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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#Chapter 2:POLARIZATION AND ULTRASONICS "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.1, Page number 2.33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "theta= 45.0 degrees\n",
+ "theta= 135.0 degrees\n",
+ "#The value of theta can be +(or)- 45 degrees and +(or)-135 degrees.\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "I=1/2\n",
+ "\n",
+ "#Calculation\n",
+ "theta1=math.acos(1/math.sqrt(2))*(180/math.pi)\n",
+ "theta2=math.acos(-1/math.sqrt(2))*(180/math.pi)\n",
+ "#Result\n",
+ "print\"theta=\",theta1,\"degrees\"\n",
+ "print\"theta=\",theta2,\"degrees\"\n",
+ "print\"#The value of theta can be +(or)- 45 degrees and +(or)-135 degrees.\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.2, Page number 2.33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ip= 60.0 degrees\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Calculation\n",
+ "ip=math.atan(1.732)*(180/math.pi)\n",
+ "\n",
+ "#Result\n",
+ "print\"ip=\",round(ip),\"degrees\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.3, Page number 2.33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "phi= 104.7 rad.\n",
+ "Since the phase difference should be with in 2pi radius, we get phi=4.169 rad.\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "d=1*10**-3\n",
+ "lamda=6000*10**-10\n",
+ "nd=0.01 #difference between the refractive indices(n1 - n2)\n",
+ "\n",
+ "#Calculation\n",
+ "phi=(2*math.pi*d*nd)/lamda\n",
+ "\n",
+ "#Result\n",
+ "print\"phi=\",round(phi,1),\"rad.\"\n",
+ "print\"Since the phase difference should be with in 2pi radius, we get phi=4.169 rad.\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.4, Page number 2.33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Thickness,t= 27.47 micro m.\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=5000*10**-10\n",
+ "mu_0=1.5533\n",
+ "mu_1=1.5442\n",
+ "\n",
+ "#Calculations\n",
+ "t=lamda/(2*(mu_0 - mu_1))\n",
+ " \n",
+ "#Result\n",
+ "print\"Thickness,t=\",round(t*10**6,2),\"micro m.\" "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.5, Page number 2.34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Birefringence of the crystal delta/mu= 0.005\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=6000*10**-10\n",
+ "t=0.003*10**-2\n",
+ "\n",
+ "#Calculations\n",
+ "delta_mu=lamda/(4*t)\n",
+ "\n",
+ "#Result\n",
+ "print\"Birefringence of the crystal delta/mu=\",delta_mu\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.6, Page number 2.34ΒΆ"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Refractive index of medium= 1.732\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "theta=60*(math.pi/180) #When the angle of refraction is 30degrees, angle of reflection will be 60degrees\n",
+ "\n",
+ "#Calculation\n",
+ "mu=math.tan(theta)\n",
+ "\n",
+ "#Result\n",
+ "print\"Refractive index of medium=\",round(mu,3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.7, Page number 2.34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Ultrasonic wavelength,lamda s = 7.47 *10**-4 m\n",
+ "Velocity of ultrasonic waves in liquid = 1495.0 ms**-1\n",
+ "#Answer varies due to rounding of numbers\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "m=1\n",
+ "lamda_l=6000*10**-10\n",
+ "theta=0.046*(math.pi/180)\n",
+ "n=2*10**6\n",
+ "\n",
+ "#Calculation\n",
+ "lamda_s=(m*lamda_l)/(math.sin(theta))\n",
+ "v=n*lamda_s\n",
+ "\n",
+ "#Result\n",
+ "print\"Ultrasonic wavelength,lamda s =\",round(lamda_s*10**4,2),\"*10**-4 m\"\n",
+ "print\"Velocity of ultrasonic waves in liquid =\",round(v),\"ms**-1\"\n",
+ "print\"#Answer varies due to rounding of numbers\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "##Example number 2.8, Page number 2.35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Velocity of blood flow = 0.1001 m s**-1\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "C=1500\n",
+ "Df=267\n",
+ "f=2*10**6\n",
+ "theta=0*math.pi/180 #degrees\n",
+ "\n",
+ "#Calculation\n",
+ "V=(C*Df)/(2*f*math.cos(theta))\n",
+ "\n",
+ "#Result\n",
+ "print\"Velocity of blood flow =\",round(V,4),\"m s**-1\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.9, Page number 2.35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Fundamental frequency,f = 4.0 *10**6 Hz.\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "t=0.7*10**-3\n",
+ "E=8.8*10**10\n",
+ "rho=2800\n",
+ "\n",
+ "#Calculation\n",
+ "f=(1/(2*t))*math.sqrt(E/rho) #Fundamental frequency\n",
+ "\n",
+ "#Result\n",
+ "print\"Fundamental frequency,f =\",round(f*10**-6),\"*10**6 Hz.\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.10, Page number 2.35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The depth of the sea = 997.5 m.\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "v=1500\n",
+ "t=1.33\n",
+ "\n",
+ "#Calculation\n",
+ "d=(v*t)/2\n",
+ "\n",
+ "#Result\n",
+ "print\"The depth of the sea =\",d,\"m.\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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