Figure shows the pure constructive and destructive interference of two waves having the same wavelength and...

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Figure shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude. Wave 1 Wave 1 Wave 2 Wave 2 2X Resultant Resultant -2X (a) Constructive interference (b) Destructive interference The interference of two waves can be described mathematically wave 1: y, (x, t) = Asin(kx – wt) wave 2: y2(x, t) = Asin (kx - wt + 4) Following the principal of superposition for linear waves, the resultant will be resultant: y(x, t) = y1(x, t) + y2(x, t) y(x, t) = Asin(kx – wt) + Asin(kx - wt + q) %3D Using a simple trigonometric identity, sin(a) + sin(b) = 2sin a+b CoS we get y(x, t) = 2Acos sin(kx – wt) Which is a traveling wave with oscillating term sin (kx – wt), and the resultant amplitude - which is a function of phase difference between the two waves, 2Acos The pure constructive interference happens when the resultant amplitude is maximum, thus the CoS ±1 which results in 2пп; п %3 1,2,3, .. (two waves are in same phase, see figure a) The pure destructive interference happens when the resultant amplitude is zero, thus the = 0 which results in p = (2n – 1)T; n = 1,2,3, . (two waves are in opposite phase, cos see figure b) Thin Film interference: Crown glass is a type of optical glass used in lenses and other optical components. It has relatively low refractive index (~1.52) and low dispersion. You can coat it with a layer of thin film to reduce the back reflection from the glass. The closest materials with good physical properties for a coating are magnesium fluoride, MGF2 with an index of 1.38. You can cover the crown glass with a thin layer of magnesium fluoride to increase the transmission from the glass using the destructive interference of light reflected from the two surfaces as seen in the image bellow. When the light reflected from thin film and the light reflected from the glass behind the thin film have TT radian phase difference, then the combined wave reflected from the front will be minimized. Thin Film interference thin film (front) thin film (back) Incident wave before striking film wave in thin film Wave after exiting thin film Vacuum wavelength of incident wave (nm) 700 Wave reflected from front thin film 1/2 A Reflection Shift n of material in front of the thin film 1 n of the thin film Wave reflected from back of thin film wave reflected 1/2 A Reflection Shift Distance Shift = 2 (thickness) off of back of thin film n of material behind the thin film thickness of thin film (nm) Run Pause Reset Show front reflection on initial wave Combined wave from front and back reflections V Show back reflection on initial wave Show Grid Your goal is to minimize the thickness of the coating layer in order to minimize the cost of coating since magnesium fluoride is an expensive material. Experiment 1: Thin Film Interference Using the following simulation, we will investigate the interference from the thin film. https://ophysics.com/16.html You have 4 main color of the visual band. Set the parameters as instructed in the following table and find the thickness of the thin film to create destructive interference in front of the device. You are looking for the smallest thickness of the film. You also need to find the second smallest thickness of the film in case you need them. Case Wavelength n of the n of the material behind the n of Smallest thickness of the thin film [nm] Second smallest thickness of the thin film [nm] to material in the front of the thin thin film film thin film for maximum have maximum transmission transmission 1 violet) 400 1 1.52 1.38 131.57 263 15 2 (blue) 500 1.52 138 164.47 328.94 3 (Green) 600 1.52 1.38 197.36 394 73 4 (Red) 700 1 1.52 138 230.26 460.52 Ques 2 The spectrum of sun light is presented to you in the following figure. n table above, suggest a minimum thickness [in nm] for your coating layer to optimize the transparency for all visible band? Explain your rational for choosing such thíckness. [hint you want to maximize transmission for all visible wavelength and not just one of them] this figure and your data Question 2: [2 points for thickness; 6 points for justification] The spectrum of sun light is presented to you in the following figure. Using this figure and your data in table above, suggest a minimum thickness [in nm] for your coating layer to optimize the transparency for all visible band? Explain your rational for choosing such thickness. [hint: you want to maximize transmission for all visible wavelength and not just one of them] 1.5 Solar radiation at ground level 1.0 0.5 0.0 Wavelength Inm) 500 1000 1500 2000 2500 Futurisim.com Spectrum Irradiance (W m?.nm) Figure shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude. Wave 1 Wave 1 Wave 2 Wave 2 2X Resultant Resultant -2X (a) Constructive interference (b) Destructive interference The interference of two waves can be described mathematically wave 1: y, (x, t) = Asin(kx – wt) wave 2: y2(x, t) = Asin (kx - wt + 4) Following the principal of superposition for linear waves, the resultant will be resultant: y(x, t) = y1(x, t) + y2(x, t) y(x, t) = Asin(kx – wt) + Asin(kx - wt + q) %3D Using a simple trigonometric identity, sin(a) + sin(b) = 2sin a+b CoS we get y(x, t) = 2Acos sin(kx – wt) Which is a traveling wave with oscillating term sin (kx – wt), and the resultant amplitude - which is a function of phase difference between the two waves, 2Acos The pure constructive interference happens when the resultant amplitude is maximum, thus the CoS ±1 which results in 2пп; п %3 1,2,3, .. (two waves are in same phase, see figure a) The pure destructive interference happens when the resultant amplitude is zero, thus the = 0 which results in p = (2n – 1)T; n = 1,2,3, . (two waves are in opposite phase, cos see figure b) Thin Film interference: Crown glass is a type of optical glass used in lenses and other optical components. It has relatively low refractive index (~1.52) and low dispersion. You can coat it with a layer of thin film to reduce the back reflection from the glass. The closest materials with good physical properties for a coating are magnesium fluoride, MGF2 with an index of 1.38. You can cover the crown glass with a thin layer of magnesium fluoride to increase the transmission from the glass using the destructive interference of light reflected from the two surfaces as seen in the image bellow. When the light reflected from thin film and the light reflected from the glass behind the thin film have TT radian phase difference, then the combined wave reflected from the front will be minimized. Thin Film interference thin film (front) thin film (back) Incident wave before striking film wave in thin film Wave after exiting thin film Vacuum wavelength of incident wave (nm) 700 Wave reflected from front thin film 1/2 A Reflection Shift n of material in front of the thin film 1 n of the thin film Wave reflected from back of thin film wave reflected 1/2 A Reflection Shift Distance Shift = 2 (thickness) off of back of thin film n of material behind the thin film thickness of thin film (nm) Run Pause Reset Show front reflection on initial wave Combined wave from front and back reflections V Show back reflection on initial wave Show Grid Your goal is to minimize the thickness of the coating layer in order to minimize the cost of coating since magnesium fluoride is an expensive material. Experiment 1: Thin Film Interference Using the following simulation, we will investigate the interference from the thin film. https://ophysics.com/16.html You have 4 main color of the visual band. Set the parameters as instructed in the following table and find the thickness of the thin film to create destructive interference in front of the device. You are looking for the smallest thickness of the film. You also need to find the second smallest thickness of the film in case you need them. Case Wavelength n of the n of the material behind the n of Smallest thickness of the thin film [nm] Second smallest thickness of the thin film [nm] to material in the front of the thin thin film film thin film for maximum have maximum transmission transmission 1 violet) 400 1 1.52 1.38 131.57 263 15 2 (blue) 500 1.52 138 164.47 328.94 3 (Green) 600 1.52 1.38 197.36 394 73 4 (Red) 700 1 1.52 138 230.26 460.52 Ques 2 The spectrum of sun light is presented to you in the following figure. n table above, suggest a minimum thickness [in nm] for your coating layer to optimize the transparency for all visible band? Explain your rational for choosing such thíckness. [hint you want to maximize transmission for all visible wavelength and not just one of them] this figure and your data Question 2: [2 points for thickness; 6 points for justification] The spectrum of sun light is presented to you in the following figure. Using this figure and your data in table above, suggest a minimum thickness [in nm] for your coating layer to optimize the transparency for all visible band? Explain your rational for choosing such thickness. [hint: you want to maximize transmission for all visible wavelength and not just one of them] 1.5 Solar radiation at ground level 1.0 0.5 0.0 Wavelength Inm) 500 1000 1500 2000 2500 Futurisim.com Spectrum Irradiance (W m?.nm)