Optics

• The law of reflection says that the reflected ray lies in the plane of incidence, and the angle of reflection equals the angle of incidence.
• The law of refraction says that the refracted ray lies in the plane of incidence, and the sine of the angle of incidence divided by the sine of the angle of refraction is a constant:
  $${\displaystyle {\frac {\sin {\theta _{1}}}{\sin {\theta _{2}}}}=n,}$$

  
  where n is a constant for any two materials and a given colour of light. If the first material is air or vacuum, n is the refractive index of the second material.

The laws of reflection and refraction can be derived from Fermat's principle which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.^[36]

Approximations

Geometric optics is often simplified by making the paraxial approximation, or "small angle approximation". The mathematical behaviour then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics and paraxial ray tracing, which are used to find basic properties of optical systems, such as approximate image and object positions and magnifications.^[37]

Reflections

Reflections can be divided into two types: specular reflection and diffuse reflection. Specular reflection describes the gloss of surfaces such as mirrors, which reflect light in a simple, predictable way. This allows for the production of reflected images that can be associated with an actual (real) or extrapolated (virtual) location in space. Diffuse reflection describes non-glossy materials, such as paper or rock. The reflections from these surfaces can only be described statistically, with the exact distribution of the reflected light depending on the microscopic structure of the material. Many diffuse reflectors are described or can be approximated by Lambert's cosine law, which describes surfaces that have equal luminance when viewed from any angle. Glossy surfaces can give both specular and diffuse reflection.

In specular reflection, the direction of the reflected ray is determined by the angle the incident ray makes with the

For flat mirrors, the law of reflection implies that images of objects are upright and the same distance behind the mirror as the objects are in front of the mirror. The image size is the same as the object size. The law also implies that mirror images are parity inverted, which we perceive as a left-right inversion. Images formed from reflection in two (or any even number of) mirrors are not parity inverted. Corner reflectors produce reflected rays that travel back in the direction from which the incident rays came.^[39] This is called retroreflection.

Mirrors with curved surfaces can be modelled by ray tracing and using the law of reflection at each point on the surface. For mirrors with parabolic surfaces, parallel rays incident on the mirror produce reflected rays that converge at a common focus. Other curved surfaces may also focus light, but with aberrations due to the diverging shape causing the focus to be smeared out in space. In particular, spherical mirrors exhibit spherical aberration. Curved mirrors can form images with a magnification greater than or less than one, and the magnification can be negative, indicating that the image is inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen.^[40]

Refractions

Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an

$${\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}}$$

where θ₁ and θ₂ are the angles between the normal (to the interface) and the incident and refracted waves, respectively.^[38]

The index of refraction of a medium is related to the speed, v, of light in that medium by

$${\displaystyle n=c/v,}$$

Snell's Law can be used to predict the deflection of light rays as they pass through linear media as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. In most materials, the index of refraction varies with the frequency of the light, known as dispersion. Taking this into account, Snell's Law can be used to predict how a prism will disperse light into a spectrum.^[41] The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton.

Some media have an index of refraction which varies gradually with position and, therefore, light rays in the medium are curved. This effect is responsible for mirages seen on hot days: a change in index of refraction air with height causes light rays to bend, creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Optical materials with varying indexes of refraction are called gradient-index (GRIN) materials. Such materials are used to make gradient-index optics.^[42]

For light rays travelling from a material with a high index of refraction to a material with a low index of refraction, Snell's law predicts that there is no θ₂ when θ₁ is large. In this case, no transmission occurs; all the light is reflected. This phenomenon is called total internal reflection and allows for fibre optics technology. As light travels down an optical fibre, it undergoes total internal reflection allowing for essentially no light to be lost over the length of the cable.^[43]

Lenses

A device that produces converging or diverging light rays due to refraction is known as a lens. Lenses are characterized by their

Ray tracing can be used to show how images are formed by a lens. For a thin lens in air, the location of the image is given by the simple equation

$${\displaystyle {\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}={\frac {1}{f}},}$$

where S₁ is the distance from the object to the lens, θ₂ is the distance from the lens to the image, and f is the focal length of the lens. In the sign convention used here, the object and image distances are positive if the object and image are on opposite sides of the lens.^[45]

Incoming parallel rays are focused by a converging lens onto a spot one focal length from the lens, on the far side of the lens. This is called the rear focal point of the lens. Rays from an object at a finite distance are focused further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens.

With diverging lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at a spot one focal length in front of the lens. This is the lens's front focal point. Rays from an object at a finite distance are associated with a virtual image that is closer to the lens than the focal point, and on the same side of the lens as the object. The closer the object is to the lens, the closer the virtual image is to the lens. As with mirrors, upright images produced by a single lens are virtual, while inverted images are real.^[46]

Lenses suffer from aberrations that distort images. Monochromatic aberrations occur because the geometry of the lens does not perfectly direct rays from each object point to a single point on the image, while chromatic aberration occurs because the index of refraction of the lens varies with the wavelength of the light.^[47]

Physical optics

In physical optics, light is considered to propagate as waves. This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics. The

Many simplified approximations are available for analysing and designing optical systems. Most of these use a single scalar quantity to represent the electric field of the light wave, rather than using a vector model with orthogonal electric and magnetic vectors.^[50] The Huygens–Fresnel equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygens' hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of superposition of waves. The Kirchhoff diffraction equation, which is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygens–Fresnel principle can be found in the articles on diffraction and Fraunhofer diffraction.

More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with materials whose electric and magnetic properties affect the interaction of light with the material. For instance, the behaviour of a light wave interacting with a metal surface is quite different from what happens when it interacts with a dielectric material. A vector model must also be used to model polarised light.

Numerical modeling techniques such as the finite element method, the boundary element method and the transmission-line matrix method can be used to model the propagation of light in systems which cannot be solved analytically. Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions.^[51]

All of the results from geometrical optics can be recovered using the techniques of

Gaussian beam propagation is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics.^[52]

Superposition and interference

In the absence of

combined waveform
wave 1
wave 2
	Two waves in phase	Two waves 180° out of phase

Since the Huygens–Fresnel principle states that every point of a wavefront is associated with the production of a new disturbance, it is possible for a wavefront to interfere with itself constructively or destructively at different locations producing bright and dark fringes in regular and predictable patterns.^[55] Interferometry is the science of measuring these patterns, usually as a means of making precise determinations of distances or angular resolutions.^[56] The Michelson interferometer was a famous instrument which used interference effects to accurately measure the speed of light.^[57]

The appearance of

Constructive interference in thin films can create a strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make

Diffraction is the process by which light interference is most commonly observed. The effect was first described in 1665 by

The first physical optics model of diffraction that relied on the Huygens–Fresnel principle was developed in 1803 by Thomas Young in his interference experiments with the interference patterns of two closely spaced slits. Young showed that his results could only be explained if the two slits acted as two unique sources of waves rather than corpuscles.[63] In 1815 and 1818, Augustin-Jean Fresnel firmly established the mathematics of how wave interference can account for diffraction.^[64]

The simplest physical models of diffraction use equations that describe the angular separation of light and dark fringes due to light of a particular wavelength (λ). In general, the equation takes the form

$${\displaystyle m\lambda =d\sin \theta }$$

This equation is modified slightly to take into account a variety of situations such as diffraction through a single gap, diffraction through multiple slits, or diffraction through a diffraction grating that contains a large number of slits at equal spacing.^[66] More complicated models of diffraction require working with the mathematics of Fresnel or Fraunhofer diffraction.^[67]

The size of such a disk is given by

$${\displaystyle \sin \theta =1.22{\frac {\lambda }{D}}}$$

where θ is the angular resolution, λ is the wavelength of the light, and D is the

Refractive processes take place in the physical optics limit, where the wavelength of light is similar to other distances, as a kind of scattering. The simplest type of scattering is

The separation of colours by a prism is an example of normal dispersion. At the surfaces of the prism, Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin(sin (θ) / n). Thus, blue light, with its higher refractive index, is bent more strongly than red light, resulting in the well-known rainbow pattern.^[41]

Material dispersion is often characterised by the Abbe number, which gives a simple measure of dispersion based on the index of refraction at three specific wavelengths. Waveguide dispersion is dependent on the propagation constant.^[74] Both kinds of dispersion cause changes in the group characteristics of the wave, the features of the wave packet that change with the same frequency as the amplitude of the electromagnetic wave. "Group velocity dispersion" manifests as a spreading-out of the signal "envelope" of the radiation and can be quantified with a group dispersion delay parameter:

$${\displaystyle D={\frac {1}{v_{\mathrm {g} }^{2}}}{\frac {dv_{\mathrm {g} }}{d\lambda }}}$$

where v_g is the group velocity.^[75] For a uniform medium, the group velocity is

$${\displaystyle v_{\mathrm {g} }=c\left(n-\lambda {\frac {dn}{d\lambda }}\right)^{-1}}$$

where n is the index of refraction and c is the speed of light in a vacuum.^[76] This gives a simpler form for the dispersion delay parameter:

$${\displaystyle D=-{\frac {\lambda }{c}}\,{\frac {d^{2}n}{d\lambda ^{2}}}.}$$

If D is less than zero, the medium is said to have positive dispersion or normal dispersion. If D is greater than zero, the medium has negative dispersion. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components slow down more than the lower frequency components. The pulse therefore becomes positively chirped, or up-chirped, increasing in frequency with time. This causes the spectrum coming out of a prism to appear with red light the least refracted and blue/violet light the most refracted. Conversely, if a pulse travels through an anomalously (negatively) dispersive medium, high-frequency components travel faster than the lower ones, and the pulse becomes negatively chirped, or down-chirped, decreasing in frequency with time.^[77]

The result of group velocity dispersion, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on

Linear

Circular

Elliptical polarisation

In the leftmost figure above, the x and y components of the light wave are in phase. In this case, the ratio of their strengths is constant, so the direction of the electric vector (the vector sum of these two components) is constant. Since the tip of the vector traces out a single line in the plane, this special case is called linear polarisation. The direction of this line depends on the relative amplitudes of the two components.^[80]

In the middle figure, the two orthogonal components have the same amplitudes and are 90° out of phase. In this case, one component is zero when the other component is at maximum or minimum amplitude. There are two possible phase relationships that satisfy this requirement: the x component can be 90° ahead of the y component or it can be 90° behind the y component. In this special case, the electric vector traces out a circle in the plane, so this polarisation is called circular polarisation. The rotation direction in the circle depends on which of the two-phase relationships exists and corresponds to right-hand circular polarisation and left-hand circular polarisation.^[81]

In all other cases, where the two components either do not have the same amplitudes and/or their phase difference is neither zero nor a multiple of 90°, the polarisation is called elliptical polarisation because the electric vector traces out an ellipse in the plane (the polarisation ellipse).^[82] This is shown in the above figure on the right. Detailed mathematics of polarisation is done using Jones calculus and is characterised by the Stokes parameters.^[83]

Changing polarisation

Media that have different indexes of refraction for different polarisation modes are called

Media that reduce the amplitude of certain polarisation modes are called dichroic, with devices that block nearly all of the radiation in one mode known as polarising filters or simply "

polarisers". Malus' law, which is named after Étienne-Louis Malus

, says that when a perfect polariser is placed in a linear polarised beam of light, the intensity, I, of the light that passes through is given by

$${\displaystyle I=I_{0}\cos ^{2}\theta _{\mathrm {i} },}$$

where I₀ is the initial intensity, and θ_i is the angle between the light's initial polarisation direction and the axis of the polariser.[88]

A beam of unpolarised light can be thought of as containing a uniform mixture of linear polarisations at all possible angles. Since the average value of cos² θ is 1/2, the transmission coefficient becomes

$${\displaystyle {\frac {I}{I_{0}}}={\frac {1}{2}}\,.}$$

In practice, some light is lost in the polariser and the actual transmission of unpolarised light will be somewhat lower than this, around 38% for Polaroid-type polarisers but considerably higher (>49.9%) for some birefringent prism types.^[89]

In addition to birefringence and dichroism in extended media, polarisation effects can also occur at the (reflective) interface between two materials of different refractive index. These effects are treated by the Fresnel equations. Part of the wave is transmitted and part is reflected, with the ratio depending on the angle of incidence and the angle of refraction. In this way, physical optics recovers Brewster's angle.^[90] When light reflects from a thin film on a surface, interference between the reflections from the film's surfaces can produce polarisation in the reflected and transmitted light.

Natural light

Most sources of electromagnetic radiation contain a large number of atoms or molecules that emit light. The orientation of the electric fields produced by these emitters may not be

correlated, in which case the light is said to be unpolarised. If there is partial correlation between the emitters, the light is partially polarised. If the polarisation is consistent across the spectrum of the source, partially polarised light can be described as a superposition of a completely unpolarised component, and a completely polarised one. One may then describe the light in terms of the degree of polarisation, and the parameters of the polarisation ellipse.^[79]

Light reflected by shiny transparent materials is partly or fully polarised, except when the light is normal (perpendicular) to the surface. It was this effect that allowed the mathematician Étienne-Louis Malus to make the measurements that allowed for his development of the first mathematical models for polarised light. Polarisation occurs when light is scattered in the

molecules.^[91]

Modern optics

Main articles:

Optical physics and Optical engineering

Modern optics encompasses the areas of optical science and engineering that became popular in the 20th century. These areas of optical science typically relate to the electromagnetic or quantum properties of light but do include other topics. A major subfield of modern optics,

quantum electronics.^[92]

Specialty areas of optics research include the study of how light interacts with specific materials as in

photonic computing as possible components of the "next generation" of computers.^[93]

Today, the pure science of optics is called optical science or

image processing. Some of these fields overlap, with nebulous boundaries between the subjects' terms that mean slightly different things in different parts of the world and in different areas of industry. A professional community of researchers in nonlinear optics has developed in the last several decades due to advances in laser technology.^[94]

Lasers

Main article: Laser

A laser is a device that emits light, a kind of electromagnetic radiation, through a process called stimulated emission. The term laser is an acronym for 'Light Amplification by Stimulated Emission of Radiation'.^[95] Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical components such as lenses. Because the microwave equivalent of the laser, the maser, was developed first, devices that emit microwave and radio frequencies are usually called masers.^[96]

The first working laser was demonstrated on 16 May 1960 by

holograms, bubblegrams, laser light shows, and laser hair removal.^[102]

Kapitsa–Dirac effect

The Kapitsa–Dirac effect causes beams of particles to diffract as the result of meeting a standing wave of light. Light can be used to position matter using various phenomena (see optical tweezers).

Applications

Optics is part of everyday life. The ubiquity of

cameras. Rainbows and mirages are examples of optical phenomena. Optical communication provides the backbone for both the Internet and modern telephony

.

Human eye

lens cortex, 22. optic nerve, 26. fovea, 30. retina

.

Main articles: Human eye and Photometry (optics)

The human eye functions by focusing light onto a layer of

vitreous humour, and reaches the retina. The cells in the retina line the back of the eye, except for where the optic nerve exits; this results in a blind spot

.

There are two types of photoreceptor cells, rods and cones, which are sensitive to different aspects of light.[103] Rod cells are sensitive to the intensity of light over a wide frequency range, thus are responsible for black-and-white vision. Rod cells are not present on the fovea, the area of the retina responsible for central vision, and are not as responsive as cone cells to spatial and temporal changes in light. There are, however, twenty times more rod cells than cone cells in the retina because the rod cells are present across a wider area. Because of their wider distribution, rods are responsible for peripheral vision.^[104]

In contrast, cone cells are less sensitive to the overall intensity of light, but come in three varieties that are sensitive to different frequency-ranges and thus are used in the perception of

colour and photopic vision. Cone cells are highly concentrated in the fovea and have a high visual acuity meaning that they are better at spatial resolution than rod cells. Since cone cells are not as sensitive to dim light as rod cells, most night vision is limited to rod cells. Likewise, since cone cells are in the fovea, central vision (including the vision needed to do most reading, fine detail work such as sewing, or careful examination of objects) is done by cone cells.^[104]

Ciliary muscles around the lens allow the eye's focus to be adjusted. This process is known as

ophthalmologists, and opticians usually consider an appropriate near point to be closer than normal reading distance—approximately 25 cm.^[103]

Defects in vision can be explained using optical principles. As people age, the lens becomes less flexible and the near point recedes from the eye, a condition known as

astigmatism results when the cornea is not spherical but instead is more curved in one direction. This causes horizontally extended objects to be focused on different parts of the retina than vertically extended objects, and results in distorted images.^[103]

All of these conditions can be corrected using

cylindrical surface lens that curves more strongly in one direction than in another, compensating for the non-uniformity of the cornea.^[105]

The optical power of corrective lenses is measured in

diopters, a value equal to the reciprocal of the focal length measured in metres; with a positive focal length corresponding to a converging lens and a negative focal length corresponding to a diverging lens. For lenses that correct for astigmatism as well, three numbers are given: one for the spherical power, one for the cylindrical power, and one for the angle of orientation of the astigmatism.^[105]

Visual effects

Main articles: Optical illusion and Perspective (graphical)

For the visual effects used in film, video, and computer graphics, see visual effects.

Optical illusions (also called visual illusions) are characterized by visually perceived images that differ from objective reality. The information gathered by the eye is processed in the brain to give a

percept that differs from the object being imaged. Optical illusions can be the result of a variety of phenomena including physical effects that create images that are different from the objects that make them, the physiological effects on the eyes and brain of excessive stimulation (e.g. brightness, tilt, colour, movement), and cognitive illusions where the eye and brain make unconscious inferences.^[106]

Cognitive illusions include some which result from the unconscious misapplication of certain optical principles. For example, the

Ptolemy that he incorrectly attributed it to atmospheric refraction when he described it in his treatise, Optics.^[8]

Another type of optical illusion exploits broken patterns to trick the mind into perceiving symmetries or asymmetries that are not present. Examples include the

transparent tissues with a grid structure produce shapes known as moiré patterns, while the superimposition of periodic transparent patterns comprising parallel opaque lines or curves produces line moiré patterns.^[109]

Optical instruments

The first telescopes, called refracting telescopes, were also developed with a single objective and eyepiece lens. In contrast to the microscope, the objective lens of the telescope was designed with a large focal length to avoid optical aberrations. The objective focuses an image of a distant object at its focal point which is adjusted to be at the focal point of an eyepiece of a much smaller focal length. The main goal of a telescope is not necessarily magnification, but rather the collection of light which is determined by the physical size of the objective lens. Thus, telescopes are normally indicated by the diameters of their objectives rather than by the magnification which can be changed by switching eyepieces. Because the magnification of a telescope is equal to the focal length of the objective divided by the focal length of the eyepiece, smaller focal-length eyepieces cause greater magnification.[113]

Since crafting large lenses is much more difficult than crafting large mirrors, most modern telescopes are reflecting telescopes, that is, telescopes that use a primary mirror rather than an objective lens. The same general optical considerations apply to reflecting telescopes that applied to refracting telescopes, namely, the larger the primary mirror, the more light collected, and the magnification is still equal to the focal length of the primary mirror divided by the focal length of the eyepiece. Professional telescopes generally do not have eyepieces and instead place an instrument (often a charge-coupled device) at the focal point instead.^[114]

Photography

The optics of photography involves both lenses and the medium in which the electromagnetic radiation is recorded, whether it be a

Exposure ∝ ApertureArea × ExposureTime × SceneLuminance[115]

In other words, the smaller the aperture (giving greater depth of focus), the less light coming in, so the length of time has to be increased (leading to possible blurriness if motion occurs). An example of the use of the law of reciprocity is the Sunny 16 rule which gives a rough estimate for the settings needed to estimate the proper exposure in daylight.^[116]

A camera's aperture is measured by a unitless number called the f-number or f-stop, f/#, often notated as ${\displaystyle N}$, and given by

${\displaystyle f/\#=N={\frac {f}{D}}\ }$

where ${\displaystyle f}$ is the focal length, and ${\displaystyle D}$ is the diameter of the entrance pupil. By convention, "f/#" is treated as a single symbol, and specific values of f/# are written by replacing the number sign with the value. The two ways to increase the f-stop are to either decrease the diameter of the entrance pupil or change to a longer focal length (in the case of a zoom lens, this can be done by simply adjusting the lens). Higher f-numbers also have a larger depth of field due to the lens approaching the limit of a pinhole camera which is able to focus all images perfectly, regardless of distance, but requires very long exposure times.^[117]

The field of view that the lens will provide changes with the focal length of the lens. There are three basic classifications based on the relationship to the diagonal size of the film or sensor size of the camera to the focal length of the lens:^[118]

• Normal lens: angle of view of about 50° (called normal because this angle considered roughly equivalent to human vision^[118]) and a focal length approximately equal to the diagonal of the film or sensor.^[119]
• Wide-angle lens: angle of view wider than 60° and focal length shorter than a normal lens.^[120]
• Long focus lens: angle of view narrower than a normal lens. This is any lens with a focal length longer than the diagonal measure of the film or sensor.^[121] The most common type of long focus lens is the telephoto lens, a design that uses a special telephoto group to be physically shorter than its focal length.^[122]

The absolute value for the exposure time required depends on how sensitive to light the medium being used is (measured by the film speed, or, for digital media, by the quantum efficiency).^[123] Early photography used media that had very low light sensitivity, and so exposure times had to be long even for very bright shots. As technology has improved, so has the sensitivity through film cameras and digital cameras.^[124]

Other results from physical and geometrical optics apply to camera optics. For example, the maximum resolution capability of a particular camera set-up is determined by the

The unique optical properties of the atmosphere cause a wide range of spectacular optical phenomena. The blue colour of the sky is a direct result of Rayleigh scattering which redirects higher frequency (blue) sunlight back into the field of view of the observer. Because blue light is scattered more easily than red light, the sun takes on a reddish hue when it is observed through a thick atmosphere, as during a

Mirages are optical phenomena in which light rays are bent due to thermal variations in the refraction index of air, producing displaced or heavily distorted images of distant objects. Other dramatic optical phenomena associated with this include the Novaya Zemlya effect where the sun appears to rise earlier than predicted with a distorted shape. A spectacular form of refraction occurs with a temperature inversion called the Fata Morgana where objects on the horizon or even beyond the horizon, such as islands, cliffs, ships or icebergs, appear elongated and elevated, like "fairy tale castles".^[127]

Rainbows are the result of a combination of internal reflection and dispersive refraction of light in raindrops. A single reflection off the backs of an array of raindrops produces a rainbow with an angular size on the sky that ranges from 40° to 42° with red on the outside. Double rainbows are produced by two internal reflections with angular size of 50.5° to 54° with violet on the outside. Because rainbows are seen with the sun 180° away from the centre of the rainbow, rainbows are more prominent the closer the sun is to the horizon.^[128]

See also

• Ion optics
• Important publications in optics
• List of optical topics
• List of textbooks in electromagnetism

References