Real-is-positive lens convention: f > 0 for a converging lens, f < 0 for a diverging lens. Real objects have u > 0. Real images have v > 0 and virtual images have v < 0. The thin-lens equation is 1/f = 1/u + 1/v, and m = −v/u.
Simple magnifier: Relaxed viewing M = D/f. Near-point viewing M = 1 + D/f, where D is the near point, normally 25 cm.
Astronomical telescope: At normal adjustment, M = −f_obj/f_eye, and length = f_obj + f_eye. Negative M indicates an inverted image. The objective and eyepiece are converging lenses.
Compound microscope: M ≈ −(L/f_obj)(D/f_eye), the standard approximation, with tube length L and near point D. This model assumes a suitable intermediate image and paraxial rays.
Corrective lenses: Lens power P = 1/f in metres, measured in dioptres (D). A negative lens corrects myopia for distant viewing by forming a virtual image at the eye's far point, under the spectacle-at-eye approximation.
Assumptions: Ideal thin lenses, paraxial rays, monochromatic light and negligible lens thickness. Lengths are in cm unless marked otherwise.