Lens

A lens is a transparent optical element with two refracting surfaces, commonly spherical, that refracts light to either converge or diverge rays. Lenses play an essential role in forming images in various optical instruments, making their understanding fundamental in physics.

Definition and Structure of a Lens

A lens is generally made from glass or other transparent material. Its surfaces are either both curved or one curved and one flat, forming part of spheres. The line passing through the centers of curvature is called the principal axis.

The central point inside the lens where a ray passes without deviation is termed the optical centre. The diameter of the spherical outline viewed from the side is known as the aperture of the lens.

A lens typically has two centers of curvature, one for each surface. The point on the principal axis where parallel rays converge or appear to diverge from is called the principal focus or simply the focus.

Types of Lenses

Lenses are categorized into simple and compound types. A simple lens uses a single piece of transparent material, whereas a compound lens is made of several simple lenses combined to minimize optical imperfections.

Spherical lenses, the most common type, include convex (converging) and concave (diverging) lenses. A convex lens is thicker at the centre and converges parallel rays to a point. A concave lens is thinner at the centre and diverges incoming parallel rays.

Other specialised lenses include aspheric lenses (non-spherical surfaces to reduce aberrations), cylindrical lenses (power along only one axis), bifocal lenses (two focal lengths), and gradient index lenses (varying refractive index profiles).

For detailed differences between mirrors and lenses, refer to Difference Between Mirror And Lens.

Principal Terms Related to Lenses

The principal axis is the straight line passing through the two centres of curvature. The centre of curvature is the centre of the sphere to which the lens surface belongs. The optical centre is the internal point through which a ray passes undeviated.

The aperture defines how much light the lens can admit. The focus is the point where rays parallel to the principal axis converge (in a convex lens) or appear to diverge from (in a concave lens).

Sign convention plays an essential role in lens calculations. For further details, see Sign Convention In Lenses and Sign Convention In Optics.

Lens Formula and Magnification

The image formation by a lens follows the lens formula, which relates object distance ($u$), image distance ($v$), and focal length ($f$), given by:

$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

Magnification ($m$) produced by a lens is the ratio of height of image ($h'$) to height of object ($h$) and is also related to object and image distances:

$m = \dfrac{h'}{h} = \dfrac{v}{u}$

For an in-depth explanation and solved examples, refer to Lens Formula And Magnification.

Combination of Lenses

When thin lenses are placed in contact, the effective focal length $f_{eq}$ can be determined using their individual focal lengths $f_1, f_2, \ldots , f_n$:

$\dfrac{1}{f_{eq}} = \dfrac{1}{f_1} + \dfrac{1}{f_2} + \ldots + \dfrac{1}{f_n}$

Such combinations are used in optical instruments to improve performance or alter image characteristics. More information is available at Combination Of Thin Lenses In Contact.

Common Optical Aberrations in Lenses

Lenses are subject to aberrations, including spherical aberration, which arises due to the use of spherical surfaces and leads to image blurring. Using a lens with an appropriate curvature or compound combinations can minimize these effects.

Chromatic aberration is caused by the dispersion of light; different colours focus at varying positions, resulting in colored edges. This can be corrected using achromatic doublets made by combining two lenses of different materials.

Applications of Lenses

Lenses are found in a variety of devices, such as magnifiers, cameras, spectacles, microscopes, and telescopes. In cameras, multiple lenses are arranged to capture and focus light efficiently, correcting for various aberrations.

In microscopes and telescopes, combinations of convex and concave lenses are used to achieve high magnification and clarity. Lenses are also crucial for vision correction in spectacles and in optical instruments for research.

Comparison with Mirrors

While both mirrors and lenses form images, lenses work through refraction, whereas mirrors use reflection. The formulas and conventions used differ, and a fundamental understanding is required for problem-solving. For a comparative discussion, visit Mirror Formula And Magnification.