Optics Calculator — Thin Lens

The thin lens equation is 1/f = 1/do + 1/di, where f is focal length, do is object distance, and di is image distance from the lens.

A negative focal length indicates a diverging (concave) lens, which always produces a virtual, upright, and diminished image on the same side as the object.

The image is real when the image distance di is positive — light rays actually converge on the opposite side of the lens from the object.

The image is virtual when di is negative — light rays diverge and the image forms on the same side as the object (e.g., in a magnifying glass).

Magnification M = -di/do. A negative value means an inverted image; absolute value greater than 1 means the image is enlarged.

When the object distance equals the focal length (do = f), rays emerge parallel after the lens and the image forms at infinity.

The equation is used in designing eyeglasses, cameras, microscopes, telescopes, and all optical systems involving lenses.

No — the calculator uses the thin lens model, which ignores spherical, chromatic, and other aberrations of real lenses.

An inverted image (negative magnification) forms when the object is beyond the focal point of a converging lens. The image is rotated 180° relative to the object.

As the object approaches the focal point of a converging lens, the real image moves farther away and becomes more magnified. Inside the focal length, the image becomes virtual and upright.