\[\begin{array}{l} I_\text{2 slits}\left(\theta\right) && = && \left\{f_1\left(\theta\right)+f_2\left(\theta\right)\right\}^2 && = && \left\{\cos 0+ \cos\left[ \left(\frac{2\pi}{\lambda}\right)d\sin\theta\right]\right\}^2 \\ I_\text{3 slits}\left(\theta\right) && = && \left\{f_1\left(\theta\right)+f_2\left(\theta\right)+f_3\left(\theta\right)\right\}^2 && = && \left\{\cos 0+ \cos \left[\left(\frac{2\pi}{\lambda}\right)d\sin\theta\right]+ \cos \left[\left(\frac{2\pi}{\lambda}\right)2d\sin\theta\right]\right\}^2 \\ I_\text{4 slits}\left(\theta\right) && = && \left\{f_1\left(\theta\right)+f_2\left(\theta\right)+f_3\left(\theta\right)+f_4\left(\theta\right)\right\}^2 && = && \left\{\cos 0+ \cos \left[\left(\frac{2\pi}{\lambda}\right)d\sin\theta\right]+ \cos \left[\left(\frac{2\pi}{\lambda}\right)2d\sin\theta\right]+ \cos \left[\left(\frac{2\pi}{\lambda}\right)3d\sin\theta\right]\right\}^2 \\ I_{n\text{ slits}}\left(\theta\right) && = && \left\{f_1\left(\theta\right)+f_2\left(\theta\right)+\dots + f_n\left(\theta\right)\right\}^2 && = && \left\{\cos 0+ \cos \left[\left(\frac{2\pi}{\lambda}\right)d\sin\theta\right]+\dots + \cos \left[\left(\frac{2\pi}{\lambda}\right)\left(n-1\right)d\sin\theta\right]\right\}^2\end{array}\]

Light is made up of particles called photons and hence inherently is quantized. Quantum optics is the study of the nature and effects of light as quantized photons. The first indication that light might be quantized came from Max Planck in 1899 when he correctly modelled blackbody radiation by assuming that the exchange of energy between light and matter only occurred in discrete amounts he called quanta. It was unknown whether the source of this discreteness was the matter or the light.[63]: 231–236  In 1905, Albert Einstein published the theory of the photoelectric effect. It appeared that the only possible explanation for the effect was the quantization of light itself. Later, Niels Bohr showed that atoms could only emit discrete amounts of energy. The understanding of the interaction between light and matter following from these developments not only formed the basis of quantum optics but also were crucial for the development of quantum mechanics as a whole. However, the subfields of quantum mechanics dealing with matter-light interaction were principally regarded as research into matter rather than into light and hence, one rather spoke of atom physics and quantum electronics.

Diffraction gratingpattern

The earliest known working telescopes were the refracting telescopes that appeared in the Netherlands in 1608. Their inventor is unknown: Hans Lippershey applied for the first patent that year followed by a patent application by Jacob Metius of Alkmaar two weeks later (neither was granted since examples of the device seemed to be numerous at the time). Galileo greatly improved upon these designs the following year. Isaac Newton is credited with constructing the first functional reflecting telescope in 1668, his Newtonian reflector.[51]

Where Euclid had limited his analysis to simple direct vision, Hero of Alexandria (c. AD 10–70) extended the principles of geometrical optics to consider problems of reflection (catoptrics). Unlike Euclid, Hero occasionally commented on the physical nature of visual rays, indicating that they proceeded at great speed from the eye to the object seen and were reflected from smooth surfaces but could become trapped in the porosities of unpolished surfaces.[5] This has come to be known as emission theory.[6]

Al-Kindi (c. 801–873) was one of the earliest important optical writers in the Islamic world. In a work known in the west as De radiis stellarum, al-Kindi developed a theory "that everything in the world ... emits rays in every direction, which fill the whole world."[10]

Putting these functions into a graphing calculator confirms what we found above, as well as what we suspect about \(n\) slits – that there are \(n-1\) dark fringes between each maximally-bright fringe.

Diffraction gratingformula

Johannes Kepler (1571–1630) picked up the investigation of the laws of optics from his lunar essay of 1600.[6] Both lunar and solar eclipses presented unexplained phenomena, such as unexpected shadow sizes, the red color of a total lunar eclipse, and the reportedly unusual light surrounding a total solar eclipse. Related issues of atmospheric refraction applied to all astronomical observations. Through most of 1603, Kepler paused his other work to focus on optical theory; the resulting manuscript, presented to the emperor on January 1, 1604, was published as Astronomiae Pars Optica (The Optical Part of Astronomy). In it, Kepler described the inverse-square law governing the intensity of light, reflection by flat and curved mirrors, and principles of pinhole cameras, as well as the astronomical implications of optics such as parallax and the apparent sizes of heavenly bodies. Astronomiae Pars Optica is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent).[32]

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Like Hero, Claudius Ptolemy in his second-century Optics considered the visual rays as proceeding from the eye to the object seen, but, unlike Hero, considered that the visual rays were not discrete lines, but formed a continuous cone.

\[1.1 = \sqrt{\dfrac{c+v}{c-v}} \;\;\;\Rightarrow\;\;\; 1.21 \left(c-v\right)= \left(c+v\right) \;\;\;\Rightarrow\;\;\; v = \dfrac{0.21}{2.21}c = 2.9\times 10^7\frac{m}{s} \nonumber\]

We know that the regions where the bright fringes peak get more concentrated light, and that there are more dark fringes between them when the number of slits is increased. One can imagine that in the limit where very many slits are used (a device called a diffraction grating), the result is very sharp, very bright lines lines at the points of maximum constructive interference, and darkness everywhere else. As we will see, this will be an extremely useful feature. But there is one assumption we have made here that needs to be emphasized. Because \(d\) is so small compared to the distance to the screen, it was easy to ignore the fact that this particular calculation required the assumption that the first bright fringe be farther from the center line than the outermost slit (we assumed that the wavelength was long enough that this had to be true). So creating a sharper interference pattern for a given wavelength of light by adding more slits at the same separation on both sides of the center line has limitations, because when the number of slits gets very large, the added slits go past the bright fringe. However, if more slits are added by squeezing them closer together (making \(d\) smaller), then for a given wavelength, then not only are there more slits, but the angle to the first bright fringe increases, thanks to the relation \(d\sin\theta=m\lambda\).

We found that the received wavelength is 10% longer than the sent wavelength, which means that the ratio of these wavelengths is 1.1. Plugging this in allows us to solve for the velocity of the source (i.e. the ship):

The early writers discussed here treated vision more as a geometrical than as a physical, physiological, or psychological problem. The first known author of a treatise on geometrical optics was the geometer Euclid (c. 325 BC–265 BC). Euclid began his study of optics as he began his study of geometry, with a set of self-evident axioms.

Today's fields of interest among quantum optics researchers include parametric down-conversion, parametric oscillation, even shorter (attosecond) light pulses, use of quantum optics for quantum information, manipulation of single atoms and Bose–Einstein condensates, their application, and how to manipulate them (a sub-field often called atom optics).

Although disputed, archeological evidence has been suggested of the use of lenses in ancient times over a period of several millennia.[38] It has been proposed that glass eye covers in hieroglyphs from the Old Kingdom of Egypt (c. 2686–2181 BCE) were functional simple glass meniscus lenses.[39] The so-called Nimrud lens, a rock crystal artifact dated to the 7th century BCE, might have been used as a magnifying glass, although it could have simply been a decoration.[40][41][42][43][44]

It turns out that we can mathematically check that the energy is in fact conserved by this mechanism. Recall that the intensity is related to power density, which means that if we integrate one of these curves over a full interval of space that the light is landing (say, between adjacent bright maxima), we get a measure of the energy landing in that region per unit time. Once again the graphing calculator comes in handy (unless integrating the intensity functions above is your idea of fun) as areas under these curves between maxima come out to be in relative proportions of 2:3:4 – the total energy landing on the screen every second really is proportional to the number of slits allowing light through!

Partially evacuated glass bulb contains spinner with four vanes, blackened on one side, silvered on the other. Turns 3000 revolutions a minute in sunlight.

So what happens if we keep going up the screen? We don't find any more maximally-bright fringes (all four waves can't be in phase), but we do find another totally dark position. It occurs when the distance \(\Delta x=d\sin\theta\) equals one-half of a wavelength. In this case, The wave that follows the blue path travels one half-wavelength farther than the wave that follows the brown path, and the waves that follow the orange and red paths also differ in the distance they travel by one half wavelength. So the blue path and red path waves cancel, as do the brown path and yellow path waves, resulting in total darkness.

His more general consideration of light as a primary agent of physical causation appears in his On Lines, Angles, and Figures where he asserts that "a natural agent propagates its power from itself to the recipient" and in On the Nature of Places where he notes that "every natural action is varied in strength and weakness through variation of lines, angles and figures."[26]

The English Franciscan, Roger Bacon (c. 1214–1294) was strongly influenced by Grosseteste's writings on the importance of light. In his optical writings (the Perspectiva, the De multiplicatione specierum, and the De speculis comburentibus) he cited a wide range of recently translated optical and philosophical works, including those of Alhacen, Aristotle, Avicenna, Averroes, Euclid, al-Kindi, Ptolemy, Tideus, and Constantine the African. Although he was not a slavish imitator, he drew his mathematical analysis of light and vision from the writings of the Arabic writer, Alhacen. But he added to this the Neoplatonic concept, perhaps drawn from Grosseteste, that every object radiates a power (species) by which it acts upon nearby objects suited to receive those species.[27] Note that Bacon's optical use of the term species differs significantly from the genus/species categories found in Aristotelian philosophy.

Hero demonstrated the equality of the angle of incidence and reflection on the grounds that this is the shortest path from the object to the observer. On this basis, he was able to define the fixed relation between an object and its image in a plane mirror. Specifically, the image appears to be as far behind the mirror as the object really is in front of the mirror.

This diagram is blown-up for clarity, but doing so makes the angles quite different from each other. With the proper scale in place the approximations of equal angles (and equal ∆x’s throughout) would be more apparent.

The Indian Buddhists, such as Dignāga in the 5th century and Dharmakirti in the 7th century, developed a type of atomism which defined the atoms which make up the world as momentary flashes of light or energy. They viewed light as being an atomic entity equivalent to energy, though they also viewed all matter as being composed of these light/energy particles.

The effects of diffraction of light were carefully observed and characterized by Francesco Maria Grimaldi, who also coined the term diffraction, from the Latin diffringere, 'to break into pieces', referring to light breaking up into different directions. The results of Grimaldi's observations were published posthumously in 1665.[36][37] Isaac Newton studied these effects and attributed them to inflexion of light rays. James Gregory (1638–1675) observed the diffraction patterns caused by a bird feather, which was effectively the first diffraction grating. In 1803 Thomas Young did his famous experiment observing interference from two closely spaced slits in his double slit interferometer. Explaining his results by interference of the waves emanating from the two different slits, he deduced that light must propagate as waves. Augustin-Jean Fresnel did more definitive studies and calculations of diffraction, published in 1815 and 1818, and thereby gave great support to the wave theory of light that had been advanced by Christiaan Huygens and reinvigorated by Young, against Newton's particle theory.

What isdiffraction gratingin Physics

\[f_r = \sqrt{\dfrac{c-v}{c+v}} f_s \;\;\;\Rightarrow\;\;\; \dfrac{c}{\lambda_r} = \sqrt{\dfrac{c-v}{c+v}} \dfrac{c}{\lambda_s} \;\;\;\Rightarrow\;\;\; \dfrac{\lambda_r}{\lambda_s} = \sqrt{\dfrac{c+v}{c-v}} \nonumber\]

It should also be mentioned that like double slits, diffraction gratings do allow for more than one bright fringe (as before, depending upon the ratio of \(d\) and \(\lambda\)). For a typical double slit experiment, the goal is usually to show a broad interference pattern – many fringes. If the slit separation is too small, then the angles between the fringes are large, resulting in very few fringes, widely separated, foiling the goal of such an experiment. But use of a diffraction grating has a different goal (very sharp bright fringes), which requires that the slits be separated by much smaller distances. This results in far fewer fringes, separated by large angles. So while the calculation for the angles of bright fringes is the same for both devices, for a given range of wavelengths, their slit separations are usually quite different.

In the 4th century BC Chinese text, credited to the philosopher Mozi, it is described how light passing through a pinhole creates an inverted image in a "collecting-point" or "treasure house".[3]

In his Catoptrica, Hero of Alexandria showed by a geometrical method that the actual path taken by a ray of light reflected from a plane mirror is shorter than any other reflected path that might be drawn between the source and point of observation.

Several later works, including the influential A Moral Treatise on the Eye (Latin: Tractatus Moralis de Oculo) by Peter of Limoges (1240–1306), helped popularize and spread the ideas found in Bacon's writings.[28]

But astronomers can do even more than identify elements in burning stars. We know what the barcode for hydrogen looks like when the source is at rest relative to the spectrometer, so when we see the hydrogen barcode pop up for a star, we can measure how much the barcode in the spectrometer is shifted compared to the stationary case, and we can use the amount of shift to determine how fast the star is moving relative to earth!

How does diffraction grating workin physics

The English bishop Robert Grosseteste (c. 1175–1253) wrote on a wide range of scientific topics at the time of the origin of the medieval university and the recovery of the works of Aristotle. Grosseteste reflected a period of transition between the Platonism of early medieval learning and the new Aristotelianism, hence he tended to apply mathematics and the Platonic metaphor of light in many of his writings. He has been credited with discussing 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.[24]

Another English Franciscan, John Pecham (died 1292) built on the work of Bacon, Grosseteste, and a diverse range of earlier writers to produce what became the most widely used textbook on optics of the Middle Ages, the Perspectiva communis. His book centered on the question of vision, on how we see, rather than on the nature of light and color. Pecham followed the model set forth by Alhacen, but interpreted Alhacen's ideas in the manner of Roger Bacon.[29]

Okay, so as our first task, we will look for the position where the first bright fringe is located. For this to occur, we need all four waves to be in phase, which means that \(\Delta x\) has to be a full wavelength, giving us the same formula for bright fringes that we found for the double slit:

Like his predecessors, Witelo (born circa 1230, died between 1280 and 1314) drew on the extensive body of optical works recently translated from Greek and Arabic to produce a massive presentation of the subject entitled the Perspectiva. His theory of vision follows Alhacen and he does not consider Bacon's concept of species, although passages in his work demonstrate that he was influenced by Bacon's ideas. Judging from the number of surviving manuscripts, his work was not as influential as those of Pecham and Bacon, yet his importance, and that of Pecham, grew with the invention of printing.[30]

a. The ship is receding, so the source of the light is moving away from the receiver. This doppler-shifts the light to a lower frequency, which corresponds to a longer wavelength. The relationship between the angle of the first bright fringe and the wavelength is:

For from whatsoever distances fires can throw us their light and breathe their warm heat upon our limbs, they lose nothing of the body of their flames because of the interspaces, their fire is no whit shrunken to the sight.[4]

Willebrord Snellius (1580–1626) found the mathematical law of refraction, now known as Snell's law, in 1621. Subsequently, René Descartes (1596–1650) showed, by using geometric construction and the law of refraction (also known as Descartes' law), that the angular radius of a rainbow is 42° (i.e. the angle subtended at the eye by the edge of the rainbow and the rainbow's centre is 42°).[33] He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.[34]

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Galileo Galilei (also sometimes cited as a compound microscope inventor) seems to have found after 1609 that he could close focus his telescope to view small objects and, after seeing a compound microscope built by Drebbel exhibited in Rome in 1624, built his own improved version.[59][60][61] The name microscope was coined by Giovanni Faber, who gave that name to Galileo Galilei's compound microscope in 1625.[62]

Diffraction gratingexperiment

A spaceship is fitted with a light beacon before blast-off. The light from this beacon is monochromatic, and when it is shone through the apparatus pictured below, the angle of deflection of the first order bright fringe is measured. The spaceship then blasts off, and after several years of accelerating through outer space, it is moving away from the Earth at a very high rate of speed, and the light from its beacon is shone through the apparatus again (which is still on Earth).

The earliest written record of magnification dates back to the 1st century CE, when Seneca the Younger, a tutor of Emperor Nero, wrote: "Letters, however small and indistinct, are seen enlarged and more clearly through a globe or glass filled with water."[45] Emperor Nero is also said to have watched the gladiatorial games using an emerald as a corrective lens.[46]

Other remarkable results are the demonstration of quantum entanglement, quantum teleportation, and (recently, in 1995) quantum logic gates. The latter are of much interest in quantum information theory, a subject which partly emerged from quantum optics, partly from theoretical computer science.

In the late 13th and early 14th centuries, Qutb al-Din al-Shirazi (1236–1311) and his student Kamāl al-Dīn al-Fārisī (1260–1320) continued the work of Ibn al-Haytham, and they were among the first to give the correct explanations for the rainbow phenomenon. Al-Fārisī published his findings in his Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).[23]

It is for this reason that diffraction gratings are generally characterized by their grating density – the number of slits per unit distance. Of course such a number can be converted into a slit separation: If a diffraction grating has a grating density of 100 slits per \(cm\), then the slits must be separated by \(d=\frac{1}{100}cm = 10^{-4}m\). This number can then be used in calculations for the angle at which bright fringes are seen.

We can also show this phenomenon mathematically, by superposing (adding) the wave functions. The waves start in phase at the slits, so all of the phase constants are equal (and we choose them to be zero at \(t=0\)), so all that remains of the wave functions is the position dependence. Once again, all that matters are the differences in distances traveled with the reference slit (whose difference with itself is zero), so the superposition intensity looks like:

After having determined the interference pattern associated with two slits, it makes one wonder what would happen if many more (equally-spaced) slits are added. We can recycle our geometrical analysis from the double slit problem to answer this question. Let's look at the example of four slits.

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Isaac Newton (1643–1727) investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light. He also showed that the coloured light does not change its properties by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This is known as Newton's theory of colour. From this work he concluded that any refracting telescope would suffer from the dispersion of light into colours. He went on to invent a reflecting telescope (today known as a Newtonian telescope), which showed that using a mirror to form an image bypassed the problem. In 1671 the Royal Society asked for a demonstration of his reflecting telescope. Their interest encouraged him to publish his notes On Colour, which he later expanded into his Opticks. Newton argued that light is composed of particles or corpuscles and were refracted by accelerating toward the denser medium, but he had to associate them with waves to explain the diffraction of light (Opticks Bk. II, Props. XII-L). Later physicists instead favoured a purely wavelike explanation of light to account for diffraction. Today's quantum mechanics, photons and the idea of wave-particle duality bear only a minor resemblance to Newton's understanding of light.

It was stated above that sharp bright fringes are very useful in applications. To see why this is so, suppose one wishes to use a diffraction device to measure the wavelength of a monochromatic light. This is straightforward – shine the light through any number of slits with a known slit spacing, and measure the angle at which the first bright fringe is deflected from the central bright fringe, then plug into \(d\sin\theta=m\lambda\) (with \(m=1\)) and solve for \(\lambda\). The only real challenge to this procedure is measuring the angle. Of course, if we shine the light onto a screen whose distance we know from the slits, we can measure the distances between the bright fringes, and compute the angle from there. But still we have a problem if we want to be precise. If a double-slit is used, then the bright fringe is rather broad, and it might be challenging to get a good measurement of its center. With a diffraction grating, the bright fringe is much better defined. Furthermore, the light we are looking at may not be very intense, and a diffraction crating lets much more of the light in, and the bright fringe is much easier to see than it would be for a double-slit.

Setting aside the issues of epistemology and theology, Grosseteste's cosmogony of light describes the origin of the universe in what may loosely be described as a medieval "big bang" theory. Both his biblical commentary, the Hexaemeron (1230 x 35), and his scientific On Light (1235 x 40), took their inspiration from Genesis 1:3, "God said, let there be light", and described the subsequent process of creation as a natural physical process arising from the generative power of an expanding (and contracting) sphere of light.[25]

Notice that the bright fringes for any number of slits occur at the same places as for the double slit (provided they have the same slit separation), and that the number of dark fringes between bright fringes goes up by one every time another slit is added. Also notice that the maximum intensity of the double slit is 4 units, the 3-slit case has a maximum intensity of 9 units, and for 4-slits it is 16 units, as we expect when the amplitude increases by one unit with the addition of each slit. But also notice that the widths of the bright fringes get narrower, indicating that the energy becomes more concentrated near the brightness maxima, and less concentrated near the dark fringes.

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As laser science needed good theoretical foundations, and also because research into these soon proved very fruitful, interest in quantum optics rose. Following the work of 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 (see degree of coherence). This led to the introduction of the coherent state as a quantum description of laser light and the realization that some states of light could not be described with classical waves. In 1977, Kimble et al. demonstrated the first source of light which required a quantum description: a single atom that emitted one photon at a time. Another quantum state of light with certain advantages over any classical state, squeezed light, was soon proposed. At the same time, development of short and ultrashort laser pulses—created by Q-switching and mode-locking techniques—opened the way to the study of unimaginably fast ("ultrafast") processes. Applications for solid state research (e.g. Raman spectroscopy) were found, and mechanical forces of light on matter were studied. The latter led to levitating and positioning clouds of atoms or even small biological samples in an optical trap or optical tweezers by laser beam. This, along with Doppler cooling was the crucial technology needed to achieve the celebrated Bose–Einstein condensation.

There is one other time when a dark fringe occurs. This happens when the distance \(\Delta x=d\sin\theta\) equals one-quarter of a wavelength. Once again, alternate slits interfere with each other, as the waves travel distances that differ by a half-wavelength.

This theory of the active power of rays had an influence on later scholars such as Ibn al-Haytham, Robert Grosseteste and Roger Bacon.[11]

The answer to this puzzle involves how concentrated the bright fringes are. All bright fringes have a point of maximum brightness that tapers down to the dark fringes. If the rate at which the brightness tapers down is greater, then the brightness (energy density) near those maximum points can go up, and the energy density near the dark fringes goes down, such that the same total energy hits the screen. But it turns out there is even a little more to it than this, as we will now see.

The earliest known examples of compound microscopes, which combine an objective lens near the specimen with an eyepiece to view a real image, appeared in Europe around 1620.[52] The design is very similar to the telescope and, like that device, its inventor is unknown. Again claims revolve around the spectacle making centers in the Netherlands including claims it was invented in 1590 by Zacharias Janssen and/or his father, Hans Martens,[53][54][55] claims it was invented by rival spectacle maker, Hans Lippershey,[56] and claims it was invented by expatriate Cornelis Drebbel who was noted to have a version in London in 1619.[57][58]

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In the fifth century BCE, Empedocles postulated that everything was composed of four elements; fire, air, earth and water. He believed that Aphrodite made the human eye out of the four elements and that she lit the fire in the eye which shone out from the eye making sight possible. If this were true, then one could see during the night just as well as during the day, so Empedocles postulated an interaction between rays from the eyes and rays from a source such as the sun. He stated that light has a finite speed.[2]

Does this mean that the result for several slits is identical to that of the double slit? Certainly not! First of all, there are many more sources of light, all interfering constructively, which means that the bright fringes are much brighter. How much brighter? Well, with four slits, as in the example here, the amplitude of a single slit is multiplied by 4, making the intensity (which goes as the square of the amplitude) 16 times greater than a single slit. For the double slit, the intensity was increased by a factor of 4 (the amplitude was doubled). Therefore doubling the number of slits increased the intensity of the bright fringes by a factor of 4. But wait, doubling the number of slits only lets in twice as much energy per second, so how is the intensity increasing so much?

Ibn al-Haytham (Alhacen) wrote about the effects of pinhole, concave lenses, and magnifying glasses in his 11th century Book of Optics (1021 CE).[45][47][48] The English friar Roger Bacon, during the 1260s or 1270s, wrote works on optics, partly based on the works of Arab writers, that described the function of corrective lenses for vision and burning glasses. These volumes were outlines for a larger publication that was never produced, so his ideas never saw mass dissemination.[49]

In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. In 1704, Newton published Opticks, in which he expounded his corpuscular theory of light. He considered light to be made up of extremely subtle corpuscles, that ordinary matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation "Are not gross Bodies and Light convertible into one another, ...and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?"[35]

b. From our answer above, the deflection angle has grown to 110% of what it was before blastoff. By our small-angle approximation, we can therefore say that the sine of the angle has grown by the same amount, which means that is how much the wavelength has shifted longer. The doppler shift formula (for light) gives a relationship between the sender’s frequency and the receiver’s frequency when the two are moving away from each other, and we can turn this into a relation between the wavelengths using Equation 2.2.10:

But even these two advantages pale in comparison to the third. We have not yet considered what happens if we look at light that is not monochromatic. Suppose the incoming light is a mix of three or four colors. The separate colors don't interfere in a static manner with each other (they can create "beats," but the frequency differences for light are so great that these will not be observable) they only observably interfere with themselves. As such, a beam of light with three colors will exhibit three separate interference patterns when passed though a single device (i.e. they all experience the same slit separation). The wave with color corresponding to the shortest wavelength will have its first bright fringe deflected by the smallest angle. If this light is passed through a double-slit, the interference patterns blend with each other, making it hard to separate the component colors. But a diffraction grating makes three sharp, distinct, first-order bright fringes, making it easy to determine the constituent colors of the incoming light.

An important part of the fields of chemistry and astronomy is the method of measurement called spectroscopy. In Physics 9D, you will learn that matter emits and absorbs light in very peculiar ways. You might think that electrons in atoms can vibrate at any frequency at all and therefore emit or absorb a nice, smooth continuous spectrum of light, but it turns out that they cannot. In fact each atom has a unique “fingerprint” of specific frequencies of light that it emits and absorbs. This means that when light emitted from a certain substance is passed through a diffraction grating, this fingerprint is manifested as a specific set of bright fringes (called spectral lines). This means that we can ascertain from a distance (in the case of astronomy, very great distances!) the composition of the matter that is emitting light. These fingerprints are so specific and unique that even if several different substances are emitting light, they can generally be sorted out.

Theodoric of Freiberg (ca. 1250–ca. 1310) was among the first in Europe to provide the correct scientific explanation for the rainbow phenomenon,[31] as well as Qutb al-Din al-Shirazi (1236–1311) and his student Kamāl al-Dīn al-Fārisī (1260–1320) mentioned above.

In his Optics Greek mathematician Euclid observed that "things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal". In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Pappus believed these results to be important in astronomy and included Euclid's Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Ptolemy.

The separation of the slits doesn’t change, so as the wavelength gets longer, the sine of the deflection angle gets bigger, which means the angle itself gets bigger.

What isgrating

Euclid did not define the physical nature of these visual rays but, using the principles of geometry, he discussed the effects of perspective and the rounding of things seen at a distance.

Ibn al-Haytham (known in as Alhacen or Alhazen in Western Europe), writing in the 1010s, received both Ibn Sahl's treatise and a partial Arabic translation of Ptolemy's Optics. He produced a comprehensive and systematic analysis of Greek optical theories.[15] Ibn al-Haytham's key achievement was twofold: first, to insist, against the opinion of Ptolemy, that vision occurred because of rays entering the eye; the second was to define the physical nature of the rays discussed by earlier geometrical optical writers, considering them as the forms of light and color.[16] He then analyzed these physical rays according to the principles of geometrical optics. He wrote many books on optics, most significantly the Book of Optics (Kitab al Manazir in Arabic), translated into Latin as the De aspectibus or Perspectiva, which disseminated his ideas to Western Europe and had great influence on the later developments of optics.[17][6] Ibn al-Haytham was called "the father of modern optics".[18][19]

objective = 400X total magnification). Tube: Where the eyepieces are dropped in. Also, they connect the eyepieces to the objective lenses. Base: ...

Ibn Sahl, a mathematician active in Baghdad during the 980s, is the first Islamic scholar known to have compiled a commentary on Ptolemy's Optics. His treatise Fī al-'āla al-muḥriqa "On the burning instruments" was reconstructed from fragmentary manuscripts by Rashed (1993).[12] The work is concerned with how curved mirrors and lenses bend and focus light. Ibn Sahl also describes a law of refraction mathematically equivalent to Snell's law.[13] He used his law of refraction to compute the shapes of lenses and mirrors that focus light at a single point on the axis.

We'll start with the bright fringe, and start working our way closer to the central bright fringe until we hit a dark fringe. Strangely, we find that the first position of total destructive interference we encounter does not occur at the halfway point, as it did for the double slit! Note that when the distance \(\Delta x=d\sin\theta\) equals three-quarters of a wavelength, then the wave that follows the blue path will travel 1.5 wavelengths farther than the wave that follows the the orange path, and as this is an odd number of half wavelengths, these waves will cancel. The same is true for the waves that follow the brown and red paths, which means that position will be completely dark.

The \(\Delta x\) in each case is the difference in distance traveled compared to the reference slit. So the extra distance traveled by the wave following the blue path is three times as great as the extra distance traveled by the wave following the orange path.

One might worry that since stars are moving relative to the earth, that we might get the elements wrong, since what we will see in the spectrometer (a device with a diffraction grating) will measure doppler-shifted wavelengths. But it isn't the exact positions of the spectral lines that tells us the elements emitting the line, but rather their relative positions. That is, every spectral line is doppler-shifted, so the "barcode" essentially looks the same for hydrogen regardless of its relative motion, because the whole barcode is just shifted toward longer wavelengths if it is moving away from the spectrometer, and toward the shorter wavelengths if moving toward the spectrometer.

This page titled 3.3: Diffraction Gratings is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Tom Weideman directly on the LibreTexts platform.

Christiaan Huygens (1629–1695) wrote several works in the area of optics. These included the Opera reliqua (also known as Christiani Hugenii Zuilichemii, dum viveret Zelhemii toparchae, opuscula posthuma) and the Traité de la lumière.

What isgratingconstant

[It should be noted that the positions of the fringes on the screen are measured from the horizontal line passing through the center of the collection of slits, as we did with the double slit.]

Optics documents Ptolemy's studies of reflection and refraction.[7] He measured the angles of refraction between air, water, and glass, but his published results indicate that he adjusted his measurements to fit his (incorrect) assumption that the angle of refraction is proportional to the angle of incidence.[8][9]

Between the 11th and 13th centuries, so-called "reading stones" were invented. Often used by monks to assist in illuminating manuscripts, these were primitive plano-convex lenses, initially made by cutting a glass sphere in half. As the stones were experimented with, it was slowly understood that shallower lenses magnified more effectively. Around 1286, possibly in Pisa, Italy, the first pair of eyeglasses was made, although it is unclear who the inventor was.[50]

Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, followed by theories on light and vision developed by ancient Greek philosophers, and the development of geometrical optics in the Greco-Roman world. The word optics is derived from the Greek term τα ὀπτικά meaning 'appearance, look'.[1] Optics was significantly reformed by the developments in the medieval Islamic world, such as the beginnings of physical and physiological optics, and then significantly advanced in early modern Europe, where diffractive optics began. These earlier studies on optics are now known as "classical optics". The term "modern optics" refers to areas of optical research that largely developed in the 20th century, such as wave optics and quantum optics.

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Abu 'Abd Allah Muhammad ibn Ma'udh, who lived in Al-Andalus during the second half of the 11th century, wrote a work on optics later translated into Latin as Liber de crepisculis, which was mistakenly attributed to Alhazen. This was a "short work containing an estimation of the angle of depression of the sun at the beginning of the morning twilight and at the end of the evening twilight, and an attempt to calculate on the basis of this and other data the height of the atmospheric moisture responsible for the refraction of the sun's rays." Through his experiments, he obtained the value of 18°, which comes close to the modern value.[22]

What isdiffraction grating

Avicenna (980–1037) agreed with Alhazen that the speed of light is finite, as he "observed that if the perception of light is due to the emission of some sort of particles by a luminous source, the speed of light must be finite."[20] Abū Rayhān al-Bīrūnī (973-1048) also agreed that light has a finite speed, and stated that the speed of light is much faster than the speed of sound.[21]

We begin once again with the assumption that the distance to the screen is significantly larger than the separation of adjacent slits: \(d\ll L\)). Starting with the lowest slit of the four as a "reference" and repeating the double-slit geometry for each slit going up from there, we have a diagram that looks like this:

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This changed with the invention of the maser in 1953 and the laser in 1960. Laser science—research into principles, design and application of these devices—became an important field, and the quantum mechanics underlying the laser's principles was studied now with more emphasis on the properties of light, and the name quantum optics became customary.

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To demonstrate this phenomenon, it becomes necessary to redraw the figure above a little closer to the actual scale. We of course cannot possibly get very close to the actual scale, as slit separations are typically fractions of millimeters, while distances to screens are usually tens or hundreds of centimeters, but we will use what space we can manage. As before, we will use the red line as the reference, and compare the distances traveled by the other three light waves.