{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 13: Fibre Optics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.1, Page number 375"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical aperture is 0.24413\n",
      "maximum entrance angle is 14.13 degrees\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "n1=1.5;     #core refractive index\n",
    "n2=1.48;    #cladding refractive index\n",
    "n=1;\n",
    "\n",
    "#Calculations\n",
    "NA=math.sqrt(n1**2-n2**2);       #numerical aperture\n",
    "i0=math.asin(NA/n);             #maximum entrance angle(radian)\n",
    "i0=i0*180/math.pi;         #maximum entrance angle(degrees)\n",
    "\n",
    "#Result\n",
    "print \"numerical aperture is\",round(NA,5)\n",
    "print \"maximum entrance angle is\",round(i0,2),\"degrees\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Example number 13.2, Page number 376"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "core refractive index is 1.6025\n",
      "acceptance angle is 8.6 degrees\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "n0=1.33;     #water refractive index\n",
    "n2=1.59;    #cladding refractive index\n",
    "NA=0.2;     #numerical aperture\n",
    "\n",
    "#Calculations\n",
    "n1=math.sqrt(NA**2+n2**2);      #core refractive index      \n",
    "NA=math.sqrt(n1**2-n2**2)/n0;       #numerical aperture\n",
    "i0=math.asin(NA);             #acceptance angle(radian)\n",
    "i0=i0*180/math.pi;         #acceptance angle(degrees)\n",
    "\n",
    "#Result\n",
    "print \"core refractive index is\",round(n1,4)\n",
    "print \"acceptance angle is\",round(i0,1),\"degrees\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.3, Page number 376"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical aperture is 0.304\n",
      "acceptance angle is 17.7 degrees\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "n1=1.36;     #core refractive index\n",
    "delta=0.025;    #relative difference\n",
    "\n",
    "#Calculations\n",
    "NA=n1*math.sqrt(2*delta);       #numerical aperture\n",
    "i0=math.asin(NA);             #acceptance angle(radian)\n",
    "i0=i0*180/math.pi;         #acceptance angle(degrees)\n",
    "\n",
    "#Result\n",
    "print \"numerical aperture is\",round(NA,3)\n",
    "print \"acceptance angle is\",round(i0,1),\"degrees\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.4, Page number 376"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical aperture is 0.3873\n",
      "acceptance angle is 22.79 degrees\n",
      "critical angle is 75.16 degrees\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "n1=1.5;     #core refractive index\n",
    "n2=1.45;     #cladding refractive index\n",
    "\n",
    "#Calculations\n",
    "delta=(n1-n2)/n1;    #relative difference\n",
    "NA=n1*math.sqrt(2*delta);       #numerical aperture\n",
    "i0=math.asin(NA);             #acceptance angle(radian)\n",
    "i0=i0*180/math.pi;            #acceptance angle(degrees)\n",
    "theta_c=math.asin(n2/n1);     #critical angle(radian)\n",
    "theta_c=theta_c*180/math.pi;            #critical angle(degrees)\n",
    "\n",
    "#Result\n",
    "print \"numerical aperture is\",round(NA,4)\n",
    "print \"acceptance angle is\",round(i0,2),\"degrees\"\n",
    "print \"critical angle is\",round(theta_c,2),\"degrees\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.5, Page number 377"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "core refractive index is 1.42\n",
      "cladding refractive index is 1.407\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "NA=0.22;    #numerical aperture\n",
    "delta=0.012;    #relative difference\n",
    "\n",
    "#Calculations\n",
    "N=1-delta;\n",
    "n1=math.sqrt(NA**2/(1-N**2));      #core refractive index\n",
    "n2=N*n1;     #cladding refractive index\n",
    "\n",
    "#Result\n",
    "print \"core refractive index is\",round(n1,2)\n",
    "print \"cladding refractive index is\",round(n2,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.6, Page number 377"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "acceptance angle is 23.6 degrees\n",
      "critical angle is 81.9 degrees\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "NA=0.40;    #numerical aperture\n",
    "delta=1/100;    #relative difference\n",
    "\n",
    "#Calculations\n",
    "i0=math.asin(NA);      #acceptance angle(radians)\n",
    "i0=i0*180/math.pi;     #acceptance angle(degrees)\n",
    "N=1-delta;\n",
    "thetac=math.asin(N);     #critical angle(radians)\n",
    "thetac=thetac*180/math.pi;     #critical angle(degrees)\n",
    "\n",
    "#Result\n",
    "print \"acceptance angle is\",round(i0,1),\"degrees\"\n",
    "print \"critical angle is\",round(thetac,1),\"degrees\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.7, Page number 378"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "core refractive index is 1.5\n",
      "cladding refractive index is 1.3\n",
      "numerical aperture is 0.75\n",
      "answer for numerical aperture varies due to rounding off errors\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "vf=3*10**8;      #velocity of light in free space(m/s)\n",
    "vc=2*10**8;      #velocity of light in core(m/s)\n",
    "thetac=60*math.pi/180;     #critical angle(radians)\n",
    "\n",
    "#Calculations\n",
    "n1=vf/vc;       #core refractive index\n",
    "n2=n1*math.sin(thetac);     #cladding refractive index\n",
    "NA=math.sqrt(n1**2-n2**2);    #numerical aperture\n",
    "\n",
    "#Result\n",
    "print \"core refractive index is\",n1\n",
    "print \"cladding refractive index is\",round(n2,1)\n",
    "print \"numerical aperture is\",NA\n",
    "print \"answer for numerical aperture varies due to rounding off errors\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.8, Page number 378"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical aperture is 0.3905\n",
      "acceptance angle is 23.0 degrees\n",
      "critical angle is 75.4 degrees\n",
      "number of reflections per metre is 5206\n",
      "answer for number of reflections in the textbook is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration \n",
    "n1=1.55;       #core refractive index\n",
    "n2=1.50;     #cladding refractive index\n",
    "d=50*10**-6;     #core diameter(micro m)\n",
    "\n",
    "#Calculations\n",
    "NA=math.sqrt(n1**2-n2**2);    #numerical aperture\n",
    "i0=math.asin(NA);      #acceptance angle(radians)\n",
    "i0=i0*180/math.pi;     #acceptance angle(degrees)\n",
    "thetac=math.asin(n2/n1);     #critical angle(radians)\n",
    "theta_c=thetac*180/math.pi;     #critical angle(degrees)\n",
    "x=d*math.tan(thetac);\n",
    "n=1/x;        #number of reflections per metre  \n",
    "\n",
    "#Result\n",
    "print \"numerical aperture is\",round(NA,4)\n",
    "print \"acceptance angle is\",round(i0),\"degrees\"\n",
    "print \"critical angle is\",round(theta_c,1),\"degrees\"\n",
    "print \"number of reflections per metre is\",int(n)\n",
    "print \"answer for number of reflections in the textbook is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.9, Page number 379"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical aperture is 0.375\n",
      "critical angle is 75.93 degrees\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration \n",
    "delta=0.03;    #relative difference\n",
    "i0=22*math.pi/180;      #acceptance angle(radians)\n",
    "\n",
    "#Calculations\n",
    "NA=math.sin(i0);    #numerical aperture\n",
    "N=1-delta;\n",
    "thetac=math.asin(N);     #critical angle(radians)\n",
    "theta_c=thetac*180/math.pi;     #critical angle(degrees)\n",
    "\n",
    "#Result\n",
    "print \"numerical aperture is\",round(NA,3)\n",
    "print \"critical angle is\",round(theta_c,2),\"degrees\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.10, Page number 379"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "velocity of light in fibre core is 2.48 *10**8 m/s\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration \n",
    "delta=0.0045;    #relative difference\n",
    "i0=0.115;      #acceptance angle(radians)\n",
    "v=3*10**8;      #velocity of light(m/s)\n",
    "\n",
    "#Calculations\n",
    "NA=math.sin(i0);    #numerical aperture\n",
    "n1=NA/math.sqrt(2*delta);     #core refractive index\n",
    "vcore=v/n1;      #velocity of light in fibre core(m/s)\n",
    "\n",
    "#Result\n",
    "print \"velocity of light in fibre core is\",round(vcore/10**8,3),\"*10**8 m/s\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.11, Page number 381"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "diameter of core is 3.79 *10**-6 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration \n",
    "V=2.405;     #V-number\n",
    "lamda=8500*10**-10;    #wavelength(m)\n",
    "n1=1.48;       #core refractive index\n",
    "n2=1.47;     #cladding refractive index\n",
    "\n",
    "#Calculations\n",
    "d=V*lamda/(math.pi*math.sqrt(n1**2-n2**2));     #diameter of core(m)\n",
    "\n",
    "#Result\n",
    "print \"diameter of core is\",round(d*10**6,2),\"*10**-6 m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.12, Page number 381"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "maximum radius for fibre is 3.76 micro m\n",
      "answer varies due to rounding off errors\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration \n",
    "V=2.405;     #V-number\n",
    "lamda=1300*10**-3;    #wavelength(micro m)\n",
    "n1=1.466;       #core refractive index\n",
    "n2=1.46;     #cladding refractive index\n",
    "\n",
    "#Calculations\n",
    "r=V*lamda/(2*math.pi*math.sqrt(n1**2-n2**2));     #maximum radius for fibre(micro m)\n",
    "\n",
    "#Result\n",
    "print \"maximum radius for fibre is\",round(r,2),\"micro m\"\n",
    "print \"answer varies due to rounding off errors\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.13, Page number 381"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "diameter of fibre core is 91.5 micro m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration \n",
    "lamda=1.3;    #wavelength(micro m)\n",
    "n1=1.5;       #core refractive index\n",
    "Nm=1100;      #number of modes\n",
    "delta=0.01;   #refractive index difference\n",
    "\n",
    "#Calculations\n",
    "d=lamda*math.sqrt(Nm/delta)/(math.pi*n1);     #diameter of fibre core(micro m)\n",
    "\n",
    "#Result\n",
    "print \"diameter of fibre core is\",round(d,1),\"micro m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.14, Page number 382"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of guided modes is 459.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration \n",
    "lamda=1.1*10**-6;    #wavelength(m)\n",
    "r=60/2*10**-6;     #radius(m)\n",
    "NA=0.25;         #numerical aperture\n",
    "\n",
    "#Calculations\n",
    "V=2*math.pi*r*NA/lamda;    \n",
    "Nm=V**2/4;     #number of guided modes\n",
    "\n",
    "#Result\n",
    "print \"number of guided modes is\",round(Nm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.15, Page number 387"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fibre loss is 12.0412 dB/km\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration \n",
    "L=500/1000;     #length(km)\n",
    "P0byPi=25/100;     #optical power\n",
    "\n",
    "#Calculations\n",
    "dB=-10*math.log10(P0byPi)/L;     #fibre loss(dB/km)\n",
    "\n",
    "#Result\n",
    "print \"fibre loss is\",round(dB,4),\"dB/km\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13.16, Page number 387"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "output power is 2.005 micro W\n",
      "answer given in the textbook is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration \n",
    "L=10;     #length(km)\n",
    "dB=2.3;   #fibre loss(dB/km)\n",
    "Pi=400;    #input power(micro W)\n",
    "\n",
    "#Calculations\n",
    "P0=10**(-dB*L/10)*Pi;         #output power(micro W)\n",
    "\n",
    "#Result\n",
    "print \"output power is\",round(P0,3),\"micro W\"\n",
    "print \"answer given in the textbook is wrong\""
   ]
  }
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