Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics
Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties. Explanation of these effects requires quantum mechanics. When considering light's particle-like properties, the light is modelled as a collection of particles called "photons". Quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, and medicine (particularly ophthalmology and optometry). Practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics.
1 History 2 Classical optics
2.1 Geometrical optics
2.1.1 Approximations 2.1.2 Reflections 2.1.3 Refractions
2.2 Physical optics
2.2.1 Modelling and design of optical systems using physical optics
2.2.2 Superposition and interference
184.108.40.206 Changing polarization 220.127.116.11 Natural light
3 Modern optics
3.1 Lasers 3.2 Kapitsa–Dirac effect
4.1 Human eye
4.1.1 Visual effects 4.1.2 Optical instruments
4.2 Photography 4.3 Atmospheric optics
5 See also 6 References 7 External links
Main article: History of optics
See also: Timeline of electromagnetism and classical optics
The Nimrud lens
The first treatise about optics by Johannes Kepler, Ad Vitellionem
paralipomena quibus astronomiae pars optica traditur (1604)
In the early 17th century,
Cover of the first edition of Newton's
Classical optics is divided into two main branches: geometrical (or
ray) optics and physical (or wave) optics. In geometrical optics,
light is considered to travel in straight lines, while in physical
optics, light is considered as an electromagnetic wave.
Main article: Geometrical 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 refraction divided by the sine of the angle of incidence 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.
Main article: Reflection (physics)
Diagram of specular reflection
Reflections can be divided into two types: specular reflection and
Main article: Refraction
displaystyle n_ 1
and another medium with index of refraction
displaystyle n_ 2
. In such situations,
displaystyle n_ 1 sin theta _ 1 =n_ 2 sin theta _ 2
displaystyle theta _ 1
displaystyle theta _ 2
are the angles between the normal (to the interface) and the incident and refracted waves, respectively. The index of refraction of a medium is related to the speed, v, of light in that medium by
n = c
where c is the speed of light in vacuum.
displaystyle theta _ 2
displaystyle theta _ 1
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.
Lenses Main article: Lens (optics) A ray tracing diagram for a converging lens. A device which produces converging or diverging light rays due to refraction is known as a lens. Lenses are characterized by their focal length: a converging lens has positive focal length, while a diverging lens has negative focal length. Smaller focal length indicates that the lens has a stronger converging or diverging effect. The focal length of a simple lens in air is given by the lensmaker's equation. 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
displaystyle S_ 1
is the distance from the object to the lens,
displaystyle S_ 2
is the distance from the lens to the image, and
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.
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 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 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. 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.
Images of black letters in a thin convex lens of focal length
f are shown in red. Selected rays are shown for letters E, I and
K in blue, green and orange, respectively. Note that E (at 2f) has an
equal-size, real and inverted image; I (at f) has its image at
infinity; and K (at f/2) has a double-size, virtual and upright image.
Main article: Physical optics
In physical optics, light is considered to propagate as a wave. This
model predicts phenomena such as interference and diffraction, which
are not explained by geometric optics. The speed of light waves in air
is approximately 3.0×108 m/s (exactly 299,792,458 m/s in
vacuum). The wavelength of visible light waves varies between 400 and
700 nm, but the term "light" is also often applied to infrared
(0.7–300 μm) and ultraviolet radiation (10–400 nm).
The wave model can be used to make predictions about how an optical
system will behave without requiring an explanation of what is
"waving" in what medium. Until the middle of the 19th century, most
physicists believed in an "ethereal" medium in which the light
disturbance propagated. The existence of electromagnetic
waves was predicted in 1865 by Maxwell's equations. These waves
propagate at the speed of light and have varying electric and magnetic
fields which are orthogonal to one another, and also to the direction
of propagation of the waves.
Modelling and design of optical systems using physical optics
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
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
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
All of the results from geometrical optics can be recovered using the
Superposition and interference
Two waves in phase
Two waves 180° out of phase
When oil or fuel is spilled, colourful patterns are formed by
. The bright fringes occur along lines where black lines intersect with black lines and white lines intersect with white lines. These fringes are separated by angle
and are numbered as order
m λ = d sin θ
displaystyle mlambda =dsin theta
is the separation between two wavefront sources (in the case of Young's experiments, it was two slits),
is the angular separation between the central fringe and the
th order fringe, where the central maximum is
m = 0
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.
More complicated models of diffraction require working with the
mathematics of Fresnel or Fraunhofer diffraction.
being twice the spacing between atoms.
sin θ = 1.22
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 diameter of the lens aperture. If the angular separation
of the two points is significantly less than the
Dispersion and scattering
Dispersion: two sinusoids propagating at different speeds make a
moving interference pattern. The red dot moves with the phase
velocity, and the green dots propagate with the group velocity. In
this case, the phase velocity is twice the group velocity. The red dot
overtakes two green dots, when moving from the left to the right of
the figure. In effect, the individual waves (which travel with the
phase velocity) escape from the wave packet (which travels with the
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. 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. "
displaystyle D= frac 1 v_ g ^ 2 frac dv_ g dlambda
displaystyle v_ g
is the group velocity. For a uniform medium, the group velocity is
n − λ
displaystyle v_ g =cleft(n-lambda frac dn dlambda right)^ -1
where n is the index of refraction and c is the speed of light in a vacuum. This gives a simpler form for the dispersion delay parameter:
D = −
displaystyle D=- frac lambda c , frac d^ 2 n dlambda ^ 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. 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 optical fibres, since if dispersion is too high, a group of pulses representing information will each spread in time and merge, making it impossible to extract the signal.
Polarization Main article: Polarization (waves) Polarization is a general property of waves that describes the orientation of their oscillations. For transverse waves such as many electromagnetic waves, it describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel. The oscillations may be oriented in a single direction (linear polarization), or the oscillation direction may rotate as the wave travels (circular or elliptical polarization). Circularly polarised waves can rotate rightward or leftward in the direction of travel, and which of those two rotations is present in a wave is called the wave's chirality. The typical way to consider polarization is to keep track of the orientation of the electric field vector as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). The shape traced out in the x-y plane by the electric field vector is a Lissajous figure that describes the polarization state. The following figures show some examples of the evolution of the electric field vector (blue), with time (the vertical axes), at a particular point in space, along with its x and y components (red/left and green/right), and the path traced by the vector in the plane (purple): The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation.
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 polarization. The direction of this line depends on the relative amplitudes of the two components. 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 polarization is called circular polarization. The rotation direction in the circle depends on which of the two phase relationships exists and corresponds to right-hand circular polarization and left-hand circular polarization. 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 polarization is called elliptical polarization because the electric vector traces out an ellipse in the plane (the polarization ellipse). This is shown in the above figure on the right. Detailed mathematics of polarization is done using Jones calculus and is characterised by the Stokes parameters.
Media that have different indexes of refraction for different
polarization modes are called birefringent. Well known
manifestations of this effect appear in optical wave plates/retarders
(linear modes) and in Faraday rotation/optical rotation (circular
modes). If the path length in the birefringent medium is
sufficient, plane waves will exit the material with a significantly
different propagation direction, due to refraction. For example, this
is the case with macroscopic crystals of calcite, which present the
viewer with two offset, orthogonally polarised images of whatever is
viewed through them. It was this effect that provided the first
discovery of polarization, by
A polariser changing the orientation of linearly polarised light. In this picture, θ1 – θ0 = θi. Media that reduce the amplitude of certain polarization modes are called dichroic, with devices that block nearly all of the radiation in one mode known as polarizing 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 _ i quad ,
I0 is the initial intensity, and θi is the angle between the light's initial polarization direction and the axis of the polariser. A beam of unpolarised light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. Since the average value of
displaystyle cos ^ 2 theta
is 1/2, the transmission coefficient becomes
displaystyle frac I I_ 0 = frac 1 2 quad
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. In addition to birefringence and dichroism in extended media, polarization 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 angle of incidence and the angle of refraction. In this way, physical optics recovers Brewster's angle. When light reflects from a thin film on a surface, interference between the reflections from the film's surfaces can produce polarization in the reflected and transmitted light.
The effects of a polarising filter on the sky in a photograph. Left
picture is taken without polariser. For the right picture, filter was
adjusted to eliminate certain polarizations of the scattered blue
light from the sky.
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
polarization 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 polarization,
and the parameters of the polarization ellipse.
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 optics, deals with specifically quantum mechanical
properties of light.
Quantum optics is not just theoretical; some
modern devices, such as lasers, have principles of operation that
depend on quantum mechanics.
Main article: Laser
Experiments such as this one with high-power lasers are part of the
modern optics research.
A laser is a device that emits light (electromagnetic radiation)
through a process called stimulated emission. The term laser is an
VLT’s laser guided star.
The first working laser was demonstrated on 16 May 1960 by Theodore
Maiman at Hughes Research Laboratories. When first
invented, they were called "a solution looking for a
problem". Since then, lasers have become a
multibillion-dollar industry, finding utility in thousands of highly
varied applications. The first application of lasers visible in the
daily lives of the general population was the supermarket barcode
scanner, introduced in 1974. The laserdisc player,
introduced in 1978, was the first successful consumer product to
include a laser, but the compact disc player was the first
laser-equipped device to become truly common in consumers' homes,
beginning in 1982. These optical storage devices use a
semiconductor laser less than a millimetre wide to scan the surface of
the disc for data retrieval.
Kapitsa–Dirac effect causes beams of particles to diffract as
the result of meeting a standing wave of light.
Model of a human eye. Features mentioned in this article are 3.
ciliary muscle, 6. pupil, 8. cornea, 10. lens cortex, 22. optic nerve,
26. fovea, 30. retina
Optical instruments Illustrations of various optical instruments from the 1728 Cyclopaedia Main article: Optical instruments Single lenses have a variety of applications including photographic lenses, corrective lenses, and magnifying glasses while single mirrors are used in parabolic reflectors and rear-view mirrors. Combining a number of mirrors, prisms, and lenses produces compound optical instruments which have practical uses. For example, a periscope is simply two plane mirrors aligned to allow for viewing around obstructions. The most famous compound optical instruments in science are the microscope and the telescope which were both invented by the Dutch in the late 16th century. Microscopes were first developed with just two lenses: an objective lens and an eyepiece. The objective lens is essentially a magnifying glass and was designed with a very small focal length while the eyepiece generally has a longer focal length. This has the effect of producing magnified images of close objects. Generally, an additional source of illumination is used since magnified images are dimmer due to the conservation of energy and the spreading of light rays over a larger surface area. Modern microscopes, known as compound microscopes have many lenses in them (typically four) to optimize the functionality and enhance image stability. A slightly different variety of microscope, the comparison microscope, looks at side-by-side images to produce a stereoscopic binocular view that appears three dimensional when used by humans. 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 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. 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.
Photography Main article: Science of photography Photograph taken with aperture f/32 Photograph taken with aperture f/5 The optics of photography involves both lenses and the medium in which the electromagnetic radiation is recorded, whether it be a plate, film, or charge-coupled device. Photographers must consider the reciprocity of the camera and the shot which is summarized by the relation
Exposure ∝ ApertureArea × ExposureTime × SceneLuminance 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. A camera's aperture is measured by a unitless number called the f-number or f-stop, f/#, often notated as
, and given by
# = N =
displaystyle f/#=N= frac f D
is the focal length, and
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. 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:
Normal lens: angle of view of about 50° (called normal because this angle considered roughly equivalent to human vision) and a focal length approximately equal to the diagonal of the film or sensor. Wide-angle lens: angle of view wider than 60° and focal length shorter than a normal lens. 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. 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. Modern zoom lenses may have some or all of these attributes. 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). 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. 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 diffraction limit associated with the pupil size and given, roughly, by the Rayleigh criterion.
Main article: Atmospheric optics
A colourful sky is often due to scattering of light off particulates
and pollution, as in this photograph of a sunset during the October
2007 California wildfires.
The unique optical properties of the atmosphere cause a wide range of
spectacular optical phenomena. The blue colour of the sky is a direct
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^ "World's oldest telescope?".
^ T.F. Hoad (1996). The Concise Oxford Dictionary of English Etymology. ISBN 978-0-19-283098-2.
^ A History Of The Eye Archived 2012-01-20 at the Wayback Machine. stanford.edu. Retrieved 2012-06-10.
^ T.L. Heath (2003). A manual of greek mathematics. Courier Dover Publications. pp. 181–182. ISBN 978-0-486-43231-1.
^ William R. Uttal (1983). Visual Form Detection in 3-Dimensional Space. Psychology Press. pp. 25–. ISBN 978-0-89859-289-4. Archived from the original on 2016-05-03.
^ a b
^ Verma, RL (1969), Al-Hazen: father of modern optics
^ Adamson, Peter (2006). "Al-Kindi¯ and the reception of Greek philosophy". In Adamson, Peter; Taylor, R.. The Cambridge companion to Arabic philosophy. Cambridge University Press. p. 45. ISBN 978-0-521-52069-0.
^ a b Rashed, Roshdi (1990). "A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses". Isis. 81 (3): 464–491. doi:10.1086/355456. JSTOR 233423.
^ Hogendijk, Jan P.; Sabra, Abdelhamid I., eds. (2003). The Enterprise of Science in Islam: New Perspectives. MIT Press. pp. 85–118. ISBN 978-0-262-19482-2. OCLC 50252039.
^ G. Hatfield (1996). "Was the Scientific Revolution Really a Revolution in Science?". In F.J. Ragep; P. Sally; S.J. Livesey (eds.). Tradition, Transmission, Transformation: Proceedings of Two Conferences on Pre-modern Science held at the University of Oklahoma. Brill Publishers. p. 500. ISBN 978-90-04-10119-7. Archived from the original on 2016-04-27.
^ G. Simon (2006). "The Gaze in Ibn al-Haytham". The Medieval History Journal. 9: 89. doi:10.1177/097194580500900105.
^ Ian P. Howard; Brian J. Rogers (1995). Binocular Vision and Stereopsis. Oxford University Press. p. 7. ISBN 978-0-19-508476-4. Archived from the original on 2016-05-06.
^ Elena Agazzi; Enrico Giannetto; Franco Giudice (2010). Representing
^ El-Bizri, Nader (2010). "Classical
^ D.C. Lindberg, Theories of Vision from al-Kindi to Kepler, (Chicago: Univ. of Chicago Pr., 1976), pp. 94–99.
^ Vincent, Ilardi (2007). Renaissance Vision from Spectacles to Telescopes. Philadelphia, PA: American Philosophical Society. pp. 4–5. ISBN 978-0-87169-259-7.
^ "The Galileo Project > Science > The Telescope" by Al Van Helden Archived 2012-03-20 at the Wayback Machine. Galileo.rice.edu. Retrieved 2012-06-10.
^ Henry C. King (2003). The History of the Telescope. Courier Dover Publications. p. 27. ISBN 978-0-486-43265-6. Archived from the original on 2016-06-17.
^ Paul S. Agutter; Denys N. Wheatley (2008). Thinking about Life: The History and Philosophy of Biology and Other Sciences. Springer. p. 17. ISBN 978-1-4020-8865-0. Archived from the original on 2016-05-16.
^ Ilardi, Vincent (2007). Renaissance Vision from Spectacles to Telescopes. American Philosophical Society. p. 210. ISBN 978-0-87169-259-7. Archived from the original on 2016-05-03.
^ Microscopes: Time Line Archived 2010-01-09 at the Wayback Machine, Nobel Foundation. Retrieved April 3, 2009
^ Watson, Fred (2007). Stargazer: The Life and Times of the Telescope. Allen & Unwin. p. 55. ISBN 978-1-74175-383-7. Archived from the original on 2016-05-08.
^ Ilardi, Vincent (2007). Renaissance Vision from Spectacles to Telescopes. American Philosophical Society. p. 244. ISBN 978-0-87169-259-7. Archived from the original on 2016-05-26.
^ Caspar, Kepler, pp. 198–202 Archived 2016-05-07 at the Wayback Machine, Courier Dover Publications, 1993, ISBN 0-486-67605-6.
^ a b A.I. Sabra (1981). Theories of light, from Descartes to Newton. CUP Archive. ISBN 978-0-521-28436-3.
^ W.F. Magie (1935). A Source Book in Physics. Harvard University Press. p. 309.
^ J.C. Maxwell (1865). "A Dynamical Theory of the Electromagnetic Field". Philosophical Transactions of the Royal Society of London. 155: 459. Bibcode:1865RSPT..155..459C. doi:10.1098/rstl.1865.0008.
^ For a solid approach to the complexity of Planck's intellectual
motivations for the quantum, for his reluctant acceptance of its
implications, see H. Kragh, Max Planck: the reluctant revolutionary,
^ Einstein, A. (1967). "On a heuristic viewpoint concerning the production and transformation of light". In Ter Haar, D. (ed.). The Old Quantum Theory. Pergamon. pp. 91–107. OCLC 534625. The chapter is an English translation of Einstein's 1905 paper on the photoelectric effect.
^ Einstein, A. (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" [On a heuristic viewpoint concerning the production and transformation of light]. Annalen der Physik (in German). 322 (6): 132–148. Bibcode:1905AnP...322..132E. doi:10.1002/andp.19053220607.
^ "On the Constitution of Atoms and Molecules". Philosophical Magazine. 26, Series 6: 1–25. 1913. Archived from the original on July 4, 2007.. The landmark paper laying the Bohr model of the atom and molecular bonding.
^ R. Feynman (1985). "Chapter 1". QED: The Strange Theory of
^ N. Taylor (2000). LASER: The inventor, the Nobel laureate, and the thirty-year patent war. New York: Simon & Schuster. ISBN 978-0-684-83515-0.
^ Ariel Lipson; Stephen G. Lipson; Henry Lipson (28 October 2010). Optical Physics. Cambridge University Press. p. 48. ISBN 978-0-521-49345-1. Archived from the original on 28 May 2013. Retrieved 12 July 2012.
^ Arthur Schuster (1904). An Introduction to the Theory of Optics. E. Arnold. p. 41. Archived from the original on 2016-05-13.
^ J.E. Greivenkamp (2004). Field Guide to Geometrical Optics. SPIE Field Guides vol. FG01. SPIE. pp. 19–20. ISBN 978-0-8194-5294-8.
^ a b c d e f g h i j Young, H.D. (1992). University Physics: Extended
Version With Modern
^ Marchand, E.W. (1978). Gradient Index Optics. New York: Academic Press.
^ a b c d e f g h i j k l m E. Hecht (1987).
^ MV Klein & TE Furtak, 1986, Optics, John Wiley & Sons, New York ISBN 0-471-87297-0.
^ Maxwell, James Clerk (1865). "A dynamical theory of the electromagnetic field" (PDF). Philosophical Transactions of the Royal Society of London. 155: 499. doi:10.1098/rstl.1865.0008. Archived (PDF) from the original on 2011-07-28. This article accompanied a December 8, 1864 presentation by Maxwell to the Royal Society. See also A dynamical theory of the electromagnetic field.
^ M. Born and E. Wolf (1999). Principle of Optics. Cambridge: Cambridge University Press. ISBN 0-521-64222-1.
^ J. Goodman (2005). Introduction to Fourier
^ A.E. Siegman (1986). Lasers. University Science Books. ISBN 978-0-935702-11-8. Chapter 16.
^ a b c d H.D. Young (1992). University
^ a b P. Hariharan (2003). Optical
^ E.R. Hoover (1977). Cradle of Greatness: National and World Achievements of Ohio's Western Reserve. Cleveland: Shaker Savings Association.
^ J.L. Aubert (1760). Memoires pour l'histoire des sciences et des beaux arts. Paris: Impr. de S.A.S.; Chez E. Ganeau. p. 149.
^ D. Brewster (1831). A Treatise on Optics. London: Longman, Rees, Orme, Brown & Green and John Taylor. p. 95.
^ R. Hooke (1665). Micrographia: or, Some physiological descriptions of minute bodies made by magnifying glasses. London: J. Martyn and J. Allestry. ISBN 978-0-486-49564-4.
^ H.W. Turnbull (1940–1941). "Early Scottish Relations with the Royal Society: I. James Gregory, F.R.S. (1638–1675)". Notes and Records of the Royal Society of London. 3: 22–38. doi:10.1098/rsnr.1940.0003. JSTOR 531136.
^ T. Rothman (2003). Everything's Relative and Other Fables in Science and Technology. New Jersey: Wiley. ISBN 978-0-471-20257-8.
^ a b c d H.D. Young (1992). University
^ R.S. Longhurst (1968). Geometrical and Physical Optics, 2nd Edition. London: Longmans. Bibcode:1967gpo..book.....L.
^ a b J.D. Jackson (1975). Classical Electrodynamics (2nd ed.). Wiley. p. 286. ISBN 978-0-471-43132-9.
^ a b R. Ramaswami; K.N. Sivarajan (1998). Optical Networks: A Practical Perspective. London: Academic Press. ISBN 978-0-12-374092-2. Archived from the original on 2015-10-27.
^ Brillouin, Léon.
^ M. Born & E. Wolf (1999). Principle of Optics. Cambridge: Cambridge University Press. pp. 14–24. ISBN 978-0-521-64222-4.
^ a b c d e f H.D. Young (1992). University
^ D.F. Walls and G.J. Milburn Quantum
^ Alastair D. McAulay (16 January 1991). Optical computer architectures: the application of optical concepts to next generation computers. Wiley. ISBN 978-0-471-63242-9. Archived from the original on 29 May 2013. Retrieved 12 July 2012.
^ Y.R. Shen (1984). The principles of nonlinear optics. New York, Wiley-Interscience. ISBN 978-0-471-88998-4.
^ "laser". Reference.com. Archived from the original on 2008-03-31. Retrieved 2008-05-15.
^ Charles H. Townes – Nobel Lecture Archived 2008-10-11 at the Wayback Machine. nobelprize.org
^ "The VLT's Artificial Star". ESO Picture of the Week. Archived from the original on 3 July 2014. Retrieved 25 June 2014.
^ C.H. Townes. "The first laser". University of Chicago. Archived from the original on 2008-05-17. Retrieved 2008-05-15.
^ C.H. Townes (2003). "The first laser". In Laura Garwin; Tim Lincoln (eds.). A Century of Nature: Twenty-One Discoveries that Changed Science and the World. University of Chicago Press. pp. 107–112. ISBN 978-0-226-28413-2.
^ What is a bar code? Archived 2012-04-23 at the Wayback Machine denso-wave.com
^ "How the CD was developed".
^ J. Wilson & J.F.B. Hawkes (1987). Lasers: Principles and Applications, Prentice Hall International Series in Optoelectronics. Prentice Hall. ISBN 978-0-13-523697-0.
^ a b c D. Atchison & G. Smith (2000).
^ a b E.R. Kandel; J.H. Schwartz; T.M. Jessell (2000). Principles of Neural Science (4th ed.). New York: McGraw-Hill. pp. 507–513. ISBN 978-0-8385-7701-1.
^ a b D. Meister. "Ophthalmic Lens Design". OptiCampus.com. Archived from the original on December 27, 2008. Retrieved November 12, 2008.
^ J. Bryner (2008-06-02). "Key to All Optical Illusions Discovered". LiveScience.com. Archived from the original on 2008-09-05.
^ "The Moon Illusion Explained" Archived 2015-12-04 at the Wayback Machine, Don McCready, University of Wisconsin-Whitewater
^ A.K. Jain; M. Figueiredo; J. Zerubia (2001). Energy Minimization Methods in Computer Vision and Pattern Recognition. Springer. ISBN 978-3-540-42523-6.
^ a b c d H.D. Young (1992). "36". University
^ P.E. Nothnagle; W. Chambers; M.W. Davidson. "Introduction to Stereomicroscopy". Nikon MicroscopyU. Archived from the original on 2011-09-16.
^ Samuel Edward Sheppard & Charles Edward Kenneth Mees (1907). Investigations on the Theory of the Photographic Process. Longmans, Green and Co. p. 214.
^ B.J. Suess (2003). Mastering Black-and-White Photography. Allworth Communications. ISBN 978-1-58115-306-4.
^ M.J. Langford (2000). Basic Photography. Focal Press. ISBN 978-0-240-51592-2.
^ a b Warren, Bruce (2001). Photography. Cengage Learning. p. 71. ISBN 978-0-7668-1777-7. Archived from the original on 2016-08-19.
^ Leslie D. Stroebel (1999). View Camera Technique. Focal Press. ISBN 978-0-240-80345-6.
^ S. Simmons (1992). Using the View Camera. Amphoto Books. p. 35. ISBN 978-0-8174-6353-3.
^ Sidney F. Ray (2002). Applied Photographic Optics: Lenses and Optical Systems for Photography, Film, Video, Electronic and Digital Imaging. Focal Press. p. 294. ISBN 978-0-240-51540-3. Archived from the original on 2016-08-19.
^ New York Times Staff (2004). The New York Times Guide to Essential Knowledge. Macmillan. ISBN 978-0-312-31367-8.
^ R.R. Carlton; A. McKenna Adler (2000). Principles of Radiographic Imaging: An Art and a Science. Thomson Delmar Learning. ISBN 978-0-7668-1300-7.
^ W. Crawford (1979). The Keepers of Light: A History and Working Guide to Early Photographic Processes. Dobbs Ferry, NY: Morgan & Morgan. p. 20. ISBN 978-0-87100-158-0.
^ J.M. Cowley (1975).
^ C.D. Ahrens (1994). Meteorology Today: an introduction to weather, climate, and the environment (5th ed.). West Publishing Company. pp. 88–89. ISBN 978-0-314-02779-5.
^ A. Young. "An Introduction to Mirages". Archived from the original on 2010-01-10.
Born, Max; Wolf, Emil (2002). Principles of Optics. Cambridge
University Press. ISBN 978-1-139-64340-5.
Hecht, Eugene (2002).
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