{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ch-2 : Ray Theory Transmission in Optical Fibers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2_1 Pg: 54"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Critical angle in degree= 75.41 degree\n",
      "\n",
      " Numerical aperture= 0.39 \n",
      "\n",
      " Acceptance angle in degree= 23.00 degree\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import asin,pi,ceil,sqrt\n",
    "n1=1.55## core refractive index\n",
    "n2=1.50## cladding refractive index\n",
    "x=asin(n2/n1)# # Critical angle in radians\n",
    "x1=x*180/(pi)## Critical angle in degree\n",
    "n_a=sqrt(n1**2-n2**2)## Numerical aperture\n",
    "x_a=asin(n_a)*180/(pi)#\n",
    "x_a1=ceil(x_a)## Acceptance angle in Degree\n",
    "print \"Critical angle in degree= %0.2f degree\"%(x1)#\n",
    "print \"\\n Numerical aperture= %0.2f \"%(n_a)#\n",
    "print \"\\n Acceptance angle in degree= %0.2f degree\"%(x_a1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.2 Pg: 56"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numerical aperture = 0.42\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sin,sqrt\n",
    "c=3*10**8## speed of light in m/s\n",
    "v=2*10**8## in m/s\n",
    "n1=c/v#\n",
    "x=75## in degree\n",
    "n2=n1*sin((x*3.14/180))#\n",
    "n_2=1.44#\n",
    "n_a=sqrt(n1**2-n_2**2)## numerical aperture\n",
    "print \"Numerical aperture = %0.2f\"%(n_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.3 Pg: 57"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numerical aperture = 0.30\n",
      "\n",
      " acceptance angle in degree = 17.46 degree\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt,asin,pi\n",
    "n1=1.50## core refractive index\n",
    "n2=1.47## cladding refractive index\n",
    "dl=(n1-n2)/n1#\n",
    "n_a=n1*(sqrt(2*dl))## numerical aperture\n",
    "x_a=(asin(n_a))*180/pi## acceptance angle in degree\n",
    "print \"Numerical aperture = %0.2f\"%(n_a)#\n",
    "print \"\\n acceptance angle in degree = %0.2f degree\"%(x_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.4 Pg: 58"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numerical aperture = 0.39\n",
      "\n",
      " acceptance angle in degree = 22.79 degree\n",
      "\n",
      " critical angle in degree = 75.20 degree\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt,asin,pi\n",
    "n1=1.50## core refractive index\n",
    "n2=1.45## cladding refractive index\n",
    "dl=(n1-n2)/n1#\n",
    "n_a=n1*(sqrt(2*dl))## numerical aperture\n",
    "x_a=(asin(n_a))*180/pi## acceptance angle in degree\n",
    "x_c=(asin(n2/n1))*180/3.14## critical angle in degree\n",
    "print \"Numerical aperture = %0.2f\"%(n_a)#\n",
    "print \"\\n acceptance angle in degree = %0.2f degree\"%(x_a)#\n",
    "print \"\\n critical angle in degree = %0.2f degree\"%(x_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.5 Pg: 58"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "core refractive ondex = 1.42\n",
      "\n",
      " cladding refractive index = 1.40\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt\n",
    "dl=0.012#\n",
    "n_a=0.22## numerical aperture\n",
    "n1=n_a/(sqrt(2*dl))## core refractive ondex\n",
    "n2=n1-(dl*n1)## cladding refractive index\n",
    "print \"core refractive ondex = %0.2f\"%(n1)#\n",
    "print \"\\n cladding refractive index = %0.2f\"%(n2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.6 Pg: 59"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "core refractive ondex = 2.47\n",
      "\n",
      " cladding refractive index = 2.45\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "from __future__ import division\n",
    "dl=0.01#\n",
    "n_a=0.35## numerical aperture\n",
    "n1=n_a/(sqrt(2*dl))## core refractive ondex\n",
    "n2=n1-(dl*n1)## cladding refractive index\n",
    "print \"core refractive ondex = %0.2f\"%(n1)#\n",
    "print \"\\n cladding refractive index = %0.2f\"%(n2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.7 Pg: 59"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "acceptance angle in degree = 7.72 degree\n",
      "\n",
      " critical angle in degree = 82.83 degree\n",
      "\n",
      " number of modes transmitted = 288\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,asin,pi,floor\n",
    "from __future__ import division\n",
    "n2=1.59## cladding refractive index\n",
    "n_a=0.2## numerical aperture\n",
    "n1=sqrt(n2**2+n_a**2)## core refractive index\n",
    "n_1=1.60## core refractive index\n",
    "n_o=1.33#\n",
    "A=(sqrt(n_1**2-n2**2))/n_o#\n",
    "x_a=(asin(A))*180/pi## acceptance angle in degree\n",
    "x_c=(asin(n2/n1))*180/pi## critical angle in degree\n",
    "y=1300*10**(-9)## in meter\n",
    "a=25*10**(-6)## in meter\n",
    "v=(2*pi*a*n_a)/y#\n",
    "V=floor(v)#\n",
    "M=V**2/2## number of modes transmitted\n",
    "print \"acceptance angle in degree = %0.2f degree\"%(x_a)#\n",
    "print \"\\n critical angle in degree = %0.2f degree\"%(x_c)#\n",
    "print \"\\n number of modes transmitted = %d\"%(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.8 Pg: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numerical aperture = 0.30\n",
      "\n",
      " the maximum entrance angle in degree = 17.46 degree\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi,asin\n",
    "from __future__ import division\n",
    "n1=1.50## core refractive index\n",
    "n2=1.47## cladding refractive index\n",
    "dl=(n1-n2)/n1#\n",
    "n_a=n1*(sqrt(2*dl))## numerical aperture\n",
    "x_e=(asin(n_a))*180/pi## the maximum entrance angle in degree\n",
    "print \"Numerical aperture = %0.2f\"%(n_a)#\n",
    "print \"\\n the maximum entrance angle in degree = %0.2f degree\"%(x_e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.9 Pg: 61"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numerical aperture = 0.29\n",
      "\n",
      " acceptance angle in degree = 16.74 degree\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi,asin\n",
    "from __future__ import division\n",
    "n1=1.44## core refractive index\n",
    "dl=0.02#\n",
    "n_a=n1*sqrt(2*dl)#\n",
    "n_a=n1*(sqrt(2*dl))## numerical aperture\n",
    "x_a=(asin(n_a))*180/pi## acceptance angle in degree\n",
    "print \"Numerical aperture = %0.2f\"%(n_a)#\n",
    "print \"\\n acceptance angle in degree = %0.2f degree\"%(x_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.10 Pg: 61"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "critical angle = 81.89 degree\n",
      "\n",
      " numerical aperture = 0.21\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi,asin\n",
    "from __future__ import division\n",
    "n1=1.50## core refractive index\n",
    "n2=(99/100)*1.50## cladding refractive index\n",
    "x_c=(asin(n2/n1))*180/pi## critical angle in degree\n",
    "n_m=sqrt(n1**2-n2**2)## numerical aperture\n",
    "print \"critical angle = %0.2f degree\"%(x_c)#\n",
    "print \"\\n numerical aperture = %0.2f\"%(n_m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.11 Pg: 61"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical aperture = 0.38\n",
      "\n",
      " fractional difference = 0.03\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "from __future__ import division\n",
    "n1=1.50## core refractive index\n",
    "n2=1.45## cladding refractive index\n",
    "n_m=sqrt(n1**2-n2**2)## numerical aperture\n",
    "dl=(n1-n2)/n1## fractional difference\n",
    "print \"numerical aperture = %0.2f\"%(n_m)#\n",
    "print \"\\n fractional difference = %0.2f\"%(dl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.12 Pg: 62"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "critical angle = 83.29 degree\n",
      "\n",
      " acceptance angle = 9.82 degree\n",
      "\n",
      " numerical aperture = 0.17\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi,asin\n",
    "from __future__ import division\n",
    "n1=1.46## core refractive index\n",
    "n2=1.45## cladding refractive index\n",
    "x_c=(asin(n2/n1))*180/pi## critical angle in degree\n",
    "n_m=sqrt(n1**2-n2**2)## numerical aperture\n",
    "x_a=(asin(n_m))*180/pi## acceptance angle in degree\n",
    "print \"critical angle = %0.2f degree\"%(x_c)#\n",
    "print \"\\n acceptance angle = %0.2f degree\"%(x_a)#\n",
    "print \"\\n numerical aperture = %0.2f\"%(n_m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.13 Pg: 62"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "core refractive index = 1.44\n",
      "\n",
      " cladding refractive index = 1.43\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "from __future__ import division\n",
    "n_m=0.204## numerical aperture\n",
    "dl=0.01## index difference\n",
    "n1=n_m/(sqrt(2*dl))## core refractive index\n",
    "n2=n1*(1-dl)## cladding refractive index\n",
    "print \"core refractive index = %0.2f\"%(n1)#\n",
    "print \"\\n cladding refractive index = %0.2f\"%(n2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.14 Pg: 62"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "critical angle = 81.89 degree\n",
      "\n",
      " numerical aperture = 0.21\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi,asin\n",
    "from __future__ import division\n",
    "n1=1.46## core refractive index\n",
    "dl=0.01## index difference\n",
    "n_2=n1-(n1*dl)## cladding refractive index\n",
    "x_c=(asin(n_2/n1))*180/pi## critical angle in degree\n",
    "n_m=sqrt(n1**2-n_2**2)## numerical aperture\n",
    "print \"critical angle = %0.2f degree\"%(x_c)#\n",
    "print \"\\n numerical aperture = %0.2f\"%(n_m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.15 Pg: 62"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "critical angle=75.16 degree\n",
      "\n",
      " acceptance angle=22.59 degree\n",
      "\n",
      " numerical aperture=0.38\n",
      "\n",
      " percentage of light=14.75%\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi,asin\n",
    "from __future__ import division\n",
    "n1=1.50## core refractive index\n",
    "n2=1.45## cladding refractive index\n",
    "x_c=(asin(n2/n1))*180/pi## critical angle in degree\n",
    "n_m=sqrt(n1**2-n2**2)## numerical aperture\n",
    "x_a=(asin(n_m))*180/pi## acceptance angle in degree\n",
    "n_c=(n_m)**2*100## percentage of light\n",
    "print \"critical angle=%0.2f degree\"%(x_c)#\n",
    "print \"\\n acceptance angle=%0.2f degree\"%(x_a)#\n",
    "print \"\\n numerical aperture=%0.2f\"%(n_m)#\n",
    "print \"\\n percentage of light=%0.2f%%\"%(n_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:2.16 Pg: 63"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical aperture=0.21\n",
      "\n",
      " acceptance angle=0.14 radian\n",
      "\n",
      " critical angle=81.89 degree\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi,asin\n",
    "from __future__ import division\n",
    "n1=1.50## core refractive index\n",
    "dl=0.01## index difference\n",
    "n_m=n1*(sqrt(2*dl))## numerical aperture\n",
    "x_a=pi*(n_m)**2## acceptance angle in radian\n",
    "n2_1=1-dl## the ratio of n2 to n1\n",
    "x_c=(asin(n2_1))*180/pi## critical angle in degree\n",
    "print \"numerical aperture=%0.2f\"%(n_m)#\n",
    "print \"\\n acceptance angle=%0.2f radian\"%(x_a)#\n",
    "print \"\\n critical angle=%0.2f degree\"%(x_c)"
   ]
  }
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