...Diffraction Grating Lab 11 Possible Sources of Error: 1) Select this If measurements are used, Most measurements require you to estimate one significant figure. This estimation is frequently different if done repeatedly, especially if done by different people, and introduces "random error". Systematic error will come from an error in your measuring apparatus. Maybe your vernier is not zeroed. Maybe the diffraction grating is cheap and the lines/cm is not accurate, etc.So every measurement will be in error because of inaccurate instruments 2) Misreading the vernier scale. Not seeing the maximum left angle or right angle spectra, thus the average angle calculation doesn't match with the right wavelength for mercury. Difficulty in seeing the lines through the telescope. 3) Error in the number of slits per meter: the error in slit width is what causes the error in the number of slits per metre, so the proportional errors are the same. 4) Distance between light source and the surface Size of the light source Attenuation as it passes through air 5) If The measurement of the grating constant from relection off the meter scale was slightly more error-prone use this: Factors that might account for the error are irregularities in the grating, mistakes in the calibration, or similar systematic flaws. In this section you can include general statements saying: * Whether your measurements confirm the stated objectives. * What fundamental physical laws...
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...282Phys. Experiment 8 Diffraction Grating 1- Objective : find the wavelength of the Laser using the diffraction pattern of Diffraction Grating. 2. Theory: A diffraction grating is made of many equally-spaced slits, the distance between two slits is d . The slits of a grating give rise to diffraction and the diffracted light interferes so as to set up interference patterns. The distance ym is the distance on the screen from the central bright spot (m = 0) to the next bright spot of order m. The condition for constructive interference is When the difference in path length between the light passing through different slits is an integral number of wavelengths of the incident light , bright m m 0, 1, 2, 3, ... Equation 1 Equation 2 Equation 3 bright d sin bright d sin bright m where : d is the distance between adjacent slits . θ is the angle the re-created image makes with the normal to the grating surface. λ is the wavelength of the light. m = 0, 1, 2, . . . is an integer. 1 282Phys. Diffracted light located at a distance L from the grating. Note that the angular separation between the spots is larger than a few degrees, so we should not use the small-angle approximations. The angular separation is: tan bright y bright L tan bright sin bright , bright tan 1 ( y bright L ) Equation 4 From equation 3 and 4 : d sin m Equation 5 ybright d sin[tan 1 ( )] m L L 2 ...
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...1. Introduction The aims of this experiment are to use diffraction gratings to measure the wavelength of light. Visible light is an electromagnetic radiation which is visible to human eye. Light source of different colors and wavelengths are often produced by a visible light source. A light source such as incandescent light bulb utilizing hot metal filaments is consisted of a continuous distribution of lights with a range of wavelengths, hence forming a white light. On the other hand, light produced from a mercury lamp and helium lamp contains only several discrete wavelength components. A number of methods can be adopted to measure the separated wavelength components. However, for this experiment, we will be focusing on using diffraction grating in which light from the above three types of sources will be dispersed into its constituent colors through diffraction grating and then we are able determine the wavelength of light. 2. Objective 2.1. By comparing and analyzing the pattern of the three different light sources, we can understand the difference between a continuous and a discrete spectrum. 2.2. To be able to understand that the light produced has a spectrum that is a characteristic of the elements from the experiment results of mercury lamp and helium lamp. 2.3. To obtain or calculate the average spacing, given the characteristics wavelengths of a mercury lamp from our first experiment. 2.4. To determine the characteristic wavelengths of a helium lamp...
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...Applied Modern Physics I X-ray diffraction / topography and spectroscopy, electron microscopy, materials science X-ray radiation is very high in energy E = h f (≈ 2 10-15 J = 1,25 104 eV so it’s the same energy an electron would have if it were accelerated by an electrical force going through a potential of 12,500 V) that’s why it penetrated skin and flesh easily, bones not quite so easily and have usage in medicine – is that the main usage??? Who was Conrad Wilhelm Röntgen, discoverer of X-rays? A medical doctor? A physicist, the very first Nobel prize winner in Physics? how did he discover X-rays? 1895, by chance, experimenting with cathode rays (doing similar things to J.J Thompson) on one end of the laboratory, there was a sheet of paper that was covered with a phosphor sitting around at the other end of the laboratory, experimenting in the dark, he noticed that phosphor lights up when he switches on his cathode ray tube, dragging out electrons and accelerating them by a potential difference, the cathode ray tube is expected to be under vacuum, but there was just enough rest gas (air) that electrons got slowed down by being scattered by the molecules, today we know: when electrons are slowed down they radiate off their lost in kinetic energy – and that is X-rays an electromagnetic wave + a stream of high energy photons traveling at the speed of light at the time nobody knows how the radiation originates and of what kind it was: wave or particles? Röntgen...
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...Gaussian Beams Enrique J. Galvez Department of Physics and Astronomy Colgate University Copyright 2009 ii Contents 1 Fundamental Gaussian Beams 1.1 Spherical Wavefront in the Paraxial region 1.2 Formal Solution of the Wave Equation . . 1.2.1 Beam Spot w(z) . . . . . . . . . . 1.2.2 Beam Amplitude . . . . . . . . . . 1.2.3 Wavefront . . . . . . . . . . . . . . 1.2.4 Gouy Phase . . . . . . . . . . . . . 1.3 Focusing a Gaussian Beam . . . . . . . . . 1.4 Problems . . . . . . . . . . . . . . . . . . . 1 1 3 6 8 8 9 10 12 15 15 17 20 21 25 25 26 26 27 29 30 31 31 33 35 35 36 39 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 High-Order Gaussian Beams 2.1 High-Order Gaussian Beams in Rectangular Coordinates 2.2 High-Order Gaussian Beams in Cylindrical Coordinates . 2.3 Irradiance and Power . . . . . . . . . . . . . . . . . . . . 2.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Wave-front interference 3.1 General Formalism . . . . . . . . . . . . . . . . 3.2 Interference of Zero-order...
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...notable for its high degree of spatial and temporal coherence, unattainable using other technologies. Spatial coherence typically is expressed through the output being a narrow beam which is diffraction-limited, often a so-called "pencil beam." Laser beams can be focused to very tiny spots, achieving a very high irradiance. Or they can be launched into a beam of very low divergence in order to concentrate their power at a large distance. Temporal (or longitudinal) coherence implies a polarized wave at a single frequency whose phase is correlated over a relatively large distance (the coherence length) along the beam.[3] A beam produced by a thermal or other incoherent light source has an instantaneous amplitude and phase which vary randomly with respect to time and position, and thus a very short coherence length. Most so-called "single wavelength" lasers actually produce radiation in several modes having slightly different frequencies (wavelengths), often not in a single polarization. And although temporal coherence implies monochromaticity, there are even lasers that emit a broad spectrum of light, or emit different wavelengths of light simultaneously. There are some lasers which are not single spatial mode and consequently their light beams diverge more than required by the diffraction limit. However all such devices are classified as "lasers" based on their method of producing that light: stimulated emission. Lasers are employed in applications where light of the required...
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...projector is a unique display system. The holographic projector system embodies a top of the range full High Definition Hologram Projector with an in-house computer system capable of feeding the projector with fully uncompressed video files. It consist of two technologies namely, the holography and the projector. Holography is a method which allows three-dimensional images to be made. It includes the use of a laser, interference, diffraction, light intensity recording, and suitable illumination of the recording. The image changes as the position and orientation of the viewing system changes in exactly the same way as if the object are still present, therefore making it three-dimensional. The projector that will be used in this project is a overhead projector. An overhead projector is a variation of the common slide projector that is used to display images to a group of people. II. Project Description Hologram Projector is a projector wherein it can reflect the full dimension of an image. It consists of a laser, interference, and diffraction, light intensity recording and suitable illumination of the recording. Hologram Projector is AC operated. It projects special white light or laser light. The light produces two- and three-dimensional images. Authentic 3-D images require laser-based holographic projectors. It can be presented from different angles and can be seen in true perspective. III. Process Description To come up with the Hologram projector’s design wasn’t...
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...Physics of sound Sound is a mechanical wave, sequence of waves is resulting from an air pressure disturbance produced by vibration, and sound propagates through the medium such as air or water. During the propagation, sound can be reflected or attenuated by the medium. Humans can hear the sound is because the vibration pass the wave in to our ear, this is called Traveling Longitudinal Waves. The propagation of the sound can be affected by the density and pressure. The temperature determines the speed of sound with in the medium, also the medium itself would affect the propagation such as wind (moving medium) if the medium is moving therefore the wave would propagated further; with the medium don’t have viscosity, sound would be easier to propagate, but if the medium have an negative viscosity such as water the it would affects the motion of the sound wave. On the top is the diagram of the travellingwave the bar above the diagram represent the concentrations of the pressures on the wave, when the curve are compression (the part above the horizontal line) it represent a high pressure; when the curve are rarefaction (the part below the horizontal line) it represent a low pressure and they change from one to another, this pattern repeats indefinitely. Speed of sound = wavelength*Frequency Wavelength (it can be written as λ) is the distance between two consecutive corresponding points of a waveform. Normally the wavelength is about a meter long. The pitch/frequency of the...
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...A Simulation to Ripple While You Work Objective: To examine reflection, interference, and diffraction in two dimensions and relate to the waves on a spring demo Everybody has at some time thrown a pebble into a puddle and observed the ripples spreading across the surface. Some of us don’t stop until the puddle has been completely filled with every loose piece of debris in the vicinity. Now let’s dive in a bit deeper into the physics. Select the Wave Interference simulation from the Sound and Waves folder 1) Before you change any settings a. What is the shape of the pulse? b. How can you explain this? Consider the wave velocity. Reflection: 2) Increase the amplitude to maximum. 3) Turn off the water and add a vertical wall (bottom right button) across the entire width of the tank. 4) Turn on the water for just a couple of drips. 5) Observe the wave reflection from the barrier a. What is the shape of the reflection? b. In what ways does it differ from the incident (incoming) wave? c. Compare this result to what you learned about reflected pulses from the wave on a spring demo? Interference: 6) Allow the faucet to run. Feel free to adjust the frequency. a. Think back to the wave on a spring demo when multiple waves tried to occupy the spring at the same time (interference). What do you think the particularly bright and dark spots represent? 7) Show the graph and observe the last...
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...Thomas Young and the Wave Nature of Light Historical Background Isaac Newton was famous not only for formulating the laws of motion but also for pioneering in the study of optics. He used a prism to show that sunlight was a mixture of the colors that make up the rainbow. In his Opticks (1704), Newton argued that light was made up of tiny particles. Slightly earlier, the Dutch physicist Christiaan Huygens wrote a Treatise on light, in which he proposed that light was a wave. It was only in 1789 that Thomas Young proposed a simple experiment that appeared to resolve the controversy by showing that light indeed behaves as a wave (according to 20th-century quantum mechanics, however, even Young’s wave description is incomplete). Young, a leading British natural philosopher, formulated an influential theory of color vision. He was also the first to decode the Egyptian hieroglyphics being brought to Europe by Napoleon’s troops. Although Newton and others had observed alternating patterns of bright and dark bands of light under certain circumstances, Young would be the first to explain these patterns, based on an analogy with water waves. Young used very simple equipment to produce patterns of light and dark bands: a candle and a card with a rectangular hole across which he stretched a single human hair. He used his observations to measure the wavelength of light. Notice that he was proposing that light is a wave and measuring its wavelength (something that cannot be directly observed...
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...A SIMULATION TO RIPPLE WHILE YOU WORK Objective: To examine reflection, interference, and diffraction in two dimensions and relate to the waves on a spring demo Everybody has at some time thrown a pebble into a puddle and observed the ripples spreading across the surface. Some of us don’t stop until the puddle has been completely filled with every loose piece of debris in the vicinity. Now let’s dive in a bit deeper into the physics. Select the Wave Interference simulation from the Sound and Waves folder 1) Before you change any settings a. What is the shape of the pulse? b. How can you explain this? Consider the wave velocity. REFLECTION: 2) Increase the amplitude to maximum. 3) Turn off the water and add a vertical wall (bottom right button) across the entire width of the tank. 4) Turn on the water for just a couple of drips. 5) Observe the wave reflection from the barrier a. What is the shape of the reflection? b. In what ways does it differ from the incident (incoming) wave? c. Compare this result to what you learned about reflected pulses from the wave on a spring demo? INTERFERENCE: 6) Allow the faucet to run. Feel free to adjust the frequency. a. Think back to the wave on a spring demo when multiple waves tried to occupy the spring at the same time (interference). What do you think the particularly bright and dark spots represent? 7) Show the graph and observe the last couple of waves in front of the wall. a. Once again, considering the wave...
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...geometry. If the tube moves the and the specimen is fixed like the C&M’s XRD, then this is known as a θ:θ geometry. If the tube is fixed and the sample moves then the geometry is θ:2θ * Is known as parafocusing * Uses slits to focus the beam. * Divergence slits focus the beam so that it hits a desired sample size * Receiving slits focus the beam to improve the resolution, if it is too small it may reduce intensity. * Due to the way the beam focuses, a varying sample height or surface roughness can cause errors within the received data. This is due to slight differences in the diffraction angle at different heights. * Can use a soller slit assembly to limit the axial divergence of the beam. * Geometry offers larger divergence with powder samples and therefore greater beam resolution. * http://epswww.unm.edu/xrd/xrdclass/05-Diffraction-Basics.pdf *...
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...rise and fall in the disturbance to what brings the sound to your ear * The square waves to what makes the flame move and bring the sound to your ear * The air molecules don’t move the disturbance does * For a 0.5 Hz your hear a click and the flame moves and resets * For 100 Hz the flame remains displaced and doesn’t recover * The transition from a click to a tone is between 20 and 50 Hz Reflection * Change in direction of a wave at an interference between two media wave returns into media from which it originated form. Wave Refraction * Change in direction of a wave when it passes from one medium to another caused by the different speeds of a wave * When water moves into different depths Wave Diffraction * Bending waves when they encounter an obstacle Absorption of waves * Reduction of energy in wave consumed by medium which it travels. * The main cause of absorption is Viscosity Interference * Two or more waves form coming together to make up a new wave Resonance * Tendency of a system to oscillate at a large amplitude at certain frequencies * Tendency to magnify a sound * The difference between an acoustic and electric guitar Wave Motion in Space and Time * Wave Motion in Space * Horizontal Axis: Distance * Vertical Axis: Distance and intensity * Example, a snap shot of a ocean wave * Important parameter is wave length * Wave motion in Time * Horizontal...
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...ISP 209L Lab 5: Optical Interference Your Name ________I_______________________________ Section __003_ Objectives (A) To observe light transmitted through a very narrow slits and verify the relationship between the slit width and angles of the transmitted light. (B) To use the properties of light to measure the diameter of a small wire accurately by Babinet's Principle. (C) ) To observe light transmitted through two very narrow slits and to verify the relationship between the slit spacing and the angular separation of the transmitted light for the principle peaks. Part A: Single-Slit Diffraction Discussion This week’s and next week’s exercises show that light acts like a wave. Essentially a wave phenomenon known as interference will creating symmetric and rather beautiful patterns. All of matter has a dual nature, acting like both particles and waves. For example, a particle of light (known as a photon) acts like a particle when in collides with an electron. However, that same particle will act like a wave if it is allowed to interfere with other photons, or even with itself. This dual nature is described by Quantum Mechanics. However, the idea of combined particle and wave nature arose well before the development of Quantum Mechanics in the study of light. Newton argued that light must be particles because it did not appear to diffract and create interference patterns like other waves. Much later, Thomas Young demonstrated that light did diffract...
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...measured by using the diffraction pattern of the light. In this experiment we used a HeNe laser and a green laser pointer with known wavelengths of 632.8x10-9m and 532.0x10-9m respectively. We aimed the lasers at a slight angle from horizontal onto a precision steel ruler with 0.5x10-3m and 1.0x10-3m rulings. When the laser is incident on the rulings, it reflects onto a surface showing the diffraction pattern. After measuring the spacing between each bright spot, we calculated the wavelength for each ruling used for the HeNe laser and for the green laser pointer. The measured wavelength for the HeNe laser at 0.5x10-3m rulings is (632.6±1.3)x10-9m and 1.0x10-3m rulings is (632.6±1.4)x10-9m. For the green laser point the measured wavelength is (632.6±1.4)x10-9m. I. Introduction Every color of light has a diffraction pattern specific to its wavelength. In this experiment we used a ruler to determine the wavelength (λ) of a HeNe laser. The HeNe laser has a known wavelength of 632.8x10-9m. We also measured the wavelength of a green laser pointer with a known wavelength of 532.9x10-9m. This experiment was first done by A. L. Schawlow in 1965 at Stanford University.1 II. Setup and Procedure We used a steel precision ruler with two different spacing’s between the rulings: d=0.5x10-3m and d=1.0x10-3m. We aimed the HeNe laser at a shallow angle (measured from the horizontal) onto the ruler as shown in figure 1. When the light hit the rulings, diffraction occurred and the...
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