Prism

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In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. At least two of the flat surfaces must have an angle between them. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use "prism" usually refers to this type. Some types of optical prism are not in fact in the shape of geometric prisms. Prisms can be made from any material that is transparent to the wavelengths for which they are designed. Typical materials include glass, plastic, and fluorite.

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.

In physics, refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed.

Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is the visible spectrum that is visible to the human eye and is responsible for the sense of sight. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), or 4.00 × 10−7 to 7.00 × 10−7 m, between the infrared and the ultraviolet. This wavelength means a frequency range of roughly 430–750 terahertz (THz).

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A dispersive prism can be used to break light up into its constituent spectral colors (the colors of the rainbow). Furthermore, prisms can be used to reflect light, or to split light into components with different polarizations.

In optics, a dispersive prism is an optical prism, usually having the shape of a geometrical triangular prism, used as a spectroscopic component. Spectral dispersion is the best known property of optical prisms, although not the most frequent purpose of using optical prisms in practice. Triangular prisms are used to disperse light, that is, to break light up into its spectral components. Different wavelengths (colors) of light will be deflected by the prism at different angles, producing a spectrum on a detector. This is a result of the prism's material index of refraction varying with wavelength. By application of Snell's law, one can see that as the wavelength changes, and the refractive index changes, the deflection angle of a light beam will change, separating the colors of the light spatially. Generally, longer wavelengths (red) thereby undergo a smaller deviation than shorter wavelengths (blue) where the refractive index is larger.

A spectral color is a color that is evoked in a normal human by a single wavelength of light in the visible spectrum, or by a relatively narrow band of wavelengths, also known as monochromatic light. Every wavelength of visible light is perceived as a spectral color, in a continuous spectrum; the colors of sufficiently close wavelengths are indistinguishable for the human eye.

A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun.

How prisms work

Light changes speed as it moves from one medium to another (for example, from air into the glass of the prism). This speed change causes the light to be refracted and to enter the new medium at a different angle (Huygens principle). The degree of bending of the light's path depends on the angle that the incident beam of light makes with the surface, and on the ratio between the refractive indices of the two media (Snell's law). The refractive index of many materials (such as glass) varies with the wavelength or color of the light used, a phenomenon known as dispersion . This causes light of different colors to be refracted differently and to leave the prism at different angles, creating an effect similar to a rainbow. This can be used to separate a beam of white light into its constituent spectrum of colors. A similar separation happens with iridescent materials, such as a soap bubble. Prisms will generally disperse light over a much larger frequency bandwidth than diffraction gratings, making them useful for broad-spectrum spectroscopy. Furthermore, prisms do not suffer from complications arising from overlapping spectral orders, which all gratings have.

In everyday use and in kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as

Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.

Prisms are sometimes used for the internal reflection at the surfaces rather than for dispersion. If light inside the prism hits one of the surfaces at a sufficiently steep angle, total internal reflection occurs and all of the light is reflected. This makes a prism a useful substitute for a mirror in some situations.

Total internal reflection (TIR) is the phenomenon that makes the water-to-air surface in a fish-tank look like a perfectly silvered mirror when viewed from below the water level (Fig. 1). Technically, TIR is the total reflection of a wave incident at a sufficiently oblique angle on the interface between two media, of which the second ("external") medium is transparent to such waves but has a higher wave velocity than the first ("internal") medium. TIR occurs not only with electromagnetic waves such as light waves and microwaves, but also with other types of waves, including sound and water waves. In the case of a narrow train of waves, such as a laser beam, we tend to speak of the total internal reflection of a "ray" (Fig. 2).

A mirror is an object that reflects light in such a way that, for incident light in some range of wavelengths, the reflected light preserves many or most of the detailed physical characteristics of the original light, called specular reflection. This is different from other light-reflecting objects that do not preserve much of the original wave signal other than color and diffuse reflected light, such as flat-white paint.

Deviation angle and dispersion

Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface. For the prism shown at right, the indicated angles are given by

In optics a ray is an idealized model of light, obtained by choosing a line that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray theory does not describe phenomena such as interference and diffraction, which require wave theory.

In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces, complicating analysis. Ray tracing solves the problem by repeatedly advancing idealized narrow beams called rays through the medium by discrete amounts. Simple problems can be analyzed by propagating a few rays using simple mathematics. More detailed analysis can be performed by using a computer to propagate many rays.

{\displaystyle {\begin{aligned}\theta '_{0}&=\,{\text{arcsin}}{\Big (}{\frac {n_{0}}{n_{1}}}\,\sin \theta _{0}{\Big )}\\\theta _{1}&=\alpha -\theta '_{0}\\\theta '_{1}&=\,{\text{arcsin}}{\Big (}{\frac {n_{1}}{n_{2}}}\,\sin \theta _{1}{\Big )}\\\theta _{2}&=\theta '_{1}-\alpha \end{aligned}}}.

All angles are positive in the direction shown in the image. For a prism in air ${\displaystyle n_{0}=n_{2}\simeq 1}$. Defining ${\displaystyle n=n_{1}}$, the deviation angle ${\displaystyle \delta }$ is given by

${\displaystyle \delta =\theta _{0}+\theta _{2}=\theta _{0}+{\text{arcsin}}{\Big (}n\,\sin {\Big [}\alpha -{\text{arcsin}}{\Big (}{\frac {1}{n}}\,\sin \theta _{0}{\Big )}{\Big ]}{\Big )}-\alpha }$

If the angle of incidence ${\displaystyle \theta _{0}}$ and prism apex angle ${\displaystyle \alpha }$ are both small, ${\displaystyle \sin \theta \approx \theta }$ and ${\displaystyle {\text{arcsin}}x\approx x}$ if the angles are expressed in radians. This allows the nonlinear equation in the deviation angle ${\displaystyle \delta }$ to be approximated by

The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees. The unit was formerly an SI supplementary unit, but this category was abolished in 1995 and the radian is now considered an SI derived unit.

${\displaystyle \delta \approx \theta _{0}-\alpha +{\Big (}n\,{\Big [}{\Big (}\alpha -{\frac {1}{n}}\,\theta _{0}{\Big )}{\Big ]}{\Big )}=\theta _{0}-\alpha +n\alpha -\theta _{0}=(n-1)\alpha \ .}$

The deviation angle depends on wavelength through n, so for a thin prism the deviation angle varies with wavelength according to

${\displaystyle \delta (\lambda )\approx [n(\lambda )-1]\alpha }$.

History

René Descartes had seen light separated into the colors of the rainbow by glass or water, [1] though the source of the color was unknown. Isaac Newton's 1666 experiment of bending white light through a prism demonstrated that all the colors already existed in the light, with different color "corpuscles" fanning out and traveling with different speeds through the prism. It was only later that Young and Fresnel combined Newton's particle theory with Huygens' wave theory to explain how color arises from the spectrum of light.

Newton arrived at his conclusion by passing the red color from one prism through a second prism and found the color unchanged. From this, he concluded that the colors must already be present in the incoming light — thus, the prism did not create colors, but merely separated colors that are already there. He also used a lens and a second prism to recompose the spectrum back into white light. This experiment has become a classic example of the methodology introduced during the scientific revolution. The results of the experiment dramatically transformed the field of metaphysics, leading to John Locke's primary vs secondary quality distinction.[ citation needed ]

Newton discussed prism dispersion in great detail in his book Opticks . [2] He also introduced the use of more than one prism to control dispersion. [3] Newton's description of his experiments on prism dispersion was qualitative. A quantitative description of multiple-prism dispersion was not needed until multiple prism laser beam expanders were introduced in the 1980s. [4]

Types of prisms

Dispersive prisms

Dispersive prisms are used to break up light into its constituent spectral colors because the refractive index depends on frequency; the white light entering the prism is a mixture of different frequencies, each of which gets bent slightly differently. Blue light is slowed down more than red light and will therefore be bent more than red light.

Reflective prisms

Reflective prisms are used to reflect light, in order to flip, invert, rotate, deviate or displace the light beam. They are typically used to erect the image in binoculars or single-lens reflex cameras – without the prisms the image would be upside down for the user. Many reflective prisms use total internal reflection to achieve high reflectivity.

The most common reflective prisms are:

Beam-splitting prisms

Some reflective prisms are used for splitting a beam into two or more beams:

Polarizing prisms

There are also polarizing prisms which can split a beam of light into components of varying polarization. These are typically made of a birefringent crystalline material.

Deflecting prisms

Wedge prisms are used to deflect a beam of light by a fixed angle. A pair of such prisms can be used for beam steering; by rotating the prisms the beam can be deflected into any desired angle within a conical "field of regard". The most commonly found implementation is a Risley prism pair. [5] Two wedge prisms can also be used as an anamorphic pair to change the shape of a beam. This is used to make a round beam from the elliptical output of a laser diode.

Rhomboid prisms are used to laterally displace a beam of light without inverting the image.

Deck prisms were used on sailing ships to bring daylight below deck, [6] since candles and kerosene lamps are a fire hazard on wooden ships.

In optometry

By shifting corrective lenses off axis, images seen through them can be displaced in the same way that a prism displaces images. Eye care professionals use prisms, as well as lenses off axis, to treat various orthoptics problems:

Prism spectacles with a single prism perform a relative displacement of the two eyes, thereby correcting eso-, exo, hyper- or hypotropia.

In contrast, spectacles with prisms of equal power for both eyes, called yoked prisms (also: conjugate prisms, ambient lenses or performance glasses) shift the visual field of both eyes to the same extent. [7]

Related Research Articles

Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. This special angle of incidence is named after the Scottish physicist Sir David Brewster (1781–1868).

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.

In optics, a Fabry–Pérot interferometer (FPI) or etalon is an optical cavity made from two parallel reflecting surfaces. Optical waves can pass through the optical cavity only when they are in resonance with it. It is named after Charles Fabry and Alfred Perot, who developed the instrument in 1899. Etalon is from the French étalon, meaning "measuring gauge" or "standard".

In geometry, a circular segment is a region of a circle which is "cut off" from the rest of the circle by a secant or a chord. More formally, a circular segment is a region of two-dimensional space that is bounded by an arc of a circle and by the chord connecting the endpoints of the arc.

Etendue or étendue is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian optics.

A prism coupler is a prism designed to couple a substantial fraction of the power contained in a beam of light into a thin film to be used as a waveguide without the need for precision polishing of the edge of the film, without the need for sub-micrometer alignment precision of the beam and the edge of the film, and without the need for matching the numerical aperture of the beam to the film. Using a prism coupler, a beam coupled into a thin film can have a diameter hundreds of times the thickness of the film. Invention of the coupler contributed to the initiation of a field of study known as integrated optics.

Rifleman's rule is a "rule of thumb" that allows a rifleman to accurately fire a rifle that has been calibrated for horizontal targets at uphill or downhill targets. The rule says that only the horizontal range should be considered when adjusting a sight or performing hold-over in order to account for bullet drop. Typically, the range of an elevated target is considered in terms of the slant range, incorporating both the horizontal distance and the elevation distance, as when a rangefinder is used to determine the distance to target. The slant range is not compatible with standard ballistics tables for estimating bullet drop.

Acousto-optics is a branch of physics that studies the interactions between sound waves and light waves, especially the diffraction of laser light by ultrasound through an ultrasonic grating.

A Liljequist parhelion is a rare halo, an optical phenomenon in the form of a brightened spot on the parhelic circle approximately 150–160° from the sun; i.e., between the position of the 120° parhelion and the anthelion.

As a ray of light enters any medium, the ray's direction is deflected, based on the entrance angle, the material's refractive index, and according to Snell's law. A beam passing through an object like a prism or water drop is deflected twice: once entering, and again when exiting. The sum of these two deflections is called the deviation angle.

A blazed grating – also called echelette grating – is a special type of diffraction grating. It is optimized to achieve maximum grating efficiency in a given diffraction order. For this purpose, maximum optical power is concentrated in the desired diffraction order while the residual power in the other orders is minimized. Since this condition can only exactly be achieved for one wavelength, it is specified for which blaze wavelength the grating is optimized. The direction in which maximum efficiency is achieved is called the blaze angle and is the third crucial characteristic of a blazed grating directly depending on blaze wavelength and diffraction order.

The first description of multiple-prism arrays, and multiple-prism dispersion, was given by Newton in his book Opticks. Prism pair expanders were introduced by Brewster in 1813. A modern mathematical description of the single-prism dispersion was given by Born and Wolf in 1959. The generalized multiple-prism dispersion theory was introduced by Duarte and Piper in 1982.

The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample. This contrast transfer function (CTF) sets the resolution of high-resolution transmission electron microscopy (HRTEM), also known as phase contrast TEM.

Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film interfere with one another, either enhancing or reducing the reflected light. When the thickness of the film is an odd multiple of one quarter-wavelength of the light on it, the reflected waves from both surfaces interfere to cancel each other. Since the wave cannot be reflected, it is completely transmitted instead. When the thickness is a multiple of a half-wavelength of the light, the two reflected waves reinforce each other, increasing the reflection and reducing the transmission. Thus when white light, which consists of a range of wavelengths, is incident on the film, certain wavelengths (colors) are intensified while others are attenuated. Thin-film interference explains the multiple colors seen in light reflected from soap bubbles and oil films on water. It is also the mechanism behind the action of antireflection coatings used on glasses and camera lenses.

A compound prism is a set of multiple triangular prism elements placed in contact, and often cemented together to form a solid assembly. The use of multiple elements gives several advantages to an optical designer:

References

1. James Gleick (8 June 2004). Isaac Newton. Vintage. ISBN   1400032954.
2. Isaac Newton (1704). Opticks . London: Royal Society. ISBN   0-486-60205-2.
3. "The Discovery of the Spectrum of Light" . Retrieved 19 December 2009.
4. F. J. Duarte and J. A. Piper (1982). "Dispersion theory of multiple-prism beam expanders for pulsed dye lasers". Opt. Commun. 43 (5): 303–307. Bibcode:1982OptCo..43..303D. doi:10.1016/0030-4018(82)90216-4.
5. Duncan, B.D.; Bos, P.J.; Sergan, V. (2003). "Wide-angle achromatic prism beam steering for infrared countermeasure applications". Opt. Eng. 42 (4): 1038–1047. Bibcode:2003OptEn..42.1038D. doi:10.1117/1.1556393.
6. Loenen, Nick (February 2012). Wooden Boat Building: How to Build a Dragon Class Sailboat. FriesenPress. ISBN   9781770974067.
7. Kaplan, M; Carmody, D. P.; Gaydos, A (1996). "Postural orientation modifications in autism in response to ambient lenses". Child Psychiatry and Human Development. 27 (2): 81–91. PMID   8936794.