Lens

A lens is a piece of glass or other transparent material with curved sides for concentrating or dispersing light rays, used singly (as in a magnifying glass) or with other lenses (as in a telescope).

A lens with positive optical power can, by itself, form images of a spatial scene/object, and a simple version is a bi-convex lens. However, positive lenses are typically combined with other lens elements to form a lens with specific properties such as particular focal length, field-of-view, and/or with low levels of distortions or optical aberrations across the image.

Lens Types

A converging lens has positive power, and is often a lens that is thicker in the middle than at the edges, and bends parallel light rays inwards to a single point. This point is called the focal point. Converging lenses form real images. The image can be inverted or upright, and larger, smaller, or the same size as the object. Converging lenses are used in cameras and telescopes to form an image of a spatial object/scene.

A diverging lens is a lens of negative power, and is often a lens that is thinner in the middle than at the edges. Light rays parallel to the lens’s axis pass through the lens and bend outwards. The light rays appear to come from a virtual point on the opposite side of the lens. This point is called the focal point. The image formed by a diverging lens is virtual, upright, and smaller than the object.

Diverging lenses are used in eyeglasses to correct nearsightedness (myopia). They spread light rays so the eye can focus on distant objects more clearly.

Camera Lens

Lenses are often employed in cameras of both the photographic and digital types; and different kinds of lens designs will produce various types of images.

Significantly the longer a lens focal length, then it will have a higher optical magnification (but at the same time typically with a narrower field-of-view). We have several district types of lens, from telephoto or long focal length lens, wide-angle or short focal length lenses, normal focal length lenses, and also variable focal length lenses; and during the making of a typical movie all types of lens are used at one point or another and to achieved specific purposes or optical effects.

It is important to note that each class of lens, and indeed each lens design, will have, or introduce, slightly (or largely) varying perspective image geometry forms, including optical ‘distortions’. For example, a wide-angle lens may introduce curvilinear perspective effects into the resultant images.

Lens-designers work hard to minimise or eliminate such curvilinear distortions, often seeking to match linear perspective type images over as wide a field-of-view as possible. However, it is important to recognise that it is by no means clear that such curvilinear perspective distortions are unnatural because many people have noted that curvilinear and spherical perspectives may be just as legitimate as linear ones, and further that the human eye does show curvilinear perspective distortions in any case (due to image projection onto a spherical retina).

Focal Length

A normal lens (ref. a positive or converging lens) for a camera has a focal length of around 50 mm, but can range from 35 mm to 85 mm. Normal lenses are also called standard lenses.

Features / Applications

  • Focal length: The focal length of a lens determines what the camera can focus on and how the image will look.
  • Human eye: Normal lenses have a similar perspective to the human eye (objects sizes, field-of-view and perceived distortions, etc), making them a good choice for portraits and travel photography.
  • Cinematography: Cinematographers often use normal lenses for a more natural look.
  • Crop factor: If you have a crop-sensor camera, you must divide the focal length by the crop factor to get the equivalent focal length.

A telephoto camera lens has a focal length higher than normal, usually 85 mm or more, thus giving a higher angular magnification than a normal lens, plus often with lower field-of-view – or less frame angular coverage captured in the image focal plane by the detector or film negative.

A wide-angle camera lens has a focal length lower than normal, usually 25 mm or less, thus giving a lower angular magnification than a normal lens, plus often with higher field-of-view – or higher frame angular coverage captured in the image focal plane by the detector or film negative.

A zoom lens is a camera lens with a variable focal length – which can be varied manually or under automatic or semi-automatic motorised control.

Image Formation

The position and size of an image formed by a lens depends on the object’s distance from the lens and the lens’s focal length; the closer the object is to the lens, the larger the image will be, and the image position will change depending on whether the object is placed inside or outside the focal point, with images formed inside the focal point being virtual and upright, while those formed beyond the focal point are real and inverted.

Lens image position and size

  • Converging lenses (convex): If the object is beyond the focal point (f), the image is real, inverted, and on the opposite side of the lens from the object. If the object is within the focal point, the image is virtual, upright, and on the same side of the lens as the object. 
  • Diverging lenses (concave): Always form virtual, upright, and smaller images on the same side of the lens as the object, regardless of the object’s position.

Calculating image position and size

  • Thin Lens Equation: To calculate the image position, the “thin lens equation” is used: 1/f = 1/u + 1/v, where “f” is the focal length, “u” is the object distance, and “v” is the image distance.
  • Magnification: To determine the image size relative to the object, use the magnification formula: m = -v/u.