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 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.
== History ==
Optics began with the development of lenses
by the ancient Egyptians and Mesopotamians.
The earliest known lenses, made from polished
crystal, often quartz, date from as early
as 700 BC for Assyrian lenses such as the
Layard/Nimrud lens. The ancient Romans and
Greeks filled glass spheres with water to
make lenses. These practical developments
were followed by the development of theories
of light and vision by ancient Greek and Indian
philosophers, and the development of geometrical
optics in the Greco-Roman world. The word
optics comes from the ancient Greek word ὀπτική
(optikē), meaning "appearance, look".Greek
philosophy on optics broke down into two opposing
theories on how vision worked, the "intromission
theory" and the "emission theory". The intro-mission
approach saw vision as coming from objects
casting off copies of themselves (called eidola)
that were captured by the eye. With many propagators
including Democritus, Epicurus, Aristotle
and their followers, this theory seems to
have some contact with modern theories of
what vision really is, but it remained only
speculation lacking any experimental foundation.
Plato first articulated the emission theory,
the idea that visual perception is accomplished
by rays emitted by the eyes. He also commented
on the parity reversal of mirrors in Timaeus.
Some hundred years later, Euclid wrote a treatise
entitled Optics where he linked vision to
geometry, creating geometrical optics. He
based his work on Plato's emission theory
wherein he described the mathematical rules
of perspective and described the effects of
refraction qualitatively, although he questioned
that a beam of light from the eye could instantaneously
light up the stars every time someone blinked.
Ptolemy, in his treatise Optics, held an extramission-intromission
theory of vision: the rays (or flux) from
the eye formed a cone, the vertex being within
the eye, and the base defining the visual
field. The rays were sensitive, and conveyed
information back to the observer’s intellect
about the distance and orientation of surfaces.
He summarised much of Euclid and went on to
describe a way to measure the angle of refraction,
though he failed to notice the empirical relationship
between it and the angle of incidence.
During the Middle Ages, Greek ideas about
optics were resurrected and extended by writers
in the Muslim world. One of the earliest of
these was Al-Kindi (c. 801–73) who wrote
on the merits of Aristotelian and Euclidean
ideas of optics, favouring the emission theory
since it could better quantify optical phenomena.
In 984, the Persian mathematician Ibn Sahl
wrote the treatise "On burning mirrors and
lenses", correctly describing a law of refraction
equivalent to Snell's law. He used this law
to compute optimum shapes for lenses and curved
mirrors. In the early 11th century, Alhazen
(Ibn al-Haytham) wrote the Book of Optics
(Kitab al-manazir) in which he explored reflection
and refraction and proposed a new system for
explaining vision and light based on observation
and experiment. He rejected the "emission
theory" of Ptolemaic optics with its rays
being emitted by the eye, and instead put
forward the idea that light reflected in all
directions in straight lines from all points
of the objects being viewed and then entered
the eye, although he was unable to correctly
explain how the eye captured the rays. Alhazen's
work was largely ignored in the Arabic world
but it was anonymously translated into Latin
around 1200 A.D. and further summarised and
expanded on by the Polish monk Witelo making
it a standard text on optics in Europe for
the next 400 years.In the 13th century in
medieval Europe, English bishop Robert Grosseteste
wrote on a wide range of scientific topics,
and discussed light from four different perspectives:
an epistemology of light, a metaphysics or
cosmogony of light, an etiology or physics
of light, and a theology of light, basing
it on the works Aristotle and Platonism. Grosseteste's
most famous disciple, Roger Bacon, wrote works
citing a wide range of recently translated
optical and philosophical works, including
those of Alhazen, Aristotle, Avicenna, Averroes,
Euclid, al-Kindi, Ptolemy, Tideus, and Constantine
the African. Bacon was able to use parts of
glass spheres as magnifying glasses to demonstrate
that light reflects from objects rather than
being released from them.
The first wearable eyeglasses were invented
in Italy around 1286.
This was the start of the optical industry
of grinding and polishing lenses for these
"spectacles", first in Venice and Florence
in the thirteenth century, and later in the
spectacle making centres in both the Netherlands
and Germany. Spectacle makers created improved
types of lenses for the correction of vision
based more on empirical knowledge gained from
observing the effects of the lenses rather
than using the rudimentary optical theory
of the day (theory which for the most part
could not even adequately explain how spectacles
worked). This practical development, mastery,
and experimentation with lenses led directly
to the invention of the compound optical microscope
around 1595, and the refracting telescope
in 1608, both of which appeared in the spectacle
making centres in the Netherlands.In the early
17th century Johannes Kepler expanded on geometric
optics in his writings, covering lenses, reflection
by flat and curved mirrors, the principles
of pinhole cameras, inverse-square law governing
the intensity of light, and the optical explanations
of astronomical phenomena such as lunar and
solar eclipses and astronomical parallax.
He was also able to correctly deduce the role
of the retina as the actual organ that recorded
images, finally being able to scientifically
quantify the effects of different types of
lenses that spectacle makers had been observing
over the previous 300 years. After the invention
of the telescope Kepler set out the theoretical
basis on how they worked and described an
improved version, known as the Keplerian telescope,
using two convex lenses to produce higher
magnification.
Optical theory progressed in the mid-17th
century with treatises written by philosopher
René Descartes, which explained a variety
of optical phenomena including reflection
and refraction by assuming that light was
emitted by objects which produced it. This
differed substantively from the ancient Greek
emission theory. In the late 1660s and early
1670s, Isaac Newton expanded Descartes' ideas
into a corpuscle theory of light, famously
determining that white light was a mix of
colours which can be separated into its component
parts with a prism. In 1690, Christiaan Huygens
proposed a wave theory for light based on
suggestions that had been made by Robert Hooke
in 1664. Hooke himself publicly criticised
Newton's theories of light and the feud between
the two lasted until Hooke's death. In 1704,
Newton published Opticks and, at the time,
partly because of his success in other areas
of physics, he was generally considered to
be the victor in the debate over the nature
of light.Newtonian optics was generally accepted
until the early 19th century when Thomas Young
and Augustin-Jean Fresnel conducted experiments
on the interference of light that firmly established
light's wave nature. Young's famous double
slit experiment showed that light followed
the law of superposition, which is a wave-like
property not predicted by Newton's corpuscle
theory. This work led to a theory of diffraction
for light and opened an entire area of study
in physical optics. Wave optics was successfully
unified with electromagnetic theory by James
Clerk Maxwell in the 1860s.The next development
in optical theory came in 1899 when Max Planck
correctly modelled blackbody radiation by
assuming that the exchange of energy between
light and matter only occurred in discrete
amounts he called quanta. In 1905 Albert Einstein
published the theory of the photoelectric
effect that firmly established the quantization
of light itself. In 1913 Niels Bohr showed
that atoms could only emit discrete amounts
of energy, thus explaining the discrete lines
seen in emission and absorption spectra. The
understanding of the interaction between light
and matter which followed from these developments
not only formed the basis of quantum optics
but also was crucial for the development of
quantum mechanics as a whole. The ultimate
culmination, the theory of quantum electrodynamics,
explains all optics and electromagnetic processes
in general as the result of the exchange of
real and virtual photons.Quantum optics gained
practical importance with the inventions of
the maser in 1953 and of the laser in 1960.
Following the work of Paul Dirac in quantum
field theory, George Sudarshan, Roy J. Glauber,
and Leonard Mandel applied quantum theory
to the electromagnetic field in the 1950s
and 1960s to gain a more detailed understanding
of photodetection and the statistics of light.
== Classical optics ==
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.
Geometrical optics can be viewed as an approximation
of physical optics that applies when the wavelength
of the light used is much smaller than the
size of the optical elements in the system
being modelled.
=== Geometrical optics ===
Geometrical optics, or ray optics, describes
the propagation of light in terms of "rays"
which travel in straight lines, and whose
paths are governed by the laws of reflection
and refraction at interfaces between different
media. These laws were discovered empirically
as far back as 984 AD and have been used in
the design of optical components and instruments
from then until the present day. They can
be summarised as follows:
When a ray of light hits the boundary between
two transparent materials, it is divided into
a reflected and a refracted ray.
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:
sin
⁡
θ
1
sin
⁡
θ
2
=
n
{\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.
==== 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.
==== 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 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 surface normal,
a line perpendicular to the surface at the
point where the ray hits. The incident and
reflected rays and the normal lie in a single
plane, and the angle between the reflected
ray and the surface normal is the same as
that between the incident ray and the normal.
This is known as the Law of Reflection.
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 retroreflect light, producing
reflected rays that travel back in the direction
from which the incident rays came.
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 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.
==== 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 interface
between a uniform medium with index of refraction
n
1
{\displaystyle n_{1}}
and another medium with index of refraction
n
2
{\displaystyle n_{2}}
. In such situations, Snell's Law describes
the resulting deflection of the light ray:
n
1
sin
⁡
θ
1
=
n
2
sin
⁡
θ
2
{\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin
\theta _{2}\ }
where
θ
1
{\displaystyle \theta _{1}}
and
θ
2
{\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
/
v
{\displaystyle n=c/v}
,where c is the speed of light in vacuum.
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. Taking this into account, Snell's Law
can be used to predict how a prism will disperse
light into a spectrum. 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 index of refraction
are called gradient-index (GRIN) materials.
Such materials are used to make gradient-index
optics.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
θ
2
{\displaystyle \theta _{2}}
when
θ
1
{\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 =====
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
1
S
1
+
1
S
2
=
1
f
{\displaystyle {\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}={\frac
{1}{f}}}
,where
S
1
{\displaystyle S_{1}}
is the distance from the object to the lens,
S
2
{\displaystyle S_{2}}
is the distance from the lens to the image,
and
f
{\displaystyle 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.
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.
=== 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.
Light waves are now generally treated as electromagnetic
waves except when quantum mechanical effects
have to be considered.
==== 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 vectors.
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 sections 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
the detailed interaction of light with materials
where the interaction depends on their electric
and magnetic properties. 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.All
of the results from geometrical optics can
be recovered using the techniques of Fourier
optics which apply many of the same mathematical
and analytical techniques used in acoustic
engineering and signal processing.
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.
==== Superposition and interference ====
In the absence of nonlinear effects, the superposition
principle can be used to predict the shape
of interacting waveforms through the simple
addition of the disturbances. This interaction
of waves to produce a resulting pattern is
generally termed "interference" and can result
in a variety of outcomes. If two waves of
the same wavelength and frequency are in phase,
both the wave crests and wave troughs align.
This results in constructive interference
and an increase in the amplitude of the wave,
which for light is associated with a brightening
of the waveform in that location. Alternatively,
if the two waves of the same wavelength and
frequency are out of phase, then the wave
crests will align with wave troughs and vice
versa. This results in destructive interference
and a decrease in the amplitude of the wave,
which for light is associated with a dimming
of the waveform at that location. See below
for an illustration of this effect.
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.
Interferometry is the science of measuring
these patterns, usually as a means of making
precise determinations of distances or angular
resolutions. The Michelson interferometer
was a famous instrument which used interference
effects to accurately measure the speed of
light.The appearance of thin films and coatings
is directly affected by interference effects.
Antireflective coatings use destructive interference
to reduce the reflectivity of the surfaces
they coat, and can be used to minimise glare
and unwanted reflections. The simplest case
is a single layer with thickness one-fourth
the wavelength of incident light. The reflected
wave from the top of the film and the reflected
wave from the film/material interface are
then exactly 180° out of phase, causing destructive
interference. The waves are only exactly out
of phase for one wavelength, which would typically
be chosen to be near the centre of the visible
spectrum, around 550 nm. More complex designs
using multiple layers can achieve low reflectivity
over a broad band, or extremely low reflectivity
at a single wavelength.
Constructive interference in thin films can
create 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 dielectric mirrors,
interference filters, heat reflectors, and
filters for colour separation in colour television
cameras. This interference effect is also
what causes the colourful rainbow patterns
seen in oil slicks.
==== Diffraction and optical resolution ====
Diffraction is the process by which light
interference is most commonly observed. The
effect was first described in 1665 by Francesco
Maria Grimaldi, who also coined the term from
the Latin diffringere, 'to break into pieces'.
Later that century, Robert Hooke and Isaac
Newton also described phenomena now known
to be diffraction in Newton's rings while
James Gregory recorded his observations of
diffraction patterns from bird feathers.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. In 1815 and
1818, Augustin-Jean Fresnel firmly established
the mathematics of how wave interference can
account for diffraction.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
m
λ
=
d
sin
⁡
θ
{\displaystyle m\lambda =d\sin \theta }
where
d
{\displaystyle d}
is the separation between two wavefront sources
(in the case of Young's experiments, it was
two slits),
θ
{\displaystyle \theta }
is the angular separation between the central
fringe and the
m
{\displaystyle m}
th order fringe, where the central maximum
is
m
=
0
{\displaystyle 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.X-ray
diffraction makes use of the fact that atoms
in a crystal have regular spacing at distances
that are on the order of one angstrom. To
see diffraction patterns, x-rays with similar
wavelengths to that spacing are passed through
the crystal. Since crystals are three-dimensional
objects rather than two-dimensional gratings,
the associated diffraction pattern varies
in two directions according to Bragg reflection,
with the associated bright spots occurring
in unique patterns and
d
{\displaystyle d}
being twice the spacing between atoms.Diffraction
effects limit the ability for an optical detector
to optically resolve separate light sources.
In general, light that is passing through
an aperture will experience diffraction and
the best images that can be created (as described
in diffraction-limited optics) appear as a
central spot with surrounding bright rings,
separated by dark nulls; this pattern is known
as an Airy pattern, and the central bright
lobe as an Airy disk. The size of such a disk
is given by
sin
⁡
θ
=
1.22
λ
D
{\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 Airy disk angular radius, then
the two points cannot be resolved in the image,
but if their angular separation is much greater
than this, distinct images of the two points
are formed and they can therefore be resolved.
Rayleigh defined the somewhat arbitrary "Rayleigh
criterion" that two points whose angular separation
is equal to the Airy disk radius (measured
to first null, that is, to the first place
where no light is seen) can be considered
to be resolved. It can be seen that the greater
the diameter of the lens or its aperture,
the finer the resolution. Interferometry,
with its ability to mimic extremely large
baseline apertures, allows for the greatest
angular resolution possible.For astronomical
imaging, the atmosphere prevents optimal resolution
from being achieved in the visible spectrum
due to the atmospheric scattering and dispersion
which cause stars to twinkle. Astronomers
refer to this effect as the quality of astronomical
seeing. Techniques known as adaptive optics
have been used to eliminate the atmospheric
disruption of images and achieve results that
approach the diffraction limit.
==== Dispersion and scattering ====
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 Thomson scattering which occurs when electromagnetic
waves are deflected by single particles. In
the limit of Thomson scattering, in which
the wavelike nature of light is evident, light
is dispersed independent of the frequency,
in contrast to Compton scattering which is
frequency-dependent and strictly a quantum
mechanical process, involving the nature of
light as particles. In a statistical sense,
elastic scattering of light by numerous particles
much smaller than the wavelength of the light
is a process known as Rayleigh scattering
while the similar process for scattering by
particles that are similar or larger in wavelength
is known as Mie scattering with the Tyndall
effect being a commonly observed result. A
small proportion of light scattering from
atoms or molecules may undergo Raman scattering,
wherein the frequency changes due to excitation
of the atoms and molecules. Brillouin scattering
occurs when the frequency of light changes
due to local changes with time and movements
of a dense material.Dispersion occurs when
different frequencies of light have different
phase velocities, due either to material properties
(material dispersion) or to the geometry of
an optical waveguide (waveguide dispersion).
The most familiar form of dispersion is a
decrease in index of refraction with increasing
wavelength, which is seen in most transparent
materials. This is called "normal dispersion".
It occurs in all dielectric materials, in
wavelength ranges where the material does
not absorb light. In wavelength ranges where
a medium has significant absorption, the index
of refraction can increase with wavelength.
This is called "anomalous dispersion".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.
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. "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:
D
=
1
v
g
2
d
v
g
d
λ
{\displaystyle D={\frac {1}{v_{g}^{2}}}{\frac
{dv_{g}}{d\lambda }}}
where
v
g
{\displaystyle v_{g}}
is the group velocity. For a uniform medium,
the group velocity is
v
g
=
c
(
n
−
λ
d
n
d
λ
)
−
1
{\displaystyle v_{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. This gives
a simpler form for the dispersion delay parameter:
D
=
−
λ
c
d
2
n
d
λ
2
.
{\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.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 ====
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.
===== Changing polarization =====
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 Erasmus Bartholinus in 1669. In addition,
the phase shift, and thus the change in polarization
state, is usually frequency dependent, which,
in combination with dichroism, often gives
rise to bright colours and rainbow-like effects.
In mineralogy, such properties, known as pleochroism,
are frequently exploited for the purpose of
identifying minerals using polarization microscopes.
Additionally, many plastics that are not normally
birefringent will become so when subject to
mechanical stress, a phenomenon which is the
basis of photoelasticity. Non-birefringent
methods, to rotate the linear polarization
of light beams, include the use of prismatic
polarization rotators which use total internal
reflection in a prism set designed for efficient
collinear transmission.
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
I
=
I
0
cos
2
⁡
θ
i
,
{\displaystyle I=I_{0}\cos ^{2}\theta _{i}\quad
,}
where
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
cos
2
⁡
θ
{\displaystyle \cos ^{2}\theta }
is 1/2, the transmission coefficient becomes
I
I
0
=
1
2
{\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.
===== 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 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.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. Polarization
occurs when light is scattered in the atmosphere.
The scattered light produces the brightness
and colour in clear skies. This partial polarization
of scattered light can be taken advantage
of using polarizing filters to darken the
sky in photographs. Optical polarization is
principally of importance in chemistry due
to circular dichroism and optical rotation
("circular birefringence") exhibited by optically
active (chiral) molecules.
== Modern optics ==
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. Light detectors,
such as photomultipliers and channeltrons,
respond to individual photons. Electronic
image sensors, such as CCDs, exhibit shot
noise corresponding to the statistics of individual
photon events. Light-emitting diodes and photovoltaic
cells, too, cannot be understood without quantum
mechanics. In the study of these devices,
quantum optics often overlaps with quantum
electronics.Specialty areas of optics research
include the study of how light interacts with
specific materials as in crystal optics and
metamaterials. Other research focuses on the
phenomenology of electromagnetic waves as
in singular optics, non-imaging optics, non-linear
optics, statistical optics, and radiometry.
Additionally, computer engineers have taken
an interest in integrated optics, machine
vision, and photonic computing as possible
components of the "next generation" of computers.Today,
the pure science of optics is called optical
science or optical physics to distinguish
it from applied optical sciences, which are
referred to as optical engineering. Prominent
subfields of optical engineering include illumination
engineering, photonics, and optoelectronics
with practical applications like lens design,
fabrication and testing of optical components,
and 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.
=== Lasers ===
A laser is a device that emits light (electromagnetic
radiation) through a process called stimulated
emission. The term laser is an acronym for
Light Amplification by Stimulated Emission
of Radiation. 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.
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.
Fibre-optic communication relies on lasers
to transmit large amounts of information at
the speed of light. Other common applications
of lasers include laser printers and laser
pointers. Lasers are used in medicine in areas
such as bloodless surgery, laser eye surgery,
and laser capture microdissection and in military
applications such as missile defence systems,
electro-optical countermeasures (EOCM), and
lidar. Lasers are also used in holograms,
bubblegrams, laser light shows, and laser
hair removal.
=== 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 visual systems in biology indicates the
central role optics plays as the science of
one of the five senses. Many people benefit
from eyeglasses or contact lenses, and optics
are integral to the functioning of many consumer
goods including cameras. Rainbows and mirages
are examples of optical phenomena. Optical
communication provides the backbone for both
the Internet and modern telephony.
=== Human eye ===
The human eye functions by focusing light
onto a layer of photoreceptor cells called
the retina, which forms the inner lining of
the back of the eye. The focusing is accomplished
by a series of transparent media. Light entering
the eye passes first through the cornea, which
provides much of the eye's optical power.
The light then continues through the fluid
just behind the cornea—the anterior chamber,
then passes through the pupil. The light then
passes through the lens, which focuses the
light further and allows adjustment of focus.
The light then passes through the main body
of fluid in the eye—the 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. 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.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.Ciliary
muscles around the lens allow the eye's focus
to be adjusted. This process is known as accommodation.
The near point and far point define the nearest
and farthest distances from the eye at which
an object can be brought into sharp focus.
For a person with normal vision, the far point
is located at infinity. The near point's location
depends on how much the muscles can increase
the curvature of the lens, and how inflexible
the lens has become with age. Optometrists,
ophthalmologists, and opticians usually consider
an appropriate near point to be closer than
normal reading distance—approximately 25
cm.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 presbyopia.
Similarly, people suffering from hyperopia
cannot decrease the focal length of their
lens enough to allow for nearby objects to
be imaged on their retina. Conversely, people
who cannot increase the focal length of their
lens enough to allow for distant objects to
be imaged on the retina suffer from myopia
and have a far point that is considerably
closer than infinity. 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.All of these
conditions can be corrected using corrective
lenses. For presbyopia and hyperopia, a converging
lens provides the extra curvature necessary
to bring the near point closer to the eye
while for myopia a diverging lens provides
the curvature necessary to send the far point
to infinity. Astigmatism is corrected with
a cylindrical surface lens that curves more
strongly in one direction than in another,
compensating for the non-uniformity of the
cornea.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.
==== 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.Cognitive
illusions include some which result from the
unconscious misapplication of certain optical
principles. For example, the Ames room, Hering,
Müller-Lyer, Orbison, Ponzo, Sander, and
Wundt illusions all rely on the suggestion
of the appearance of distance by using converging
and diverging lines, in the same way that
parallel light rays (or indeed any set of
parallel lines) appear to converge at a vanishing
point at infinity in two-dimensionally rendered
images with artistic perspective. This suggestion
is also responsible for the famous moon illusion
where the moon, despite having essentially
the same angular size, appears much larger
near the horizon than it does at zenith. This
illusion so confounded Ptolemy that he incorrectly
attributed it to atmospheric refraction when
he described it in his treatise, Optics.Another
type of optical illusion exploits broken patterns
to trick the mind into perceiving symmetries
or asymmetries that are not present. Examples
include the café wall, Ehrenstein, Fraser
spiral, Poggendorff, and Zöllner illusions.
Related, but not strictly illusions, are patterns
that occur due to the superimposition of periodic
structures. For example, 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.
==== 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 ===
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
× SceneLuminanceIn 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
N
{\displaystyle N}
, and given by
f
/
#
=
N
=
f
D
{\displaystyle f/\#=N={\frac {f}{D}}\ }
where
f
{\displaystyle f}
is the focal length, and
D
{\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.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.
=== Atmospheric optics ===
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 sunrise or sunset. Additional
particulate matter in the sky can scatter
different colours at different angles creating
colourful glowing skies at dusk and dawn.
Scattering off of ice crystals and other particles
in the atmosphere are responsible for halos,
afterglows, coronas, rays of sunlight, and
sun dogs. The variation in these kinds of
phenomena is due to different particle sizes
and geometries.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".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.
== See also ==
Ion optics
Important publications in optics
List of optical topics
