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Table of contents :
1.0 Splitting of Light into Colors
1.3 Summary of Results
2.0 Double Slit Experiment
2.3 Summary of Results
3.0 Measurement of Speed of Light ( Fizeau )
3.3 Summary of Results
4.0 Michelson - Morley Experiment
4.3 Summary of Results
5.0 Photoelectric Effect ( Einstein )
5.3 Summary of Results
THE FIVE MOST IMPORTANT SCIENCE EXPERIMENTS……..EVER!! This research focuses on five famous experiments in science: splitting (dispersion) of light into colors, Young’s Double-Slit experiment, Fizeau’s measurement of speed of light, Michelson-Morley experiment, and Einstein’s photoelectric effect. Specifically, the research provides each experiment’s background information, method, succinct overview of the results, and implications.
1.0 Splitting of Light into Colors 1.1 Background Also called white light, the visible spectrum encompasses an array of its component colors. The colors can be seen once light penetrates through a triangular prism. Having penetrated the prism, the spectrum forms the seven colors of the rainbow – violet, red, blue, orange, indigo, green, and yellow. This phenomenon of light splitting into its component colors had challenged physicists for many years. It created a controversy regarding the nature of the visible spectrum during the 1600s, putting prisms at the center of the controversy. The controversy was intensified by two schools of thought among the scientific community of the time; with one school believing that light was a particle while the other contending that it was a wave. The renowned English mathematician and physicist, Sir Isaac Newton was inclined to the latter school of thought. In contrast, the prominent Dutch philosopher by the name Christiaan Huygens held that light was a particle rather than a wave. Eventually, the controversy surrounding the splitting or dispersion of light led to the consensus among scientists that light exhibited both particlelike and wave-like properties. This insight was gained in the 1900s after the emergency of the quantum theory, and for nearly three centuries, the
scientists from each school of thought continued conducting experiments in an endeavor to affirm their standpoint. One of such experiments made use of prisms. The modern understanding of the dispersion of light can be traced to Newton’s series of experiments published in 1672. He was the first physicist to understand the rainbow by refracting visible light using a prism, splitting it into its constituent colors.
1.2 Method Newton began experimenting with different colors during the midseventeenth century. During the time, it was widely held that color was merely a mixture of darkness and light. There was also a widely held belief that prisms often color the light passing through them. It is important to note that Hooke had already proposed the theory of color and had established a scale of colors of varying intensity, ranging from dull blue to brilliant red. On realizing that the theory was false, Newton decided to set up a prism experiment and projected the visible spectrum onto a wall. He further reflected it back in order to invalidate the theory that the color of the light emerging from prisms was produced by the prisms. Newton’s experiment would form the foundation for the understanding that white light consisted of various constituent colors. Figure 1 below illustrates the phenomenon observed when white light is incident upon one of the slanting surfaces of the prism.
Figure 1: A monochromatic light incident on the prism’s surface. From Figure 1 (b), it is evident that when light enters through a transparent glass prism, it emerges on the other side of the prism forming rainbow colors. If the rainbow colors are reflected back through the prism, they recombine forming white light, a phenomenon called the principle of reversibility of light. To this end, Newton was able to discredit the theory that the prism colors the visible spectrum (white light).
1.3 Summary of Results It was later discovered that the separation of the visible spectrum into its constituent colors occurs as a result of diffraction and refraction of the light. Defined as the bending of light waves towards the normal, refraction occurs due to the fact that the speed of light in the glass prism (and any other dense medium) is lower than its speed in air (or less dense medium). Thus, the splitting of light unto rainbow colors is possible since the visible spectrum encompasses photons with varying wavelengths. Each of these wavelengths undergoes refraction differently, forming different angles with the normal. From Figure 1 (a) it is evident that when a ray of light enters the prism (dense medium) from air, it is bent or refracted from the normal. Conversely, the ray is refracted away from the normal to the surface with which emerges to the air. Loosely defined as the spreading out of light, diffraction refers to the phenomenon occurring as the visible light passes through a narrow slit. In this case, the individual photons constituting the light behave just like mechanical waves passing through an aperture (narrow opening). As they pass through the aperture, the waves not only bend around corners but also spread out. Such waves would definitely generate dark and light fringes once they are allowed to hit a screen.
While diffraction is wave characteristic, refraction can be explained in terms of the propagation of the fundamental particles. In order to gain deep insight into the concept of refraction, it is important to light itself and its interaction with the material through which it propagates. Light can be thought of as pulse of electromagnetic energy. Were light to be a mere wave, it could have needed the medium through which it can travel to reach the Earth’s surface. However, the Michelson-Morley experiment, which we will examine later, proved that light does not require material medium (ether) in which to travel through. Thus, despite its wave characteristic, light is not purely a wave. As an electromagnetic phenomenon, light consists of both magnetic and electric fields, in which the changing magnetic field induces an electric field and vice versa. The beam of light actually results from the frequency of the fields’ changes. The speed of light remains constant while travelling through a vacuum. However, the photons (packets) of energy constituting light interacts with the medium’s atoms as light travels through such medium and thus decreasing the speed of light. The speed decreases with an increase in the density of the medium. The ratio of incident light’s velocity to that of the refracted light is referred to the refractive index for the
interface. It is given by the equation; n =
where, n = refractive index,
vR = velocity of refracted light, and vI = velocity of incident light. From Newton’s experiment, the prism was able to disperse the white spectrum because as the beam hits the air-glass (prism) interface, its direction changes. The magnitude of change in direction is dependent on the interface’s refractive index (n). The refractive index can be expressed in terms of Snell’s Law as; sin θR/SinθI, where θR = angle of refraction, θI, = angle of incident, and n = refractive index. It is noteworthy that the velocity of any wave is the function of its wavelength (λ) and its frequency. However, the frequency (f) of the white spectrum remains constant as it travels from one medium to another. This means that it is the wavelength (λ) which changes as the light penetrates through the interface in order to maintain the refractive index (n) constant. Thus, light with a shorter wavelength undergoes greater refraction than that with a longer wavelength. Overall, the visible spectrum consists of light with varying wavelengths of photons. Within such spectrum, violet monochromatic light has the shortest wavelength while red monochromatic light has the longest. As such, it follows that red light is least deviated while violet light is the most deviated as these rays move from air (or vacuum) to the glass prism
(or other medium). Other colors are also refracted differently and hence the formation of the various colors of the rainbow. The white light splits into its component colors on the opposite side of a triangular prism because each constituent color’s angles of refraction and incident are different. The angle of deviation is defined as the angle differential between the incident and the emergent rays. For a rectangular prism, this angle is equal to zero. However, for a triangular prism, each monochromatic light emerges with a different angle of deviation, resulting in the formation of rainbow colors.
1.4 Implications The splitting of light is important because it led to the understanding of how the rainbow is formed. It is noteworthy that the rainbow is only visible when the observer is at a certain angle to the rain shower or clouds and the Sun is behind the observer. Just like prisms, the water droplets in the sky also refract white light, splitting it into components of different colors. However, unlike prisms, the droplets are spherical in shape. The light incident at the rain drop that emerges at the other side does not produce rainbows. Instead, the light that produces the rainbows is the one that undergoes total internal reflection within the droplet, emerging from the same side of the given droplet (see Figure 2).
Figure 2: Rainbow formation by raindrops Figure 2 above depicts rainbow formation through total internal reflection and refraction of solar rays in water drops. The rainbow seems to be an incomplete circle that is centered on the so-called antisolar point. It lies on the line drown from the Sun and passing through the observer’s eye. The rainbow’s colors from its inner to its outer circumference are violet, indigo, blue, green, yellow, orange, and red, respectively. Given that the
raindrops’ diameters are larger than the sunlight’s wavelength, the primary bow can be described based on the classical geometrical optics theory. It is important to note that sunlight has a downward trajectory. While the totally internally reflected light can emerge from the raindrop at any angle, the greatest concentration of light exits at an angle of deviation of 42º. Dispersion of light is also largely applicable in today’s world. Particularly, quite a number of spectrometers employ a certain grating in dispersing light. Having dispersed the light, the spectrometers can either maintain the grating fixed or scan it. The various components of the visible spectrum can then be filtered out by placing a suitable filter across the already dispersed light. Optical filters have widespread applicability in various domains such as wavelength division multiplexing (WDM). Such technique (WDM) is often useful in fiber optic communication.
2.0 Double Slit Experiment 2.1Background The double slit experiment is among the most prominent physics experiments. Such experiment demonstrated the wave nature of electromagnetic spectrum. During the early 19th century, most scientists held that light was composed of tiny particles rather than waves. Christiaan Huygens was the first scientist to think of light as a wave, which was contrary to Isaac Newton’s believe. From his experiments on light, Huygens came up with what was later known as Huygens’ Principle. The principle states that each point on a wave-front acts as a source that emits secondary wavelets, diffracting in all direction at the same speed as that of propagation of the primary waves. This implies that each point on particular wave-front seems to be generating secondary circular waves. In most cases, the secondary waves recombine and continue with the propagation. Although Huygens’ Principle was largely applicable to the reflection and diffraction of light, Newton did not believe that it provided valid explanations for such phenomena. Instead, he held that there must be other different explanations for the diffraction and interference of light. Generally, Newton’s view prevailed owing to his tremendous stature during
the time. As such, Huygens’ Principle was largely disregarded that it was not sufficient enough to prove the dual nature of light. It was not until 1801 the English physician and physicist, Thomas Young proved the wave nature of light using the double slit experiment. With this experiment, Young revealed that a monochromatic light passing through two vertical slits undergoes diffraction, forming a pattern of various vertical lines that spread out on a horizontal manner. Were it not for interference and diffraction, the light could have emerged through the slits to merely form just two lines on the screen. Young’s experiment led to the widespread acceptance of light’s wave property.
2.2 Method Figure 3 below depicts the experimental set-up used in Young’s double slit experiment.
Figure 3: Young's double slit experiment As depicted in Figure 3, Young illuminated a single-wavelength (monochromatic) light through a pair of slits placed parallel to each other. As it emerged from the other side of the screen, the monochromatic light from the two slits was diffracted, forming a pattern of vertical lines on the screen. It is noteworthy that the pair of slits served as two different point sources. Having performed this experiment using monochromatic light, Young then repeated it using light from the Sun, in which the Sun’s rays served as a single source. In this regard, he first passed the light through one of the slits to make somewhat coherent. Coherent refers to waves with a
definite phase correlation or arriving in phase. The opposite of coherent is incoherent, which refers to waves with random phase correlation. The main reason underlying passing the light through the slits was to create two coherent sources of light capable of undergoing interference once they passed through the slits. While Young was able to obtain alternate bright and dark fringes (lines) on the screen when using a monochromatic light source, this did not occur when using sunlight as a point source.
2.3 Summary of Results When the single-wavelength light was used, the resulting dark and bright lines indicated destructive and constructive interference, respectively. Constructive interference was obtained once two waves in phase interfered or superimposed with each other, forming a single wave with larger amplitude than their respective amplitudes. In contrast, destructive interference occurred whenever two waves that were out of phase interfered, resulting in the cancellation of their amplitudes. Waves out of phase are the ones that were shifted from each other by half a wavelength. Figure 4 below illustrates destructive and destructive interference.
Figure 4: (a) constructive and (b) destructive interference The constructive and destructive interference depicted above can be explained on the basis of diffraction and interference as shown in Figure 4. Pure constructive interference (bright fringes) was observed where two troughs or two crests superimposed upon each other, forming larger amplitude whose magnitude was equal to the sum of the magnitudes of the two individual crests or troughs. In contrast, pure destructive interference (dark lines) was observed where a crest interfered with a trough, forming a single wave of zero amplitude. From the wave nature of light perspective, light is thought of as consisting of waves, each with troughs and crests. The light that had already undergone interference must fall on the white screen and undergo scattering into the observers’ eyes for them to see the resulting pattern. It is also noteworthy that the destructive and constructive interference regions spread out of the two slits at well-defined angles to the initial monochromatic beam of light. As we shall see later, such angles depend on the length between the two slits (d) and the wavelength of the monochromatic waves (λ). The two slits generate two coherent wave sources that can undergo interference. Upon penetrating through the slits, light is diffracted away from each of the slits due to the narrowness of the slits. Such waves
interfere and overlap in destructive and constructive manner forming dark regions and bright lines, respectively. Such pattern of alternate dark and bright fringes can only be observed once the already interfered waves fall onto the screen and undergoes scattering. Figure 5 illustrates the pattern observed on the screen after the interference of the waves.
Figure 5: Interference pattern observed on the screen
In order to gain insight into the interference pattern observed, it is important to take into consideration the manner in which the waves from each slit travel to the screen. Each slit is at a certain distance way from any point on the screen. When the path difference between any two waves arriving at a point on the screen is a whole wavelength, constructive interference takes place. In contrast, destructive interference occurs when the path difference is half a wavelength. In general, constructive interference occurs whenever the path difference is a whole number of wavelengths such as λ, 2λ, 3λ . . . nλ. The converse is true since destructive interference takes place whenever the path difference is half-integral number of λ such as λ, λ . . . λ. Figure 6 illustrates the occurrence of both constructive and destructive interference based on the path difference.
Figure 6: (a) Destructive interference (dark) and (b) constructive interference (bright) on the basis of the waves’ path difference From Figure 6 above, simple geometry indicates that the path difference between two waves is equals to dsinθ. As mentioned earlier, constructive interference only occurs when the path difference is a whole number of λ. Thus, dsinθ = n λ, for n = 0, 1 . . . (constructive interference), where λ is the monochromatic light’s wavelength, θ denotes the angle of the wave from the beam’s initial direction, and d is the distance or length between two slits. Destructive interference is represented by the equation; dsinθ = (n +
λ, for n = 0, 1 . . .
When the slits’ distance from the screen is far much greater than that between the two slits, the difference between each slit’s path to a certain shared point on the screen (Δl) is equals top dsinθ as depicted in the Figure 7.
Figure 7: Δl is equals top dsinθ, when the distance of each slit is > >than d Overall, the double slit interference’s equations reveal that alternate dark and bright fringes are formed on the screen. When the slits are vertical, the interference fringes are formed, spreading out horizontally on both sides of the incident, single-wavelength beam. The brightest fringe is the one at the center while the brightness of other fringes declines away from the center on either side. Figure 8 below is an illustration of alternate dark and bright fringes obtained having performed Young’s double-slit experiment.
Figure 8: Alternate dark and light fringes formed on the screen
2.4 Implications Young ‘s double slit experiment is among the most significant studies in the history of physics. While physicists did not immediately appreciate this experiment, it would form a basis for quantum mechanics nearly a century later. As a quantum mechanics-based experiment, Young’s double-slit experiment affirmed the wave-particle property of various fundamental micro-objects like photons and electrons. The experiment is also important in optics. It was Niels Bohr who postulated the wave particle duality of light in his effort to provide an explanation for the double –slit experiment. The main idea underlying the wave-particle duality is that all fundamental particles exhibit both particle-like and wave-like properties based on the properties being investigated. Bohr’s insights resulted in the development of not only quantum mechanics but also quantum field theory. Notably, the quantum field theory forms the foundation for particle physics’ Standard Model. The model provides the most accurate insight into the working mechanism of particles. The double-slit experiment would later form the basis for investigating the wave-particle property of various other particles apart from the photons that were used in the original experiment. However, the
notion of utilizing different particles other than photons only emerged after the introduction of quantum mechanics and the concepts of de Broglie, when scientists postulated that all the elementary particles might exhibit the wave property, with their characteristic wavelengths based on their respective momenta. The Double-slit experiment’s single electron version was conducted in 1974. Recently, the latest version of the experiment utilized carbon’s C60 allotrope, also called buckyballs or buckminsterfullerene.
3.0 Measurement of Speed of Light (Fizeau) 3.1 Background The speed of light is among the most well-developed physics values given that it was measured with utmost accuracy to an extent that it is used to define the meter. However, prior to the seventeenth century, physicists and other scientists including but not limited to Rene Descartes and Johannes Kepler believed that light had an infinite speed. They thought that light can traverse any distance instantaneously. However, Galileo Galilei questioned such premise and made attempts to establish the speed of light from an experimental perspective. However, Galileo’s experimental techniques were largely crude. He stood on a certain hilltop with his assistant standing on another distant hilltop. Each of them had a lamp that produced light and could be uncovered to generate light and covered to cut off the light. Given that the distance between the lamps was known, Galileo attempted to measure the time elapsing between two flashes of light in an endeavor to determine the speed of light. However, he ended up with vague and inconclusive results. His results notwithstanding, he drew the conclusion that light travelled much faster than sound.
The first viable experiment to ascertain the speed of light was conducted by the Danish astronomer, Ole Roemer in 1649. This astronomer observed Jupiter’s moons and noted the occurrence of their respective eclipses at different times. This phenomenon was attributed to Jupiter’s different relative positions with respect to the Earth. Roemer made a correct deduction regarding this phenomenon by arguing that it was as a result of the moons travelling a greater distance once the Earth was further from them. In other words, the effect did not occur as a result of the moons’ orbits’ actual shifts. Using the diameter of the orbit of the Earth that was acceptable during the time, he drew a conclusion that the speed of light was 240,000 km/s. Though Roemer’s value was still far from the actual speed of light, it formed a solid foundation for subsequent experiments that were aimed at determining the actual speed of light. In 1728 for instance, an English physicist, James Bradley contributed to the increasing body of knowledge by calculating the speed with which light travels in a vacuum using stellar aberration. Bradley’s conclusion was that light travelled at a speed of 301,000 km/s. While the results were getting closer to the actual value, several decades elapsed before the French scientist by the name ArmandHippolyte-Louis Fizeau developed a terrestrial experiment for measuring the speed of light.
Born in Paris, France, Fizeau’s father was a professor of medicine as well as a physicist. Given that his father had left him with considerable wealth once he died, Fizeau was able to pursue his interests freely without having to worry of making a living. Focusing on scientific research, Fizeau’s initial intent was to become a physician. However, he changed his mind, opting to undertake astronomy at the Paris Observatory.
3.2 Method Fizeau is accredited for being the first physicist to measure the speed of light terrestrially in 1849. The concept underlying his experiment was to measure the time it would have taken a light pulse to traverse between a source of light and a mirror placed approximately 8 kilometers away from the source. Fizeau used a rotating cogwheel consisting of 720 notches to cut off the beam of light and establish its flight time. It is noteworthy that the cogwheel was capable of rotating at varying speeds. Jan Frercks provides details of the original terrestrial experiment used by Fizeau, which is depicted in Figure 9 below.
Figure 9: Layout of Fizeau’s optical arrangement for determining the speed of light Figure 9 above illustrates a reproduction of Fizeau’s schematic diagram depicting the light path. Such path is virtually retained completely until the final realization. The light emanating from the source is focused by a lens. Part of the light is reflected on the cogwheel’s circumference. A
telescope then bundles and directs the reflected light until it arrives at the other telescope. On the other hand, a mirror held in between the objective lens’s focus reflects the light back in such a way that it strikes the initial telescope again. The glass plate transmits a portion of the rest of the light, which can be observed with the help of an eyepiece. However, Fizeau’s schematic diagram does not provide an explanation on how the arrangement was developed. Additionally, all the mechanical devices required by the experiment were inexistent during the time. Nonetheless, he correctly envisioned the correct number of cogs of the cogwheel and the distance between the two telescopes that would have produced the desired results. Fizeau’s experiment has been reproduced in recent studies such as the study by Claude Semay, Francesco Lo Bue, Soizic Melin, and Francis Michel. In such study, the technicians and physicists based at the University of Mons in Belgium used modern devices to reproduce Fizeau’s experiment, allowing members of the public to determine the speed of light. They used low laser (5mW) as the light source and replaced the cogwheel with a chopper that was driven electrically. A CCD camera was used to film the reflected light, which was then sent to a computer to facilitate the members of the public to make measurements. The experiment adhered to
the same principles developed by Fizeau only that it used modern equipment instead of those proposed by Fizeau. The chopper wheel of 445 slots and1 02 mm diameter served as the core of the optical set up. The wheel’s maximum speed of rotation was 100 rps. Such speed implied that it would take an adjacent slot 1.1 × 10−5 seconds to replace a particular slot. Unlike Fizeau’s experiment where the reflected light and the light source had to pass through a single slot, Semay et al.’s experiment’s reflected light and the light source “passed through diametrically opposite points of the wheel”. The significance of such modification of the experiment was to minimize the challenge associated with unwanted reflections. This meant that the beam of light traversing through the firing line at rest did not necessarily pass to the return line unaltered. Nevertheless, the experimenters were able to finely adjust the transmission’s degree using the micrometer screws. In practice, the return line’s lens groupings were initially adjusted at rest in or order to allow the maximum amount of light to reach the CCD camera. An increase in the wheel’s rotation speed resulted in progressive blockage of the reflected light until minimal light was observed. Increasing the speed of rotation further allowed the observer to see successive minima and maxima of the signal. However, the set up produced just two
successive minima since the time taken for the light to travel in the two-way journey between the reflector and the laser was 3.6 x 10-5. The experimenters placed a green interference filter whose wavelength corresponded to the lesser light’s wavelength in front of the CCD camera in order to improve the contrast while eliminating unwanted light.
3.3 Summary of Results While analyzing the amount of laser light received by the CCD camera, Semay et al. employed simple yet popular software for amateur astronomy referred to as RSpec. With such software, it was possible for the experimenters to select an image generated by the camera and measure its light intensity. The camera reached minimum amount of light upon reducing the peak intensity to a small residual peak or background noise level. The measurements were based on the detection of only 2 consecutive minima of the laser light owing to the fact that it was challenging to ascertain the precise position of peak intensity. Assuming that two frequencies, f1 and f2 (measured in in Hertz) were detected, with f1 > f2, then the time it takes the laser light to cover the twoway journey is given by the expression 1/( f1 - f2 ) seconds. Finally, the speed of light obtained from the measurement is determined by: cm = 2d(f1 - f2) km/s, Where cm is the speed of light (measured), and d = distance between the reflector and the optical device = 5368 meters. Figure 10 is a graphical representation of the various values of cm determined by the public.
Figure 10: cm values measured by the public
3.4 Implications The terrestrial determination of the speed of light by Fizeau’s experiment is of great importance in the sense that it forms the basis for the modern theories of physics. Although still being investigated, such theories postulate that gravitational particles (waves) travel at a speed equals to that of light. Such theorization is critical in studying gravitational waves’ effect based on colliding neutron stars and black holes. From a theoretical perspective, the waves can only travel at a speed close to that of light but cannot exceed it. Similarly, the time-travel theories are based on the speed of light. Time travel is a concept that denotes travelling between two different points in time rather than in space. Such theories have dominated sci-fi movies, in which humans are able to get in some kind of spaceship and arrive in the future or past. For one to accomplish time travel, the spaceship must travel at a speed close to that of light. In practice, the speed of light has enabled scientists to accurately determine the distance between the Earth and other bodies, including the moon, the Sun, and the stars.
4.0 Michelson-Morley Experiment 4.1 Background Performed in 1887, the Michelson Morley experiment is among most renowned and celebrated experiments. The experiment was focused on searching for the presence of ether drifts on the shifts of interferometer fringe. It entailed interfering beams of light that travelled orthogonally to each other on a movable device. The experiment was specifically designed to detect the speed with which the Earth travels at in its own orbital through the theorized ether, employing the projected shift in the light’s speed as a result of the motion of against or with the ether wind. Michelson-Morley experiment was a second-order experiment due to the two-way journey of the light beam. In other words, the shift in fringe that the experiment sought for varied proportionally with the second power of the orbital velocity of the Earth divided by light’s velocity (c). The experiment yielded null results since the observed fringe-shift was substantially less than the projected shift. The results were attributed to the revolution of the Earth. The original experiment sought to ascertain whether or not luminiferous ether existed in the universe by trying to examine the impact of the apparent ether wind’s speed on the speed of light as a result of the
motion of the earth around the Sun. In 1964, T. S. Jaseja and other researchers introduced an advanced version of the Michelson-Morley experiment. Using laser technology, such researchers were able to produce an enhanced system that was 25 times more sensitive than the original one. However, they did not detect any shift in the beat frequency of the system within the accuracy of its measurement. Jaseja experiment was later improved by Brillet and Hall in 1979, who sought for the light speed anisotropy on the basis of the cavity resonator’s resonant frequency-shift. They claimed to have achieved a significantly greater improvement than the former version of the experiment. The modern versions of the original experiment performed by Michelson and Morley employ electromagnetic resonators in analyzing light speed isotropy. Generally, such modern systems focus on comparing two orthogonal resonators’ resonant frequencies in response to either rotational or orbital motion. Such modern systems have progressively lowered the light speed anisotropy’s limit.
4.2 Method Figure 11 depicts the fundamental apparatus utilized in the Michelson-Morley experiment. The system moves through the theorized ether at a velocity v and direction PM1. At the beam splitter P, light originating from the source S gets split to form two different beams. One of the two beams strike the first mirror M1 and then returns to P, at which it undergoes reflection into the interferometer I. On the other hand, the other beam undergoes reflection at point P to strike the second mirror M2 and is reflected back travelling through point P into the interferometer I. At the interferometer I, both beams undergo interference forming a particular interference pattern.
Figure 11: Michelson-Morley experiment Taking the moving system due to ether drift as the frame of reference, the resultant speed of light towards MI between MI and P is given by c – v. Similarly, the speed towards P is equals to c + c. In addition, the resulting speed of light towards both directions between M2 and P is equals to (c2 – v2)1/2. For the two optical path lengths l2 = PM2 and l1 = PM1, the time it would take the light beam to traverse from point P to the first mirror M1 is calculated as follows: t1(a) =
Similarly, the time taken t1(b) for the beam of light to traverse from the first mirror M1 to point P can be computed using equation (2) below: t1(b) =
From equations (1) and (2) above, it follows that the time taken by the light beam to cover the round-trip journey can be calculated as shown by equation 3 below: T1 = t1(b) + t1(a) = 2l1/c(1 – v2/c2)…………………. (3)
In a similar manner, using relevant equations as equations (1) to (3), it can be shown that the time t2(a) it would take the beam to traverse from point P to the other mirror M2 is computed using equation 4: t2(a) = l2/ √ (c2 – v2) ………………………………… (4) A similar equation for the time the beam of light would take while travelling from the second mirror M2 to b is: t2(b) = l2/ √ (c2 – v2) ……………….. (5) Thus, the time taken to cover the round –trip journey along PM2 can be computed as: T2 = t2(b) + t2(a) = 2l2/ c√(1 – v2/c2)……………………. (6) The approximate time difference T1 – T2 = ΔT = is computed as shown in equation (6): T1 – T2 = ΔT = 2l1v2/c3 +2(l1-l2)/c – l2v2/c3………… (7)
Assuming that the system is turned through an angle of 90 degrees in the direction of movement, then the approximate differential time because: T'1 – T'2 = ΔT' = 2l1v2/c3 +2(l1-l2)/c – l2v2/c3……… (8) The change in such time differences becomes: ΔT– ΔT' = Δ = (l1+l2)v2/c3 ………....... (9) If l2 = l1 = l, equation (9) reduces to: Δ =2lv2/c3 = 2l/c* v2/c2 …………………. (10) A shift in fringe will be observed in the interferometer, which would be equivalent to δ = Δ. The second-order time difference (Δ = 2l/c* v2/c2) is reduced significantly as a result of lengthy contraction emanating from the movement of the apparatus through the theorized ether. Such reduction in time difference (Δ) accounts for the failure of MichelsonMorley-based experiments to detect ether drift.
4.3 Summary of Results Even though Michelson-Morley experiment was repeated severally, the results were always negative. This indicated that the apparatus did not detect any ether wind in the universe. The results negated the possibility of occurrence of luminiferous ether in the universe, compelling Einstein to solely rely on the geometrical (mathematical) space-time model in explaining his theory of relativity. The model was devoid of conceptualizing any substance. As such, scientists have been contending that ether did not exist and that the experiment conducted by Morley and Michelson was correct. However, latest scientific evidence derived from modern cosmology and quantum physics has contrasted with the results of Michelson-Morel experiment. Such evidence suggests indicates that the physical vacuum is not actually an absolute vacuum since 95% of the universe’s total massenergy ware in the alleged vacuum. Such mass energy existed as dark substances (dark energy, dark matter). Similarly, the Higgs field, which was proven recently suggests for the presence of a false vacuum. In addition, the stress-energy tensor of Einstein consists of hydrodynamic features, including momentum flux, momentum density, shear stress, pressure,
density (T00), and mass (energy of the vacuum). Furthermore, Higgs field’s cosmological constant depends on mass (or vacuum energy). It is important to note that, prior to the Michelson-Morley Experiment, Einstein has suggested for the presence of ether in his general theory of relativity. In his theory, he argued that there existed ether in space since it (space) exhibited physical qualities. Thus, the theory does not conceptualize the existence of space without any ether. In general, the Michelson-Morley experiment was actually a wrong test, which has also been invalidated from a theoretical perspective. Given that the apparent wind has no impact on the wave speed, it follows that the MichelsonMorley experiment could not detect the presence of any ether in the universe even if it was adequately sensitive. A recent experiment by Stephan J. G. Gift used a modified version of the original Michelson-Morley experiment to determine the presence of induced ether drift. The modified experiment replaced mirrors in the original system with synchronized GPS clocks. Such clocks facilitate the experimenter to accurately determine a one-way light travel, unlike the Michelson-Morey experiment that relied on a two-way trip. Moreover, the researcher-oriented arm PM (see Figure 11) along a latitude line and positioned arm PM2 along arm PM1’s direction towards the East. With
such arrangement, the researcher was able to detect ether drift emanating from the Earth’s rotation.
4.4 Implications The Michelson-Morley experiment is important in today’s scientific world. Particularly, the Michelson interferometer that was utilized in the experiment serves as a basis for the modern optical interferometry designs. Its fundamental working mechanism involves the splitting of a singlewavelength light beam into two different beams with equal amplitudes. One of the two beams strike a movable mirror while the other strikes a fixed mirror, generating two different lengths of beams whose convergence occurs at the screen of the detector. This in turn produces an interference pattern characteristic of the beam’s wavelength. Such technique allows researchers to measure small changes in length, refractive indices of transparent media, and the wavelength of monochromatic light. The Michelson-Morley experiment has widespread applicability areas. Notably, it formed the basis for the development of Einstein’s special relativity model, even though it failed to reveal the presence of hypothetical ether wind. The Michelson interferometer is also applied in detecting the presence of gravitational waves. Similarly, it is also used in determining the upper atmosphere’s Doppler shifts and widths and revealing its winds and temperatures. The Instrument also forms the core of the so-called Fourier transform spectroscopy. The interferometer also has applications in fiber
optics, optical coherence tomography, and astronomical interferometry. In general, the interferometer that resulted from the Michelson-Morey experiment has many applications that they cannot be exhaustively discussed here.
5.0 Photoelectric Effect (Einstein) 5.1 Background When light rays of sufficient frequency shines on the surface of a metal, it dislodges electrons from that surface, a phenomenon called photoelectric effect. Also called photo ionization or photoemission, photoelectric effect is the process through which electrons are ejected from a metal’s surface as a result of an electromagnetic radiation (light) incident upon it. The process occurs as a result of the energy transferred from photons to the electrons. The phenomenon is not limited to metals as it can also occur in other conductors. The material that exhibit photoelectric effect is called a photoemissive material the ejected electrons are referred to as photoelectrons. Based on the wave nature of light, classical physicists theorized that once the electric field created by light hits on a metal plate; it transfers heat energy to the electrons causing them to vibrate. Such physicist also postulated that the intensity (brightness) of the incident light was directly proportional to the energy possessed by the light. In 1887, Heinrich Hertz became the first scientist to observe photoemission while experimenting with a spark gap generator. This scientist observed that the sparks created between two metal spheres within a certain transmitter triggered other sparks that moved between two other
spheres within the receiver. Hertz further noticed that the spark gap generator’s sensitivity increased when ultraviolet (U.V.) or visible light was incident on it. It was not until 10 years later (1897) when J. J. Thompson found that such increase in sensitivity was due to light energizing and pushing on the photoelectrons. Subsequent experiments conducted to investigate photoemission yielded results that were inconsistent with classical wave nature of light. In this regard, classical physicists drew from the wave theory to make three critical predictions: (1) the energy of the ejected electrons increases with increase in the incident light’s intensity, (2), the incident light should is capable of ejecting electrons regardless of its frequency, provided that its intensity is sufficient enough, and (3) continuous exposure of the metal surface to low-intensity light is necessary for photoemission to occur. However, through experimentation, the classical physicists’ predictions were invalidated. It turned out that the energy possessed by the ejected electrons is independent of the light intensity. It was also established that the incident light’s frequency must exceed a certain critical value, known as the threshold frequency, for photo ionization to occur. The third prediction was also invalid since it was established that electrons are dislodged from the surface once light falls on it. Thus, the classical physicists failed to
explain photoemission based on the wave nature of light, paving way for Albert Einstein.
5.2 Method Heinrich Hertz’s assistant, Philipp Lenard is accredited for conducting the earliest, definitive experiment on photo ionization. In his experiment, Lenard used a thoroughly cleaned metal sample placed housed a vacuum glass tube in order to study photoelectric c effect on the mental surface without any other oxidants or contaminants. Another metal plate was held opposite the sample. The evacuated glass tube was constrained or positioned in such a way that it allowed light to fall to fall only on the metal sample. Such tube was referred to as a photocell (see Figure 12 below).
Figure 12: Photocell As depicted in Figure 12, the tube was connected to an external circuit with a microammeter, voltmeter, and a variable supply of electric power. The surface of the sample metal was then illuminated with light of varying intensities and frequencies.
Once the light was shone on the metal surface, electrons were dislodged out of it, leaving the surface with a slight positive charge. Note that the other metal plate is connected to the negative terminal of the power supply and hence it is negatively charged. It would push the photoelectrons ejected from the metal sample back to the sample metal. Given that the circuit generated a very small current, it was measured using the microammeter. Supplying low voltage from the eternal circuit implied that least energetic photoelectrons were trapped at the surface of the photoemissive plate, reducing the current flowing through the microammeter. More and more electrons were trapped with increase in voltage until none leave the sample metal’s surface. The voltage at which none of the photoemissions left the surface of the photoemissive metal was referred to as the stopping potential. Lenard’s photocell experiment revealed that the intensity of the light incident on the photoemissive material did not influence the photoelectrons’ maximum kinetic energy. In 1914, the experiment conducted by an American physicist by the name Robert Millikan found that photoemission could not occur until the incident light is greater than a particular cutoff value known as the threshold frequency. Given that the photoelectric effect was consisted with the classical dual nature of light, Albert Einstein had to step in to explain it from the wave nature perspective.
Lenard’s discovery about the characteristics underpinning photoemission had posed challenges to classical electromagnetic wave nature theory of light. Particularly, this model could not provide convincing explanation regarding the qualitative evidence about light, despite that such evidence had been replicated in a number of studies. Albert Einstein developed a mathematical model of photoemission on the basis of the premise that light existed in discrete amounts of energy, referred to as quanta. Such quanta would later be renamed as photons. It is noteworthy that the concept of light quanta was derived from Max Planck’s 1901 experiments on blackbody radiation. By then, the concept was still elusive given that even Planck himself did not understand much about it. In his prominent 1905 thesis, Einstein argued that light exists in packets of energy (quanta) with energy equals to hf, where h represented Planck’s (6.63 × 10−34 Js) constant and f denoted the frequency of light. Einstein further argues that once the quanta penetrate the body’s surface layer, at least some of their energy is converted into the photoemissions’ kinetic energy. Moreover, he theorized that, while leaving the surface of the photoemissive material, each electron has to do some work, denoted by W. Such work is characteristic of the photoemissive material. The photoelectrons dislodged at right angles from the photoemissive material’s
surface would have the greatest velocities. Each photon’s maximum kinetic (Kmax) energy is denoted by Kmax = hf – W The equation above can be written as: Kmax = hf – hfo = h(f – fo), where fo is the threshold frequency. But hfo = ϕ where is the work function ϕ of the photoemissive material. Thus, Kmax = E– ϕ, where, E is the energy of the absorbed quanta (photon).
5.3 Summary of Results In a nutshell, Einstein was able to show that the photoelectrons’ maximum kinetic energy (Kmax) depends on material on the photoemissive material’s surface and the frequency of the incident light illuminating the surface (see Figure 13).
Figure 13: Kinetic energy of photoelectrons versus frequency of incident radiation Figure 13 above show that the photoelectrons’ kinetic energy increases as the frequency increases and vice versa. Each curve intercepts with the energy axis, indicating the threshold frequency below which photoemission cannot occur. The different photoemissive materials used were titanium,
beryllium, and potassium. Their characteristic curves cut the energy axis at different points, indicating that each material has its own characteristic work function (ϕ).
5.4 Implications The discovery of photoelectric effect was not in vain as it of great importance to other scientific discoveries. Notably, it led to the appreciation of the wave-particle nature of light. This helped in solving the challenges that faced earlier classical physicists who assumed that light was purely a wave. Thomas Young’s Double Slit experiment explains the wave nature of light since it can undergo destructive and constructive interference. On the other hand, Einstein drew from Max Plank’s concept of quanta to show the particle nature of light. In the long run, scientists appreciated the waveparticle duality of electromagnetic radiation. In addition, Bohr’s hydrogen atom mode is based on the photoelectric effect. Based on trial and error method, Bohr endeavored to derive a formula describing Balmer’s line spectra. This scientist used the concept of Einstein, Planck, and Rutherford’s model of an atom as well as the classical explanation of a particle moving in a circular motion. In his study, Bohr made a number of assumptions. One of the assumptions was that an electron in the hydrogen atom moves in a circular manner. The other assumption was that some angular momenta of the electron were allowed while others were not. The third premise was that the electrons moving around the allowed orbits do not emit electromagnetic waves, implying the
stability of such orbits. Bohr further theorized that the emission or absorption of electromagnetic radiation occurs only when the electron shifts from certain allowed orbit to the next. Finally, he theorized that the emission of a photon takes place only once the electron shifts from a higher-energy orbit to a lower one. Figure 14 below depicts the depiction of lithium atom based on the planetary Bohr’s model.
Figure 14: depiction of lithium atom based on the planetary Bohr’s model Similarly, spectroscopy is also largely based on photoemission. It refers to a technique employed in identifying a material on the basis of its own emission spectrum. Such technique is widely applied in Remote Sensing and Astronomy. Basically, the technique is exploited when conducting flame tests. In these tests, an electron within a certain element is
excited to release a photon. The emitted photon’s wavelength can be utilized in identifying the element since it corresponds to the shift in energy level.
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