Interference Diffraction And Polarization Of Light Pdf
- and pdf
- Tuesday, April 6, 2021 5:11:26 PM
- 5 comment
File Name: interference diffraction and polarization of light .zip
The formation of an image in the microscope relies on the complex interplay between two critical optical phenomena: diffraction and interference.
- Optics Express
- Reflection, Refraction, and Diffraction
- We apologize for the inconvenience...
- Microscopy U - The source for microscopy education
The formation of an image in the microscope relies on the complex interplay between two critical optical phenomena: diffraction and interference. Light passing through the specimen is scattered and diffracted into divergent waves by tiny details and features present in the specimen. Some of the divergent light scattered by the specimen is captured by the objective and focused onto the intermediate image plane, where the superimposed light waves are recombined or summed through the process of interference to produce a magnified image of the specimen.
The seemingly close relationship between diffraction and interference occurs because they are actually manifestations of the same physical process and produce ostensibly reciprocal effects. Most of us observe some type of optical interference almost every day, but usually do not realize the events in play behind the often-kaleidoscopic display of color produced when light waves interfere with each other.
One of the best examples of interference is demonstrated by the light reflected from a film of oil floating on water. Another example is the thin film of a soap bubble illustrated in Figure 1 , which reflects a spectrum of beautiful colors when illuminated by natural or artificial light sources. The dynamic interplay of colors in a soap bubble derives from simultaneous reflection of light from both the inside and outside surfaces of the exceedingly thin soap film.
The two surfaces are very close together separated by only a few micrometers and light reflected from the inner surface interferes both constructively and destructively with light reflected from the outer surface.
The interference effect is observed because light reflected from the inner surface of the bubble must travel farther than light reflected from the outer surface, and variations in the soap film thickness produce corresponding differences in the distances light waves must travel to reach our eyes.
When the waves reflected from the inner and outer surfaces of the soap film recombine, they will interfere with each other to either remove or reinforce some wavelengths of white light by destructive or constructive interference as illustrated in Figure 2.
The result is a dazzling display of color that seems to gyrate along the surface of the bubble as it expands and contracts with wind currents. Simply turning the soap bubble, or moving it closer or farther away, causes the colors to change, or even disappear altogether.
If the extra distance traveled by the light waves reflected from the inner surface is exactly equal to the wavelength of those bouncing away from the outer surface, then the light waves will recombine constructively to form bright colors.
In areas where the waves are out of step with each other, even by some fractional portion of a wavelength, destructive interference effects will begin to occur, attenuating or canceling the reflected light and the color. Music, movie, and computer enthusiasts are also exposed to the interference phenomenon each time they load a compact disk into the audio player or a CD-ROM drive.
The very close spacing of these tracks mimics the ultra-fine lines present on a diffraction grating to produce a spectacular rainbow-like effect of color when ordinary white light is reflected from the surface. Like the soap bubble, the color is derived from interference between reflected light waves bouncing from neighboring tracks on the disk. Interference is responsible for the often-brilliant iridescent coloring displayed by hummingbirds, a variety of beetles and other insects whose wings cast a metallic luster, and several species of magnificent butterflies.
For example, the wings of the diamond beetle are covered with a microscopic crisscrossed diffraction grating having approximately 2, lines per inch. White light reflected from the wings of the beetle produces a stunning spectral display of interference patterns similar to that originating from the surface of a compact disk. A similar effect is created by the tortoise beetle, which has wing casings composed of multiple chitin layers, rendering them iridescent in reflected light.
Interestingly, this insect can vary the moisture content of the thin films to produce thickness variations, changing the predominant reflected interference color from gold to reddish-copper. Another spectacular example of naturally occurring interference, the Morpho didius butterfly thrives in the Amazon rain forest and exhibits one of the most beautiful forms of iridescence seen in the insect world. The intense blue wing color is the consequence of color-producing structures fastened to the scales layering the butterfly's wings.
Each scale is composed of two sheet-like, extremely thin lamella, an upper and lower, which are separated by a void held apart with vertical rods. The lamellae support an even smaller network of Christmas tree-shaped ridges containing plates or branches projecting laterally from a central stalk. Plates on the ridges arising from thin layers of chitin that are separated by air spaces at distances equal to one-half the wavelength of blue light mimic a natural diffraction grating.
The ridges have evolved with spacing at the correct intervals for light waves reflecting from the plates to undergo constructive and destructive interference. The result is a deep iridescent blue color that covers almost the entire wing structure, although no blue light is actually reflected from the wing scales.
The classical method of describing interference includes presentations see Figure 4 that depict the graphical recombination of two or more sinusoidal light waves in a plot of amplitude, wavelength, and relative phase displacement.
In effect, when two waves are added together, the resulting wave has an amplitude value that is either increased through constructive interference, or diminished through destructive interference. To illustrate the effect, consider a pair of light waves from the same source that are coherent having an identical phase relationship and traveling together in parallel presented on the left-hand side of Figure 4.
If the vibrations produced by the electric field vectors which are perpendicular to the propagation direction from each wave are parallel to each other in effect, the vectors vibrate in the same plane , then the light waves may combine and undergo interference. If the vectors do not lie in the same plane, and are vibrating at some angle between 90 and degrees with respect to each other, then the waves cannot interfere with one another.
The light waves illustrated in Figure 4 are all considered to have electric field vectors vibrating in the plane of the page. In addition, the waves all have the same wavelength, and are coherent, but vary with respect to amplitude. The waves on the right-hand side of Figure 4 have a phase displacement of degrees with respect to each other. Assuming all of the criteria listed above are met, then the waves can interfere either constructively or destructively to produce a resultant wave that has either increased or decreased amplitude.
If the crests of one of the waves coincide with the crests of the other, the amplitudes are determined by the arithmetic sum of the amplitudes from the two original waves. For example, if the amplitudes of both waves are equal, the resultant amplitude is doubled. In Figure 4 , light wave A can interfere constructively with light wave B , because the two coherent waves are in the same phase, differing only in relative amplitudes.
Bear in mind that light intensity varies directly as the square of the amplitude. Thus, if the amplitude is doubled, intensity is quadrupled. Such additive interference is called constructive interference and results in a new wave having increased amplitude. If the crests of one wave coincide with the troughs of the other wave in effect, the waves are degrees, or half a wavelength, out of phase with each other , the resultant amplitude is decreased or may even be completely canceled, as illustrated for wave A and wave C on the right-hand side of Figure 4.
This is termed destructive interference , and generally results in a decrease of amplitude or intensity. In cases where the amplitudes are equal, but degrees out of phase, the waves eliminate each other to produce a total lack of color, or complete blackness.
All of the examples presented in Figure 4 portray waves propagating in the same direction, but in many cases, light waves traveling in different directions can briefly meet and undergo interference. After the waves have passed each other, however, they will resume their original course, having the same amplitude, wavelength, and phase that they had before meeting.
Real-world interference phenomena are not as clearly defined as the simple case depicted in Figure 4. For example, the large spectrum of color exhibited by a soap bubble results from both constructive and destructive interference of light waves that vary in amplitude, wavelength, and relative phase displacement.
A combination of waves having amplitudes that are approximately equal, but with differing wavelengths and phases, can produce a wide spectrum of resultant colors and amplitudes.
In addition, when two waves of equal amplitude and wavelength that are degrees half a wavelength out of phase with each other meet, they are not actually destroyed, as suggested in Figure 4.
All of the photon energy present in these waves must somehow be recovered or redistributed in a new direction, according to the law of energy conservation photons are not capable of self-annihilation.
Instead, upon meeting, the photons are redistributed to regions that permit constructive interference, so the effect should be considered as a redistribution of light waves and photon energy rather than the spontaneous construction or destruction of light. Therefore, simple diagrams, such as the one illustrated in Figure 4 , should only be considered as tools that assist with the calculation of light energy traveling in a specific direction.
Among the pioneers in early physics was a nineteenth century English scientist named Thomas Young, who convincingly demonstrated the wave-like character of light through the phenomenon of interference using diffraction techniques. Young's experiments provided evidence in contrast to the popular scientific opinion of the period, which was based on Newton's corpuscular particle theory for the nature of light. In addition, he is also responsible for concluding that different colors of light are made from waves having different lengths, and that any color can be obtained by mixing together various quantities of light from only three primary colors: red, green, and blue.
In , Young conducted a classical and often-cited double-slit experiment providing important evidence that visible light has wave-like properties. His experiment was based on the hypothesis that if light were wave-like in nature, then it should behave in a manner similar to ripples or waves on a pond of water.
Where two opposing water waves meet, they should react in a specific manner to either reinforce or destroy each other. If the two waves are in step the crests meet , then they should combine to make a larger wave.
In contrast, when two waves meet that are out of step the crest of one meets the trough of another , the waves should cancel and produce a flat surface in that area. In order to test his hypothesis, Young devised an ingenious experiment. Using sunlight diffracted through a small slit as a source of semi-coherent illumination, he projected the light rays emanating from the slit onto another screen containing two slits placed side by side.
Light passing through the slits was then allowed to fall onto a third screen the detector. Young observed that when the slits were large, spaced far apart and close to the detection screen, then two overlapping patches of light formed on the screen.
However, when he reduced the size of the slits and brought them closer together, the light passing through the slits and onto the screen produced distinct bands of color separated by dark regions in a serial order. Young coined the term interference fringes to describe the bands and realized that these colored bands could only be produced if light were acting like a wave.
The basic setup of the double slit experiment is illustrated in Figure 5. Red filtered light derived from sunlight is first passed through a slit to achieve a semi-coherent state. Light waves exiting the first slit are then made incident on a pair of slits positioned close together on a second barrier. A detector screen is placed in the region behind the slits to capture overlapped light rays that have passed through the twin slits, and a pattern of bright red and dark interference bands becomes visible on the screen.
The key to this type of experiment is the mutual coherence of the light diffracted from the two slits at the barrier. Although Young achieved this coherence through the diffraction of sunlight from the first slit, any source of coherent light such as a laser can be substituted for light passing through the single slit. The coherent wavefront of light impacting on the twin slits is divided into two new wavefronts that are perfectly in step with each other.
Light waves from each of the slits must travel an equal distance to reach point A on the screen illustrated in Figure 5 , and should reach that point still in step or with the same phase displacement.
Because the two waves reaching point A possess the necessary requirements for constructive interference, they should add together to produce a bright red interference fringe on the screen.
In contrast, neither of the points B on the screen is positioned equidistant from the two slits, so light must travel a greater distance from one slit to reach point B than from the other. The wave emanating from the slit closer to point B take for example the slit and point B on the left-hand side of Figure 5 does not have as far to travel to reach its destination, as does a wave traveling from the other slit.
As a consequence, the wave from the closest slit should arrive at point B slightly ahead of the wave from the farthest slit. Because these waves will not arrive at point B in phase or in step with each other , they will undergo destructive interference to produce a dark region interference fringe on the screen. Interference fringe patterns are not restricted to experiments having the double slit configuration, but can be produced by any event that results in the splitting of light into waves that can be canceled or added together.
The success of Young's experiment was strong testimony in favor of the wave theory, but was not immediately accepted by his peers. The events in place behind phenomena such as the rainbow of colors observed in soap bubbles and Newton's rings to be discussed below , although explained by this work, were not immediately obvious to those scientists who firmly believed that light propagated as a stream of particles.
Other types of experiments were later devised and conducted to demonstrate the wave-like nature of light and interference effects.
Most notable are the single mirror experiment of Humphrey Lloyd, and the double mirror and bi-prism experiments devised by Augustin Fresnel for polarized light in uniaxial birefringent crystals. Fresnel concluded that interference between beams of polarized light could only be obtained with beams having the same polarization direction.
In effect, polarized light waves having their vibration directions oriented parallel to each other can combine to produce interference, whereas those that are perpendicular do not interfere.
Sir Isaac Newton, the famous seventeenth century English mathematician and physicist, was one of the first scientists to study interference phenomena. He was curious about how the brilliant display of color on the surfaces of soap bubbles arose, especially considering the bubbles were composed of a colorless liquid soap solution.
Newton correctly speculated that the color might be attributed to the close proximity of the inner and outer surfaces of the bubbles, and devised an experimental approach designed to mimic the colored patterns observed. In his famous Newton's Rings experiment see Figure 6 , Newton placed a convex lens having a large curvature radius on a flat glass plate and applied pressure through a brass frame to hold the lens and glass plate together, but still separated by a very thin void filled with air and having the same dimensions as visible light.
When he viewed the plates by reflected sunlight, he observed a series of concentric bands having both light and dark colored regions.
The orderly progression of the rings surprised Newton. Near the center of the contact point, the rings were larger and had ordered color patterns starting with black, then progressing through faint blue, white, orange, red, purple, blue, green and yellow. The bands had greater intensity and were thicker at the center, grew thinner as they progressed outward, and finally trailed off at the edges of the brass frame.
Reflection, Refraction, and Diffraction
Previously in Lesson 3 , the behavior of waves traveling along a rope from a more dense medium to a less dense medium and vice versa was discussed. The wave doesn't just stop when it reaches the end of the medium. Rather, a wave will undergo certain behaviors when it encounters the end of the medium. Specifically, there will be some reflection off the boundary and some transmission into the new medium. But what if the wave is traveling in a two-dimensional medium such as a water wave traveling through ocean water? Or what if the wave is traveling in a three-dimensional medium such as a sound wave or a light wave traveling through air? What types of behaviors can be expected of such two- and three-dimensional waves?
We apologize for the inconvenience...
In physics , interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive interference result from the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Interference effects can be observed with all types of waves, for example, light , radio , acoustic , surface water waves , gravity waves , or matter waves. The resulting images or graphs are called interferograms.
Microscopy U - The source for microscopy education
In , Albert Einstein was thinking about photons and excited atoms. He considered an atom excited by a certain amount of energy and what would happen if that atom were hit by a photon with the same amount of energy. He suggested that the atom would emit a photon with that amount of energy, and it would be accompanied by the original photon.
Interference, Diffraction and Polarization of Light. Authors; Authors and affiliations Download chapter PDF. Cite chapter. How to cite?
We head back to the recording studio to study interference and diffraction of sound waves. We investigate qualitatively how diffraction affects sound waves of various frequencies. We also explore how constructive and destructive interference patterns are created and what that means for what we hear coming from a sound source. Develop and use mathematical models to explain mechanical and electromagnetic waves as a propagating disturbance that transfers energy. Develop and use models to describe and calculate characteristics related to the interference and diffraction of waves single and double slits. Plan and carry out investigations to describe changes in diffraction patterns associated with geometry and wavelength for mechanical and electromagnetic waves.
Сэр! - Беккер поднял обе руки, точно признавая свое поражение. - Меня не интересует ваша колонка. Я из канадского консульства.
Все десять присутствовавших при этом человек в напряженном ожидании молчали, когда вдруг заработавший принтер выдал им открытый текст: шифр был взломан. ТРАНСТЕКСТ вскрыл ключ, состоявший из шестидесяти четырех знаков, за десять с небольшим минут, в два миллиона раз быстрее, чем если бы для этого использовался второй по мощности компьютер АНБ. Тогда бы время, необходимое для дешифровки, составило двадцать лет. Производственное управление АНБ под руководством заместителя оперативного директора коммандера Тревора Дж.
- Сейчас найду. Вот. Все прочитали: - Разница в весе незначительна… разделяются вследствие газовой диффузии… 10,032498X10134 в сравнении с 1939484X1023. - Ну вот, наконец-то! - вскрикнул Джабба. - Это и есть их вес.
Так, значит, вы не по поводу моей колонки. - Нет, сэр. Казалось, старик испытал сильнейшее разочарование.
Мы признаем, что у нас есть ТРАНСТЕКСТ, а Танкадо вручает нам шифр-убийцу. Мы вводим ключ и спасаем банк данных. Добро пожаловать, цифровой вымогатель.
Этот термин возник еще во времена первого в мире компьютера Марк-1 - агрегата размером с комнату, построенного в 1944 году в лаборатории Гарвардского университета. Однажды в компьютере случился сбой, причину которого никто не мог установить. После многочасовых поисков ее обнаружил младший лаборант. То была моль, севшая на одну из плат, в результате чего произошло короткое замыкание. Тогда-то виновников компьютерных сбоев и стали называть вирусами.
С мобильника, - мысленно повторил Нуматака. - Это кое-что. К счастью для японской экономики, у американцев оказался ненасытный аппетит к электронным новинкам. - Провайдер находится в районе территориального кода двести два.
Шаги все приближались. Беккер оказался на прямом отрезке, когда вдруг улочка начала подниматься вверх, становясь все круче и круче. Он почувствовал боль в ногах и сбавил скорость. Дальше бежать было некуда.
- Что предпочитаешь. - У меня черный пояс по дзюдо. Беккер поморщился. - Предпочитаю вид спорта, в котором я могу выиграть.
Он вспомнил кровоподтеки на груди Танкадо. - Искусственное дыхание делали санитары. - Понятия не имею. Я уже говорила, что мы ушли до их прибытия. - Вы хотите сказать - после того как стащили кольцо.
Мидж открыла жалюзи и посмотрела на горы, потом грустно вздохнула и перевела взгляд на шифровалку. Вид купола всегда приносил ей успокоение: он оказался маяком, посверкивающим в любой час суток. Но сегодня все было по-другому. Она поймала себя на мысли, что глаза ее смотрят в пустоту.
Но он не был готов к тому, что произошло в следующее мгновение.