{
"metadata": {
"name": "",
"signature": "sha256:5e77310b83fb16f4b45eb92df638029fc5fbb7881beb71539bf2e332dc67f090"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2 Diffraction of light"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.1 Page no 85"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"w=6*10**-7\n",
"a=12*10**-7\n",
"\n",
"#Calculation\n",
"import math\n",
"A=math.asin(w/a)*180/3.14\n",
"\n",
"#Result\n",
"print\"Half angular width of central bright maxima is\",round(A,0),\"degree\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Half angular width of central bright maxima is 30.0 degree\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.2 Page no 85"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"a =0.2*10**-3 #m\n",
"D =2.0 # n m\n",
"x=5*10**-3\n",
"\n",
"#Calculation\n",
"w=(a*x)/D\n",
"w1=w*1*10**10\n",
"\n",
"#Result\n",
"print\"Wavelength of light is\", w1,\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Wavelength of light is 5000.0 A\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.3 Page no 85"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"f=100 #cm\n",
"L=6000*10**-8\n",
"d=0.01\n",
"\n",
"#Calculation\n",
"x=1.22*f*L/d\n",
"\n",
"#Result\n",
"print\"Separation is\",x,\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Separation is 0.732 cm\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.4 Page no 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"w=6*10**-7 #m\n",
"D=2\n",
"x=5.0*10**-3\n",
"\n",
"#Calculation\n",
"a=(w*D)/x\n",
"\n",
"#Result\n",
"print\"Slit width is\", a*10**4,\"*10**-4 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slit width is 2.4 *10**-4 m\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.5 Page no 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"w=589*10**-9\n",
"D=1\n",
"a=0.1*10**-3\n",
"\n",
"#Calculation\n",
"import math\n",
"A=math.asin(w/a)\n",
"A1=2*A\n",
"y=D*A1\n",
"y1=y*100\n",
"\n",
"#Result\n",
"print\"Angular width of central maxima is\", round(A1,3),\"radian\"\n",
"print\"Linear width of central maxima is\",round(y1,3),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Angular width of central maxima is 0.012 radian\n",
"Linear width of central maxima is 1.178 cm\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.6 Page no 86"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"a=22.0*10**-5\n",
"L=5500*10**-8\n",
"n=1\n",
"n1=2\n",
"\n",
"#Calculation\n",
"import math\n",
"a1=L/a\n",
"A=math.asin(a1)*180/3.14\n",
"a2=math.asin(2*L/a)*180/3.14\n",
"\n",
"#Result\n",
"print\"Angular position of two minima is\",round(A,2), \"Degree and\", round(a2,0),\"Degree\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Angular position of two minima is 14.48 Degree and 30.0 Degree\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.7 Page no 87"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"n=1\n",
"L=5890*10**-10\n",
"a=3*10**-4\n",
"\n",
"#Calculation\n",
"import math\n",
"A=math.asin((L/a)*180/3.14)\n",
"A1=math.asin((3*L)/(2.0*a))*180/3.14\n",
"\n",
"#Result\n",
"print\"Angle is\", round(A1*10**2,0),\"Degree\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Angle is 17.0 Degree\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.8 Page no 87"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"L=4890*10**-10\n",
"a=5*10**-3\n",
"f=0.4\n",
"\n",
"#Calculation\n",
"x1=f*L/a\n",
"x2=3*L*f/(2*a)\n",
"x=x2-x1\n",
"\n",
"#Result\n",
"print\"Distance between first dark fringe and new bright fringe is\", x,\"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Distance between first dark fringe and new bright fringe is 1.956e-05 m\n"
]
}
],
"prompt_number": 40
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.9 Page no 88"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"L=5000*10**-8 #cm\n",
"a=5000.0\n",
"\n",
"#Calculation\n",
"n=1/(L*a)\n",
"\n",
"#Result\n",
"print\"Highest order spectrum is\",n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Highest order spectrum is 4.0\n"
]
}
],
"prompt_number": 41
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.10 Page no 88"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"c=1/5000.0\n",
"w1=5890*10**-8 #cm\n",
"n =2\n",
"\n",
"#Calculation\n",
"import math\n",
"theta = math.asin ((n*w1)/c)*180/3.14\n",
"w2 =5896*10** -8\n",
"theta1 = math.asin ((n*w2)/c)*180/3.14\n",
"a= theta1 - theta \n",
"w =5893*10**-8\n",
"dw=w2 -w1\n",
"N=w/( dw*n)\n",
"N1= floor (N)\n",
"\n",
"#Result\n",
"print\"(a) Angular width is\",round(theta,3),\"Degree\"\n",
"print\"(b) Angular separation is\",round(a,3),\"Degree\"\n",
"print\"(c) No. of lines is\",N1,\"Grating\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Angular width is 36.104 Degree\n",
"(b) Angular separation is 0.043 Degree\n",
"(c) No. of lines is 491.0 Grating\n"
]
}
],
"prompt_number": 42
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.11 Page no 89"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"w1=589*10**-9\n",
"w2 =5896*10**-10 \n",
"dw=w2-w1 # change o f wave l eng th\n",
"w=( w1+w2) /2.0 #mid wavelength\n",
"n =1\n",
"\n",
"#Calculation\n",
"N=w/(n*dw)\n",
"N1= floor (N)\n",
"\n",
"#Result\n",
"print\"Number of lines is\", N1,\"grating\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Number of lines is 982.0 grating\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.12 Page no 89"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"n1=2\n",
"n2=3.0\n",
"L=6360 #A\n",
"\n",
"#Calculation\n",
"L2=n1*L/n2\n",
"\n",
"#Result\n",
"print\"Wavelength is\",L2,\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Wavelength is 4240.0 A\n"
]
}
],
"prompt_number": 44
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.13 Page no 89"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"L1=5400*10**-8\n",
"L2=4050.0*10**-8\n",
"a=30 #Degree\n",
"b=1350.0*10**-8\n",
"\n",
"#Calculation\n",
"A=b/(L1*L2*2)\n",
"\n",
"#Result\n",
"print\"Number of lines is\", round(A,0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Number of lines is 3086.0\n"
]
}
],
"prompt_number": 48
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.14 Page no 90"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"a=30 #Degree\n",
"L=5000*10**-8\n",
"x=0.01 #Radian\n",
"\n",
"#Calculation\n",
"import math\n",
"A=math.tan(a*3.14/180.0)\n",
"X=1/A\n",
"L1=L*x*X\n",
"\n",
"#Result\n",
"print\"Difference in two wavelength is\", round(L1*10**8,1),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Difference in two wavelength is 86.7 A\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.15 Page no 90"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#Given\n",
"c=1/4000.0 # grating element\n",
"w=5000*10**-8\n",
"n =3\n",
"\n",
"#Calculation\n",
"import math\n",
"D=n/(c* math.sqrt (1 -((n*w/c)**2) ))\n",
"\n",
"#Result\n",
"print\"Dispersive power is\",D*10**-4,\"*10**4 rad/sec\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dispersive power is 1.5 *10**4 rad/sec\n"
]
}
],
"prompt_number": 59
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.16 Page no 90"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"a=30 #Degree\n",
"n=2.0\n",
"A=5000.0\n",
"\n",
"#Calculation\n",
"import math\n",
"L=math.sin(a*3.14/180.0)/(n*A)\n",
"\n",
"#Result\n",
"print\"Wavelength is\", round(L*10**8,0),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Wavelength is 4998.0 A\n"
]
}
],
"prompt_number": 84
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.17 Page no 91"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"l =5 #length of grating\n",
"N =16000\n",
"w =6000\n",
"n =2.0\n",
"\n",
"#Calculation\n",
"T=N*l\n",
"R=T*n\n",
"dw=w/(T*n)\n",
"\n",
"#Result\n",
"print\"(a) Resolving power is\",R\n",
"print\"(b) Wavelength is\",dw,\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Resolving power is 160000.0\n",
"(b) Wavelength is 0.0375 A\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.18 Page no 91"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"w1=5500 #A\n",
"w2=5501\n",
"n=2\n",
"W1=8500\n",
"W2=8501\n",
"\n",
"#Calculation\n",
"w=(w1+w2)/2.0\n",
"W=w2-w1\n",
"N=w/W\n",
"W11=(W1+W2)/2.0\n",
"W12=W2-W1\n",
"N1=W11/W12\n",
"\n",
"#Result\n",
"print\"The required rosolving power\", N1,\"is less than the actual power\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The required rosolving power 8500.5 is less than the actual power\n"
]
}
],
"prompt_number": 94
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.19 Page no 92"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"c =12.5*10**-5\n",
"w=5*10**-5\n",
"N =40000\n",
"\n",
"#Calculation\n",
"n=c/w\n",
"n1= floor (n)\n",
"P=n1*N\n",
"\n",
"#Result\n",
"print\"Resolving power is\",P"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resolving power is 80000.0\n"
]
}
],
"prompt_number": 87
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.20 Page no 92"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"n=2500.0\n",
"w=0.5\n",
"n1=1\n",
"L=5890*10**-8\n",
"a=5000\n",
"L2=5896*10**-8\n",
"L3=5893*10**-8\n",
"c=6*10**-8\n",
"\n",
"#Calculation\n",
"import math\n",
"A=w/n\n",
"A1=math.asin(L*a)*180/3.14\n",
"A2=math.asin(L2*a)*180/3.14\n",
"A3=A2-A1\n",
"N=L3/c\n",
"\n",
"#Result\n",
"print\"Angular separation between Two sodium lines are\", round(A1,1),\"degree and\",round(A2,1),\"degree\"\n",
"print\"Number of lines required is\",round(N,0),\"lines\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Angular separation between Two sodium lines are 17.1 degree and 17.2 degree\n",
"Number of lines required is 982.0 lines\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.21 Page no 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"l=2 #inches\n",
"n=40000\n",
"N=3\n",
"\n",
"#Calculation\n",
"r=n*l\n",
"p=N*r\n",
"\n",
"#Result\n",
"print\"The resolving power in third order is\",p"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The resolving power in third order is 240000\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.22 Page no 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"N=40000.0\n",
"a=12.5*10**-5\n",
"w=80000\n",
"\n",
"#Calculation\n",
"n=w/N\n",
"L=a/n\n",
"L1=L*10**8/(n*N)\n",
"L2=L*10**8+L1\n",
"\n",
"#Result\n",
"print\"Range of wavelength is\", round(L2,2),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Range of wavelength is 6250.08 A\n"
]
}
],
"prompt_number": 35
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.23 Page no 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"L=0.5*10**-8\n",
"\n",
"#Calculation\n",
"import math\n",
"w=math.sin(10*3.14/180.0)*L/(math.cos(10*3.14/180.0)*(3/(60.0*60.0))*(math.pi/180.0))\n",
"W=w+L\n",
"N=W/(L*2)\n",
"N1=(N*2*w)/(L*2)\n",
"\n",
"#Result\n",
"print\"Minimum grating is\", round(w*10**5,0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Minimum grating is 6.0\n"
]
}
],
"prompt_number": 60
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.24 Page no 94"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"w=5000 #A\n",
"N=30000\n",
"n=2.0\n",
"\n",
"#Calculation\n",
"W=w/(n*N)\n",
"\n",
"#Result\n",
"print\"Smallest wavelength separation is\", round(W,3),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Smallest wavelength separation is 0.083 A\n"
]
}
],
"prompt_number": 64
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.25 Page no 95"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"f =50 #focal length of convex lens in cm\n",
"w=5*10**-5 #wavelength used in cm\n",
"n =1\n",
"\n",
"#Calculation\n",
"import math\n",
"r= math.sqrt (n*f*w)\n",
"\n",
"#Result\n",
"print\"Radius is\",r,\"cm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Radius is 0.05 cm\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.26 Page no 95"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"d =0.2 #diameter of ring\n",
"n =1\n",
"w=5*10**-5\n",
"\n",
"#Calculation\n",
"r=d/2.0\n",
"f=(r**2) /(w*n)\n",
"\n",
"#Result\n",
"print\"Position of brightest spot is\",f,\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Position of brightest spot is 200.0 cm\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.27 Page no 95"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"f =1 #focal length in m\n",
"n =1\n",
"w =5893*10**-10\n",
"n1 =3\n",
"n2=5\n",
"\n",
"#Calculation\n",
"r= math.sqrt (n*f*w)\n",
"r1= math.sqrt (n1*f*w)\n",
"r2= math.sqrt (n2*f*w)\n",
"\n",
"#Result\n",
"print\"Radius is\",round(r*10**4,2),\"*10**-4 m,\",round(r1*10**3,3),\"*10**-3 m,\",round(r2*10**3,3),\"*10**-3 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Radius is 7.68 *10**-4 m, 1.33 *10**-3 m, 1.717 *10**-3 m\n"
]
}
],
"prompt_number": 72
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.28 Page no 95"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"f1=8\n",
"w1=6000*10**-8\n",
"w2=4800.0*10**-8\n",
"\n",
"#Calculation\n",
"f2=f1*w1/w2\n",
"\n",
"#Result\n",
"print\"Focal length is\",f2,\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Focal length is 10.0 cm\n"
]
}
],
"prompt_number": 76
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.29 Page no 95"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"n=1\n",
"\n",
"#Calculation\n",
"f1=n\n",
"\n",
"#Result\n",
"print\"Principal focal length is\",f1,\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principal focal length is 1 cm\n"
]
}
],
"prompt_number": 78
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.30 Page no 96"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"r =200 #radius of curvature in cm\n",
"\n",
"#Calculation\n",
"f=r\n",
"\n",
"#Result\n",
"print\"Principle focal length is\",f*10**-2,\"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principle focal length is 2.0 m\n"
]
}
],
"prompt_number": 74
}
],
"metadata": {}
}
]
}