance images at
with transverse magnification . A 50 mm lens with an object 250 mm in front of it forms an image 62.5 mm behind it, inverted and a quarter of the size. As the object recedes to infinity the image plane approaches the back focal plane, which is why the two are often confused; for close objects, as in macro photography, microscopy and relay optics, the image plane lies well beyond the focal plane. For systems with several elements, the same conjugate relations hold with distances measured from the principal planes, and an ABCD matrix with between two planes means those planes are conjugate.
Focal plane and image plane
The back focal plane is where a collimated beam comes to focus and where a lens forms the Fourier transform of the field in its front focal plane; spectrometers, spatial filters and far-field measurements work there. The image plane is where the object is reproduced. In an infinity-corrected microscope the two are separated deliberately: the objective puts the specimen's image at infinity, and a tube lens forms the real image on the camera, leaving a parallel-beam space for filters and beamsplitters.
Curvature and tolerance
A real lens forms its sharpest image on a curved surface rather than a plane, because of field curvature, and flat-field designs are corrected to bring it close to a plane. How far the detector can move along the axis and still see a sharp image is the depth of focus, which grows with the working f-number, as its square in the diffraction limit.
Finding it on a bench
The image plane is found by moving a screen, camera or card along the axis until the image of a sharp target, a back-lit edge or grid, is crisp, or more precisely by scanning a camera through focus and taking the position of maximum edge contrast or MTF. For laser work, where the object is often a fiber end or a pinhole, the image plane is where the spot is smallest.
References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 5; W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008), Ch. 2.