{
"metadata": {
"name": "",
"signature": "sha256:f4c05fd79d4d56cbd4b08f847aeb0bba767b388c9bbe1bea8066d97e3ac78212"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"5: Diffraction"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.1, Page number 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"lamda=600*10**-9; #wavelength(m)\n",
"theta=35; #angle at which first minimum falls(degrees)\n",
"\n",
"#Calculation \n",
"theta=theta*math.pi/180; #angle at which first minimum falls(radian)\n",
"d=((n*lamda)/math.sin(theta))*10**6; #width of the slit(micro m)\n",
"\n",
"#Result\n",
"print \"The width of the slit is\",round(d,2),\"micro m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The width of the slit is 1.05 micro m\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.2, Page number 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"D=0.95; #distance of the screen from the slit(m)\n",
"lamda=589*10**-9; #wavelength(m)\n",
"d=0.5*10**-3; #width of the slit(m)\n",
"\n",
"#Calculation \n",
"y=((2*D*lamda)/d)*10**3; #width of a central band(mm)\n",
"\n",
"#Result\n",
"print \"The width of the central band is\",round(y,2),\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The width of the central band is 2.24 mm\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.3, Page number 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"D=1.1; #distance of the screen from the slit(m)\n",
"lamda=589*10**-9; #wavelength(m)\n",
"y=4.5*10**-3; #distance of first minimum on either side of central maximum(m)\n",
"\n",
"#Calculation \n",
"d=((D*lamda)/y)*10**3 #slit width(mm)\n",
"\n",
"#Result\n",
"print \"The slit width is\",round(d,3),\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The slit width is 0.144 mm\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.4, Page number 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=4;\n",
"lamda=589.6*10**-9; #wavelength(m)\n",
"D=0.95; #distance of the screen from the slit(m)\n",
"w=0.28*10**-3; #width of the slit(m)\n",
"\n",
"#Calculation \n",
"d=((n*lamda*D)/w)*10**3; #distance between centres(mm)\n",
"\n",
"#Result\n",
"print \"The distance between centres of central maximum and the fourth dark fringe is\",int(d),\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The distance between centres of central maximum and the fourth dark fringe is 8 mm\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.5, Page number 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"s=5*math.pi/2; #secondary maximum\n",
"\n",
"#Calculation \n",
"I=(math.sin(s)/s)**2; #I2/I0\n",
"\n",
"#Result\n",
"print \"Ratio of intensities of central & second secondary maximum is\",round(I,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ratio of intensities of central & second secondary maximum is 0.016\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.6, Page number 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"lamda=450*10**-9; #wavelength(m)\n",
"n=2;\n",
"dlambda=1*10**-9; #difference in wavelength(m)\n",
"\n",
"#Calculation \n",
"N=lamda/(n*dlambda); #minimum number of lines per cm \n",
"\n",
"#Result\n",
"print \"The minimum number of lines per cm is\",N/2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The minimum number of lines per cm is 112.5\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.7, Page number 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"lamda=650*10**-9; #wavelength(m)\n",
"d=2*10**-6; #width of the slit(m)\n",
"\n",
"#Calculation \n",
"theta=math.asin((n*lamda)/d); #angle at which first minimum will be observed(radian)\n",
"theta=theta*180/math.pi; #angle at which first minimum will be observed(degrees)\n",
"\n",
"#Result\n",
"print \"The angle at which first minimum will be observed is\",round(theta,3),\"degrees\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The angle at which first minimum will be observed is 18.966 degrees\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.8, Page number 87"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"lamda=600*10**-9; #wavelength(m)\n",
"y=2*10**-3; #width of the central band(m)\n",
"D=1; #distance of the screen from the slit(m)\n",
"\n",
"#Calculation \n",
"d=((2*D*lamda)/y)*10**3; #slit width(mm)\n",
"\n",
"#Result\n",
"print \"The slit width is\",d,\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The slit width is 0.6 mm\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.9, Page number 87"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"y=6*10**-3; #first minimum is observed(m)\n",
"d=90*10**-6; #slit width(m)\n",
"D=0.98; #distance of the screen from the slit(m)\n",
"\n",
"#Calculation \n",
"lamda=((y*d)/D)*10**9; #wavelength(nm)\n",
"\n",
"#Result\n",
"print \"The wavelength of light used is\",int(lamda),\"nm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The wavelength of light used is 551 nm\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.10, Page number 87"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"lambda1=450*10**-9; #wavelength of first spectral line(m)\n",
"d=1/5000; #number of lines\n",
"\n",
"#Calculation \n",
"theta1=math.asin((n*lambda1)/d); \n",
"theta1=round(theta1*10**2*180/math.pi);\n",
"theta2=theta1+2.97;\n",
"theta2=theta2*math.pi/180;\n",
"lambda2=d*math.sin(theta2)/n; #wavelength of second spectral line(nm)\n",
"\n",
"#Result\n",
"print \"The wavelength of second spectral line is\",int(lambda2*10**7),\"nm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The wavelength of second spectral line is 550 nm\n"
]
}
],
"prompt_number": 41
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 5.11, Page number 87"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=3;\n",
"lamda=700*10**-9; #wavelength(m)\n",
"theta=90; #angle(degrees)\n",
"\n",
"#Calculation \n",
"theta=theta*math.pi/180; #angle(radian)\n",
"d=n*lamda/math.sin(theta); #grating element(m)\n",
"\n",
"#Result\n",
"print \"The minimum grating element required to observe the entire third order spectrum is\",d*10**6,\"*10**-6 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The minimum grating element required to observe the entire third order spectrum is 2.1 *10**-6 m\n"
]
}
],
"prompt_number": 45
}
],
"metadata": {}
}
]
}