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Diffstat (limited to 'Engineering_Physics/Chapter5_1.ipynb')
| -rwxr-xr-x | Engineering_Physics/Chapter5_1.ipynb | 207 |
1 files changed, 32 insertions, 175 deletions
diff --git a/Engineering_Physics/Chapter5_1.ipynb b/Engineering_Physics/Chapter5_1.ipynb index 86db7d36..ba6e0e69 100755 --- a/Engineering_Physics/Chapter5_1.ipynb +++ b/Engineering_Physics/Chapter5_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:7539e2f35ea93dc5f143cbd45df18f4d6a1bee4d35a1729fab5d759b4b27d8ff" + "name": "Chapter5" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,281 +11,139 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "5: Polarization" - ] + "source": "5: Crystal Physics" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.1, Page number 113" - ] + "source": "Example number 5.1, Page number 149, theoretical" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 5.2, Page number 150" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "mew_g = 1.72; #Refractive index of glass\n", - "mew_w = 4/3; #Refractive index of water\n", - "\n", - "#Calculation\n", - "#For polarization to occur on flint glass, tan(i) = mew_g/mew_w\n", - "#Solving for i\n", - "i_g = math.atan(mew_g/mew_w); #angle of incidence for complete polarization for flint glass(rad)\n", - "a = 180/math.pi; #conversion factor from radians to degrees\n", - "i_g = i_g*a; #angle of incidence(degrees)\n", - "i_g = math.ceil(i_g*10**2)/10**2; #rounding off the value of i_g to 2 decimals\n", - "#For polarization to occur on water, tan(i) = mew_w/mew_g\n", - "#Solving for i\n", - "i_w = math.atan(mew_w/mew_g); #angle of incidence for complete polarization for water(rad)\n", - "i_w = i_w*a; #angle of incidence(degrees)\n", - "i_w = math.ceil(i_w*10**3)/10**3; #rounding off the value of i_w to 3 decimals\n", - "\n", - "#Result\n", - "print \"The angle of incidence for complete polarization to occur on flint glass is\",i_g, \"degrees\"\n", - "print \"The angle of incidence for complete polarization to occur on water is\",i_w, \"degrees\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 8; #number of atoms per cell\na = 5.43*10**-8; #lattice constant(cm)\nw = 28.1; #atomic weight(gm)\nN = 6.02*10**23; #avagadro number\n\n#Calculation\nac = n/(a**3); #atomic concentration(atoms/cm**3)\nd = ac*w/N; #density of Si(g/cm**3)\nd=math.ceil(d*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"density of Si is\",d,\"g/cm**3\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The angle of incidence for complete polarization to occur on flint glass is 52.22 degrees\n", - "The angle of incidence for complete polarization to occur on water is 37.783 degrees\n" - ] + "text": "density of Si is 2.333 g/cm**3\n" } ], - "prompt_number": 5 + "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.2, Page number 113" - ] + "source": "Example number 5.3, Page number 151" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "I0 = 1; #For simplicity, we assume the intensity of light falling on the second Nicol prism to be unity(W/m**2)\n", - "theta = 30; #Angle through which the crossed Nicol is rotated(degrees)\n", - "\n", - "#Calculation\n", - "theeta = 90-theta; #angle between the planes of transmission after rotating through 30 degrees\n", - "a = math.pi/180; #conversion factor from degrees to radians\n", - "theeta = theeta*a; ##angle between the planes of transmission(rad)\n", - "I = I0*math.cos(theeta)**2; #Intensity of the emerging light from second Nicol(W/m**2)\n", - "T = (I/(2*I0))*100; #Percentage transmission of incident light\n", - "T = math.ceil(T*100)/100; #rounding off the value of T to 2 decimals\n", - "\n", - "#Result\n", - "print \"The percentage transmission of incident light after emerging through the Nicol prism is\",T, \"%\"" - ], + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\na = 5; #lattice constant(Angstrom)\n\n#Calculation\na = a*10**-10; #lattice constant(m)\n#to calculate the planar concentration, only equilateral triangular region is considered of length a*math.sqrt(2) and height a*math.sqrt(3/2)\nl = a*math.sqrt(2); #length of face diagonal(m)\nh = a*math.sqrt(3/2); #height of triangle(m)\nA = l*h/2; #area of shaded portion(m**2)\n#every atom at the corner contributes 1/6 to this area.\nn111 = (3/6)*(1/A); #planar concentration(atoms/m**2)\n\n#Result\nprint \"surface density of atoms is\",n111,\"atoms/m**2\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The percentage transmission of incident light after emerging through the Nicol prism is 12.51 %\n" - ] + "text": "surface density of atoms is 2.30940107676e+18 atoms/m**2\n" } ], - "prompt_number": 6 + "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.3, Page number 113" - ] + "source": "Example number 5.4, Page number 152" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lamda = 6000; #Wavelength of incident light(A)\n", - "mew_e = 1.55; #Refractive index of extraordinary ray\n", - "mew_o = 1.54; #Refractive index of ordinary ray\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-8; #Wavelength of incident light(cm)\n", - "t = lamda/(4*(mew_e-mew_o)); #Thickness of Quarter Wave plate of positive crystal(cm)\n", - "\n", - "#Result\n", - "print \"The thickness of Quarter Wave plate is\",t, \"cm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\na = 4.049; #lattice constant(Angstrom)\nh = 2;\nk = 2;\nl = 0; #miller indices of(2 2 0)\n\n#Calculation\nd = a/math.sqrt(h**2+k**2+l**2); #spacing of planes(Angstrom)\nd=math.ceil(d*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"spacing of planes is\",d,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The thickness of Quarter Wave plate is 0.0015 cm\n" - ] + "text": "spacing of planes is 1.432 Angstrom\n" } ], - "prompt_number": 7 + "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.4, Page number 114" - ] + "source": "Example number 5.5, Page number 152" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#Calculation\n", - "#the thickness of a half wave plate of calcite for wavelength lamda is\n", - "#t = lamda/(2*(mew_e - mew_o)) = (2*lamda)/(4*(mew_e - mew_o))\n", - "\n", - "#Result\n", - "print \"The half wave plate for lamda will behave as a quarter wave plate for 2*lamda for negligible variation of refractive index with wavelength\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nd110 = 2.03; #distance between planes(Angstrom)\nh = 1;\nk = 1;\nl = 0; #miller indices of(1 1 0)\n\n#Calculation\na = d110*math.sqrt(h**2+k**2+l**2); #size of unit cell(Angstrom)\na=math.ceil(a*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"size of unit cell is\",a,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The half wave plate for lamda will behave as a quarter wave plate for 2*lamda for negligible variation of refractive index with wavelength\n" - ] + "text": "size of unit cell is 2.871 Angstrom\n" } ], - "prompt_number": 8 + "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.5, Page number 114" - ] + "source": "Example number 5.6, Page number 152" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "\n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lamda = 500; #Wavelength of incident light(nm)\n", - "mew_e = 1.5508; #Refractive index of extraordinary ray\n", - "mew_o = 1.5418; #Refractive index of ordinary ray\n", - "t = 0.032; #Thickness of quartz plate(mm)\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-9; #Wavelength of incident light(m)\n", - "t = t*10**-3; #Thickness of quartz plate(m)\n", - "dx = (mew_e - mew_o)*t; #Path difference between E-ray and O-ray(m)\n", - "dphi = (2*math.pi)/lamda*dx; #Phase retardation for quartz for given wavelength(rad)\n", - "dphi = dphi/math.pi;\n", - "\n", - "#Result\n", - "print \"The phase retardation for quartz for given wavelength is\",dphi, \"pi rad\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\na = 5.64; #lattice constant(Angstrom)\nh1 = 1;\nk1 = 0;\nl1 = 0; #miller indices of(1 0 0)\nh2 = 1;\nk2 = 1;\nl2 = 0; #miller indices of(1 1 0)\nh3 = 1;\nk3 = 1;\nl3 = 1; #miller indices of(1 1 1)\n\n#Calculation\nd100 = a/math.sqrt(h1**2+k1**2+l1**2); #spacing of planes[100](Angstrom)\nd110 = a/math.sqrt(h2**2+k2**2+l2**2); #spacing of planes[110](Angstrom)\nd111 = a/math.sqrt(h3**2+k3**2+l3**2); #spacing of planes[111](Angstrom)\nd111=math.ceil(d111*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"spacing of plane [100] is\",d100,\"Angstrom\"\nprint \"spacing of plane [110] is\",round(d110),\"Angstrom\"\nprint \"spacing of plane [111] is\",d111,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The phase retardation for quartz for given wavelength is 1.152 pi rad\n" - ] + "text": "spacing of plane [100] is 5.64 Angstrom\nspacing of plane [110] is 4.0 Angstrom\nspacing of plane [111] is 3.26 Angstrom\n" } ], - "prompt_number": 9 + "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 5.6, Page number 114" - ] + "source": "Example number 5.7, Page number 153" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "C = 52; #Critical angle for total internal reflection(degrees)\n", - "\n", - "#Calculation\n", - "a = math.pi/180; #conversion factor from degrees to radians\n", - "C = C*a; #Critical angle for total internal reflection(rad)\n", - "#From Brewster's law, math.tan(i_B) = 1_mew_2\n", - "#Also math.sin(C) = 1_mew_2, so that math.tan(i_B) = math.sin(C), solving for i_B\n", - "i_B = math.atan(math.sin(C)); #Brewster angle at the boundary(rad)\n", - "b = 180/math.pi; #conversion factor from radians to degrees\n", - "i_B = i_B*b; #Brewster angle at the boundary(degrees)\n", - "\n", - "#Result\n", - "print \"The Brewster angle at the boundary between two materials is\",int(i_B), \"degrees\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nr = 1.605; #radius of atom(Angstrom)\n\n\n#Calculation\nr = r*10**-10; #radius of atom(m)\na = 2*r; #size of unit cell(m)\nc = a*math.sqrt(8/3);\nV = 3*math.sqrt(3)*a**2*c/2; #volume of unit cell(m**3)\n\n#Result\nprint \"volume of unit cell is\",V,\"m**3\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The Brewster angle at the boundary between two materials is 38 degrees\n" - ] + "text": "volume of unit cell is 1.40330266432e-28 m**3\n" } ], - "prompt_number": 13 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 10 + "prompt_number": 7 } ], "metadata": {} |