Lens Imaging Calculator

A lens forms images by refracting light. A converging lens brings parallel rays toward a focal point, while a diverging lens spreads rays as if they came from a focal point. The thin-lens model simplifies a real lens into an ideal element with a focal length and negligible thickness.

The thin-lens equation relates object distance, image distance, and focal length. It captures where an image forms when an object is placed at a given distance. The model is a first-order approximation, but it explains cameras, magnifiers, eyeglasses, projectors, and basic optical instruments.

A real image forms where light rays actually converge and can be projected onto a screen or sensor. A virtual image forms where rays appear to originate when traced backward; it cannot be projected directly onto a screen. A magnifying glass used close to an object creates a virtual enlarged image. A camera lens forms a real image on the sensor.

The distinction depends on object position relative to focal length. For a converging lens, objects outside the focal length form real images on the opposite side. Objects inside the focal length form virtual images on the same side as the object.

Magnification compares image size with object size. A negative magnification often indicates an inverted image under common sign conventions; a positive value indicates upright orientation. The magnitude tells how much larger or smaller the image is.

Sign conventions vary across textbooks and optical design contexts. The physical interpretation is more important than memorizing a convention. A ray diagram can confirm whether an image is real or virtual, upright or inverted, enlarged or reduced.

Real lenses have thickness, aperture limits, aberrations, dispersion, coatings, curvature details, and alignment errors. Spherical aberration, chromatic aberration, distortion, field curvature, and diffraction can all affect image quality. Multi-element lens systems exist to control these imperfections.

The thin-lens equation remains useful because it gives the paraxial starting point: where the image should form and how large it should be under ideal conditions. Practical optics then refines that baseline for real materials and finite apertures.