I.

Introduction

Lens (optics), in optical systems, glass or other transparent substance so shaped that it will refract the light from any object, and form a real or virtual image of the object.

The ways in which lenses form images depend on the laws of refraction. A lens can typically be thought of as being made up of a number of prism-shaped pieces. A ray passing through the optical centre of the lens will continue along the principal axis (an imaginary line passing at right angles to the plane of the lens through its centre) without deviation. Rays of light striking the lens parallel to the principal axis are refracted by the “prisms” in such a way that they all pass through a single point, the principal focus of the lens. The distance from the centre of the lens to the principal focus is known as the focal length of the lens. A powerful lens has a short focal length, whereas a weaker lens has a longer focal length. A converging lens will cause the rays of light to converge on the principal focus, and an image will be formed which is inverted. A diverging lens will cause the rays to diverge towards the principal focus, and an upright image will be formed.

The image formed by a lens depends on the nature of the lens, and will either be real or virtual. Real images are those which can be cast on to a screen, whereas virtual images are images which cannot be cast on to a screen, but are nevertheless perceived by the eye. The actual positions of images may be calculated using the lens formula:

1/v + 1/u = 1/f

where u is the distance of the object from the lens, and v is the distance of the image.

To use this formula, it is essential to observe the convention that real object or image distances are positive, and virtual object or image distances are negative. The focal length, f, is taken as positive for a converging lens, and as negative for a diverging lens. For a diverging lens, the image is therefore virtual, upright, and diminished. Such lenses are used in spectacles for correcting short-sightedness.

Lenses are also used in cameras (see Photographic Techniques), microscopes, telescopes, and other optical instruments. Other imaging systems may be effectively used as lenses in other regions of the electromagnetic spectrum, such as the magnetic lenses in electron microscopes. See also Optics; Eye.