Lab5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 5 Notebook\n",
    "written by Corey Beard ccbeard@uci.edu\n",
    "\n",
    "This notebook will attempt to simulate Physics 52C Lab 5 related to Inverse Photoelectric Effect. \n",
    "\n",
    "Certain cells will be editable, and are meant to mimic students adjusting settings on laboratory equipment. Certain cells are uneditable, and are meant to simulate nature, producing values as read by your instrument, depending on your settings.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy.optimize as optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### This next cell is the main function that returns currents depending on the color of your diode, and the voltage values you are measuring. \n",
    "\n",
    "**It should not be edited.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Current(V,Color):    \n",
    "    # This function will take in a voltage and diode color, and spit out the corresponding current\n",
    "        \n",
    "    V_Red=1.8\n",
    "    V_Blue=2.3\n",
    "    V_Yellow=1.9\n",
    "    V_Green=2.0\n",
    "    V_Violet=2.6\n",
    "    V_UV=2.7\n",
    "    \n",
    "    #elec = 1.602*10**(-19)\n",
    "    #k = 1.38*10**(-23)\n",
    "    #T = 300\n",
    "    \n",
    "    if Color == 'Red':\n",
    "        if V < V_Red:\n",
    "            out = 0.0 \n",
    "        else:\n",
    "            out = np.exp(V-V_Red)-1\n",
    "    elif Color == 'Blue':\n",
    "        if V < V_Blue:\n",
    "            out = 0.0 \n",
    "        else:\n",
    "            out = np.exp(V-V_Blue)-1 \n",
    "    elif Color == 'Yellow':\n",
    "        if V < V_Yellow:\n",
    "            out = 0.0 \n",
    "        else:\n",
    "            out = np.exp(V-V_Yellow)-1 \n",
    "    elif Color == 'Green':\n",
    "        if V < V_Green:\n",
    "            out = 0.0 \n",
    "        else:\n",
    "            out = np.exp(V-V_Green)-1 \n",
    "    elif Color == 'Violet':\n",
    "        if V < V_Violet:\n",
    "            out = 0.0 \n",
    "        else:\n",
    "            out = np.exp(V-V_Violet)-1 \n",
    "    elif Color == 'UV':\n",
    "        if V < V_UV:\n",
    "            out = 0.0 \n",
    "        else:\n",
    "            out = np.exp(V-V_UV)-1 \n",
    "    else:\n",
    "        print('Make sure Color is set as Red, Blue, Yellow, Green, Violet or UV')\n",
    "        \n",
    "    if out > 0.0001: return out/5*(1+np.random.normal(0,0.05))    \n",
    "    else: return np.abs(0.0001*(1+np.random.normal(0,0.05)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**These are default parameters. And should not be edited also.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "Resistor_R = 100.0 #Resistance of the resistor, in Ohms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3.2 Diode I-V Characteristics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here your goal is to see how current flows through a circuit as you change voltage, when using diodes of different colors. \n",
    "\n",
    "**Lab guide says use the 635nm LED, so we'll use the \"red\" colored LED.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cell below returns the current for an input voltage value. Lab guide says describe the behavior of current\n",
    "as the voltage is decreased from a high value. Input different voltage values and see what the output current is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input volts (Volt): {}.format(Volts)\n",
      "Output Current 0.00010014567512904014 (mA)\n"
     ]
    }
   ],
   "source": [
    "LED_color = 'Red'  #LED color - for this section its fixed to Red\n",
    "Volts=1.79 #input the voltage - edit this cell and rerun as needed \n",
    "I=Current(Volts,LED_color)\n",
    "print('Input volts (Volt): {}.format(Volts)')\n",
    "print('Output Current {} (mA)'.format(I))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Turn down the voltage until the current is close to zero as possible. This iw when the LED is barely glowing. What is the  minimum current you can determine?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**This may be easier to answer with the next step by making a graph of 15-20 values of V vs I.** \n",
    "\n",
    "To help with this we give a python code to generate all the measurements in one go. First the variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Min_Voltage = 0.0 #The minimium voltage\n",
    "Max_Voltage = 3.0 # The maximum voltage \n",
    "Measurements = 20 #Number of voltage measurements you plant to take for each LED\n",
    "LED_color = 'Red'  #LED color - for this section its fixed to Red"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is the routine that generates V vs I data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Voltage (Volt)  Current (mA)\n",
      "0             0.00      0.000104\n",
      "1             0.15      0.000093\n",
      "2             0.30      0.000101\n",
      "3             0.45      0.000104\n",
      "4             0.60      0.000103\n",
      "5             0.75      0.000095\n",
      "6             0.90      0.000103\n",
      "7             1.05      0.000099\n",
      "8             1.20      0.000097\n",
      "9             1.35      0.000101\n",
      "10            1.50      0.000096\n",
      "11            1.65      0.000096\n",
      "12            1.80      0.000106\n",
      "13            1.95      0.032357\n",
      "14            2.10      0.071624\n",
      "15            2.25      0.104626\n",
      "16            2.40      0.175277\n",
      "17            2.55      0.205946\n",
      "18            2.70      0.266815\n",
      "19            2.85      0.361885\n"
     ]
    }
   ],
   "source": [
    "Volts = np.arange(Min_Voltage,Max_Voltage,(Max_Voltage-Min_Voltage)/Measurements)\n",
    "I = []\n",
    "for v in Volts:\n",
    "    I.append(Current(v,LED_color))\n",
    "\n",
    "df = pd.DataFrame({\"Voltage (Volt)\": Volts, \"Current (mA)\": I})\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. Make a plot of the above V vs I data.**\n",
    "\n",
    "Section says plot for both linear and on a semi-log graph. Try to get more measurements close to the I low region as possible. You can make these plots within python or outside of python like excel. Please enter code/plots below or insert (or upload) images/photos of the grpah. If you need semi-log paper, you can print them from here: http://www.physics.utah.edu/~gernot/elem_labs/Graph_paper.htm\n",
    "\n",
    "We encourage codes written within Python whenever possible. To help we give the example for the plot below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Here we give an example python code to plot red LED V vs I data***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "\n",
    "plot_color = LED_color\n",
    "if LED_color == 'UV':\n",
    "    plot_color = 'black'\n",
    "\n",
    "plt.subplot(121)\n",
    "\n",
    "plt.scatter(Volts,I,color=plot_color)\n",
    "plt.title(LED_color+' LED Current as a Function of Voltage')\n",
    "plt.xlabel('Voltage (V)')\n",
    "plt.ylabel('Current (mA)')\n",
    "\n",
    "\n",
    "plt.subplot(122)\n",
    "\n",
    "plt.scatter(Volts,np.log(I),color=plot_color)\n",
    "plt.title('Semi-Log plot of ' + LED_color+' LED Current as a Function of Voltage')\n",
    "plt.xlabel('Voltage (V)')\n",
    "plt.ylabel('Log(Current) (Log(mA))')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that on the above semi-log graph, the large gap of I values when it decrease since we only sample V values uniformly when generating the data. You can resample or add more data points than 20 to try to fill this gap. \n",
    "\n",
    "Even with more data you'll notice a break; this is how the LED behaves and consistent with lab measurements. See below with a large number (1000) of measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#best not to edit any below\n",
    "plt.figure(figsize=(6,6))\n",
    "Measurements = 1000 #Number of voltage measurements you plant to take for each LED\n",
    "Volts = np.arange(Min_Voltage,Max_Voltage,(Max_Voltage-Min_Voltage)/Measurements)\n",
    "I = []\n",
    "for v in Volts:\n",
    "    I.append(Current(v,LED_color))\n",
    "\n",
    "plt.scatter(Volts,np.log(I),color=plot_color)\n",
    "plt.title('Sem-log plot of ' + LED_color+' LED Current as a Function of Voltage')\n",
    "plt.xlabel('Voltage (V)')\n",
    "plt.ylabel('Log(Current) (Log(mA))')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Voltage value where I drop rapidly is the **turn-on voltage** that LED starts to light up."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5.3.3 Dependence of Voltage on Wavelength"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This section involves measuring the turn-on voltages and their uncertainties for all six LEDs.\n",
    "\n",
    "The six LEDS, wavelength are as follows:\n",
    "\n",
    "|  Color |lambda  |\n",
    "|-------|--------|\n",
    "|UV     | 375 nm |\n",
    "|-------|--------|\n",
    "|Violet | 400 nm |\n",
    "|-------|--------|\n",
    "|Blue   | 470 nm |\n",
    "|-------|--------|\n",
    "|Green  | 535 nm |\n",
    "|-------|--------|\n",
    "|Yellow | 580 nm |\n",
    "|-------|--------|\n",
    "|Red    | 635 nm | \n",
    "\n",
    "\n",
    "\n",
    "This can be done by changing the color of the LED in above code and plotting each LED curve. \n",
    "\n",
    "We reproduce the code and curve below. To be consistent with lab, try to estimate turn-on voltages with just 20 measurements so the uncertainty is a better reflection of the expected lab measurements.\n",
    "\n",
    "**Change LED color below and rerun and estimate turn-on voltages and an uncertainty to turn-on voltage.**\n",
    "\n",
    "Record data on a paper. After several boxes below you will find a pyhton box to enter voltages and uncertainties to arrays for further calculations. If easier, the second box below provides a way to get data of all six LEDs in a single table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Measurements = 20 #Number of voltage measurements you plant to take for each LED - keep to 20 for lab\n",
    "\n",
    "Min_Voltage = 1.0 #The minimium voltage, may need to change\n",
    "Max_Voltage = 4.0 # The maximum voltage, may need to change\n",
    "\n",
    "LED_color = 'Blue'  #Edit this entry for six LEDs. Options are: UV, Violet, Blue, Green, Yellow, Red\n",
    "\n",
    "\n",
    "#best not to edit below\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "\n",
    "plot_color = LED_color\n",
    "if LED_color == 'UV':\n",
    "    plot_color = 'black'\n",
    "\n",
    "Volts = np.arange(Min_Voltage,Max_Voltage,(Max_Voltage-Min_Voltage)/Measurements)\n",
    "I = []\n",
    "for v in Volts:\n",
    "    I.append(Current(v,LED_color))\n",
    "\n",
    "plt.scatter(Volts,np.log(I),color=plot_color)\n",
    "plt.title('Sem-log plot of ' + LED_color+' LED Current as a Function of Voltage')\n",
    "plt.xlabel('Voltage (V)')\n",
    "plt.ylabel('Log(Current) (Log(mA))')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is a pyhton code to generate all data in one go. And a single plot of all six LED data graphed together. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    V Volt  UV I(mA)  Violet I    Blue I   Green I  Yellow I  Red I(mA)\n",
      "0     1.00  0.000107  0.000111  0.000091  0.000105  0.000101   0.000096\n",
      "1     1.15  0.000101  0.000096  0.000101  0.000102  0.000092   0.000092\n",
      "2     1.30  0.000103  0.000103  0.000093  0.000104  0.000102   0.000103\n",
      "3     1.45  0.000094  0.000103  0.000104  0.000101  0.000109   0.000100\n",
      "4     1.60  0.000099  0.000100  0.000104  0.000106  0.000097   0.000096\n",
      "5     1.75  0.000092  0.000105  0.000109  0.000103  0.000095   0.000095\n",
      "6     1.90  0.000104  0.000096  0.000096  0.000108  0.000100   0.021105\n",
      "7     2.05  0.000104  0.000093  0.000098  0.010814  0.032353   0.061596\n",
      "8     2.20  0.000100  0.000099  0.000103  0.042931  0.069238   0.095729\n",
      "9     2.35  0.000101  0.000098  0.010300  0.085798  0.123052   0.136257\n",
      "10    2.50  0.000100  0.000112  0.043173  0.133656  0.155817   0.204327\n",
      "11    2.65  0.000104  0.010406  0.079937  0.188715  0.227063   0.261360\n",
      "12    2.80  0.021263  0.046698  0.128170  0.231577  0.307666   0.334863\n",
      "13    2.95  0.055012  0.079002  0.189698  0.340588  0.396093   0.426310\n",
      "14    3.10  0.099460  0.134922  0.243971  0.429335  0.454816   0.502591\n",
      "15    3.25  0.136357  0.178670  0.300087  0.479878  0.524041   0.655794\n",
      "16    3.40  0.194950  0.263743  0.415428  0.604797  0.669161   0.848379\n",
      "17    3.55  0.265316  0.332559  0.512043  0.736525  0.821455   0.877286\n",
      "18    3.70  0.332519  0.406600  0.617745  0.926735  1.001329   1.124564\n",
      "19    3.85  0.414339  0.548693  0.765649  1.041409  1.201658   1.301468\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Measurements = 20 #Number of voltage measurements you plant to take for each LED - keep to 20 for lab\n",
    "\n",
    "Min_Voltage = 1.0 #The minimium voltage, may need to change\n",
    "Max_Voltage = 4.0 # The maximum voltage, may need to change\n",
    "\n",
    "#best not to edit below\n",
    "\n",
    "colors = ['UV','Violet','Blue','Green','Yellow','Red']\n",
    "plot_colors =  ['black','violet','blue','green','yellow','red']\n",
    "data = {}\n",
    "#get the data for all the colors\n",
    "for i in range(len(colors)):\n",
    "    temp = []\n",
    "    for j in range(len(Volts)):\n",
    "        temp.append(Current(Volts[j],colors[i]))\n",
    "    data[colors[i]]=temp\n",
    "  \n",
    "df = pd.DataFrame({\"V Volt\": Volts, \"UV I(mA)\": data[colors[0]],\\\n",
    "                   \"Violet I\": data[colors[1]],\\\n",
    "                   \"Blue I\": data[colors[2]],\\\n",
    "                   \"Green I\": data[colors[3]],\\\n",
    "                   \"Yellow I\": data[colors[4]],\\\n",
    "                   \"Red I(mA)\": data[colors[5]]})\n",
    "print(df)\n",
    "\n",
    "#nowa single plot them all together\n",
    "plt.figure(figsize=(8,8))\n",
    "for i in range(len(colors)):\n",
    "    plt.scatter(Volts,data[colors[i]],color=plot_colors[i])\n",
    "plt.title('Current as a Function of Voltage For 6 Diodes')\n",
    "plt.ylabel('Current (mA)')\n",
    "plt.xlabel('Voltage (V)')\n",
    "plt.legend(colors)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using data generated above make a Table of LED wavelength, LED frequency, V$_x$ (turn on volatge/Volts), $\\sigma$(V$_x$) (uncertainty in turn-on voltage/Volts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***text says also record current at the minimum, since this is not needed for 5.3.4 below, lets ignore recording current data***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we generate wavelength (copied from entries in first text cell under 5.3.3) and frequency arrays. There is nothing to edit below except to Run the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#all wavelengths are in nm\n",
    "\n",
    "#this cell is fixed values so best not edit\n",
    "\n",
    "c=3e8 #light speed m/s\n",
    "\n",
    "lambda_UV = 375\n",
    "lambda_Violet = 400\n",
    "lambda_Blue = 470\n",
    "lambda_Green = 535\n",
    "lambda_Yellow = 580\n",
    "lambda_Red = 635\n",
    "\n",
    "lambda_array = np.array([lambda_UV,lambda_Violet,lambda_Blue,lambda_Green,lambda_Yellow,lambda_Red])\n",
    "freq_array = c/(lambda_array*1e-9)/1e12 # freq in THz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Use the figure or data above to estimate the turn on voltage for each LED color, and record it in the cell below.** \n",
    "\n",
    "In above you may have already done the work and recorded the turn-on voltages and uncertainities on a paper. Below enter those values, separated by LED color.\n",
    "\n",
    "The entries are left blank now. **If you run this code without entries you will get an error. If you want to run the code, at least enter dummy values and replace them later with measurements from data.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-15-770a9af0731a>, line 8)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-15-770a9af0731a>\"\u001b[0;36m, line \u001b[0;32m8\u001b[0m\n\u001b[0;31m    Vx_UV =              #turn-on voltage enter here - to an accuracy consistent with error\u001b[0m\n\u001b[0m                                                                                           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "# This is where  you enter data. \n",
    "# Vx_color is the value of turn-on voltage\n",
    "# Vxerr_color is the value of uncertainty or error on turn-on voltage\n",
    "\n",
    "\n",
    "#UV LED\n",
    "\n",
    "Vx_UV =              # turn-on voltage enter here - to an accuracy consistent with error\n",
    "Vxerr_UV=            # error enter here. \n",
    "\n",
    "# for other LEDs follow as above.\n",
    "\n",
    "#Violet LED\n",
    "\n",
    "Vx_Violet = \n",
    "Vxerr_Violet= \n",
    "\n",
    "#Blue LED\n",
    "\n",
    "Vx_Blue = \n",
    "Vxerr_Blue=\n",
    "\n",
    "#Green LED\n",
    "Vx_Green = \n",
    "Vxerr_Green=\n",
    "\n",
    "#Yellow LED\n",
    "Vx_Yellow = \n",
    "Vxerr_Yellow=\n",
    "\n",
    "#Red LED\n",
    "Vx_Red = \n",
    "Vxerr_Red=\n",
    "\n",
    "#this is for later use so best not to edit below\n",
    "\n",
    "volt_array = np.array([Vx_UV,Vx_Violet,Vx_Blue,Vx_Green,Vx_Yellow,Vx_Red])\n",
    "err_array = np.array([Vxerr_UV,Vxerr_Violet,Vxerr_Blue,Vxerr_Green,Vxerr_Yellow,Vxerr_Red])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This next cell creates a table of your values, and **should not be edited.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'volt_array' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-16-0c8dbbe0b4d8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mdf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m\"Wavelength (microns)\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mlambda_array\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Freq (THz)\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mfreq_array\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Turn-on Volt (V)\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mvolt_array\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Volt Error (V)\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0merr_array\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'volt_array' is not defined"
     ]
    }
   ],
   "source": [
    "df = pd.DataFrame({\"Wavelength (microns)\": lambda_array, \"Freq (THz)\": freq_array, \"Turn-on Volt (V)\": volt_array, \"Volt Error (V)\": err_array})\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. Explain below how you estimate the uncertainty or error on turn-on voltage. It is completely fine to make a rough estimate of the error based on your V vs I graphs by eye. You are also free to use some statistical analysis method, but not required.** "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5.3.4 Least Squares Fitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Plot the turn on voltages $V_x$ as a function of the frequency, include error bars capturing the uncertainty for $V_x$. You can plot the data outside of python. If you do please insert an image or upload your graph.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For reference below is a python code to plot the data entered above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'volt_array' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-17-0c890004608e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcolors\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0mx\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfreq_array\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m     \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mvolt_array\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m     \u001b[0myerr\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0merr_array\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'volt_array' is not defined"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "for i in range(len(colors)):\n",
    "    x=freq_array\n",
    "    y=volt_array\n",
    "    yerr=err_array\n",
    "\n",
    "ax.errorbar(x,y,xerr=0,yerr=yerr,fmt='ro')\n",
    "ax.set_xlabel('Freq (THz)')\n",
    "ax.set_ylabel('Turn-on Voltage Vx (Volt)')\n",
    "ax.set_title('Turn on Voltage as a Function of Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Now follow Taylor Chapter 8 to determine the best-fit values for a line of the form $y=A+B*x$ to describe the data, where $y$ would be turn-on voltage and $x$ freq (in THz).**\n",
    "\n",
    "Here the linear fit is such that $B$ denotes gradient and $A$ is the intercept. \n",
    "\n",
    "Note that Taylor Chapter 8 has equations to determine A and B in the case errors of y values are ignored. If you used those equations please state below. It is recommended, but not required, to do a model fit with y errors.\n",
    "Model fitting data with errors involve weighting each data point by the variance and correcting the normalization for the weights used. Equations accounting for non-uniform y errors are given on Page 198 of Taylor and also derived and shown in boxes in Problem 8.9.\n",
    "\n",
    "**2. What are the best fit values of A and B and their errors, $\\delta A$ and $\\delta B$?**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. Also add the best-fit line to your graph of data, you can update the graph in 1 or insert below.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4. State which method (including y errors or y errors ignored) was used to determine A and B, and their errors $\\delta A$ and $\\delta B$.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5. Update the graph in 2 above to also include two additional lines (plotted as dotted lines) that represent the cases of $B \\pm \\delta B$.**\n",
    "\n",
    "Insert an image of your graph below or upload a separate image to Canvas. You are also free to show these two lines in graph related to item 2 in above.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**6. Use the value of B and error $\\delta B$ to calculate $h/e$ and its error and compare with the accepted value.** "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparison results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***For comparison, we use a built-in routine in scipy to do a least-squares model fit to the data. Below should not be edited. You should check on e/h value and its error below for comparison.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'volt_array' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-18-0fa667564f08>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mpfit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpcov\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moptimization\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurve_fit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfreq_array\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvolt_array\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpfit\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpfit\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'volt_array' is not defined"
     ]
    }
   ],
   "source": [
    "def func(x,a,b):\n",
    "    return a + b*x\n",
    "\n",
    "pfit, pcov = optimization.curve_fit(func, freq_array, volt_array)\n",
    "a = pfit[0]\n",
    "b = pfit[1]\n",
    "perr= np.sqrt(np.diag(pcov))\n",
    "aerr = perr[0]\n",
    "berr = perr[1]\n",
    "\n",
    "x = np.linspace(freq_array[0],freq_array[5],1000)\n",
    "y = a + b*x\n",
    "yup = (a) + (b + berr)*x\n",
    "ydown = (a) + (b - berr)*x\n",
    "plt.figure(figsize=(6,6))\n",
    "for i in range(len(colors)):\n",
    "    plt.errorbar(freq_array[i],volt_array[i],yerr=err_array[i],fmt='o',color=plot_colors[i])\n",
    "    \n",
    "plt.plot(x,y,color='black')\n",
    "plt.plot(x,yup,color='gray',linestyle='dotted')\n",
    "plt.plot(x,ydown,color='gray',linestyle='dotted')\n",
    "plt.title('Turn on Voltage as a Function of Frequency')\n",
    "plt.ylabel('Turn on Voltage (V)')\n",
    "plt.xlabel('Frequency (THz)')\n",
    "info = ['Linear Fit','Estimated Errors','Estimated Errors','Measured Values']\n",
    "plt.legend(info)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "accepted = 4.13e-15\n",
    "measured = b/(10**12)\n",
    "error = berr/(10**12)\n",
    "\n",
    "print(\"Accepeted h/e in J/s/C units:\",accepted)\n",
    "print(\"Measured h/e from data entered in 5.3.3:\",measured)\n",
    "print(\"Uncertainty on measured h/e:\",error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5.4 Reflection Questions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Explain why and LED's brightness is proportional to the current flowing through it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Why must and LED that produces green photons have a bigger voltage drop than one producing red photons? (Explain in words)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Explain the difference between photoelectric effect and the inverse photoelectric effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. Explain the sign of the y-intercept in the least squares fit in terms of energy balance. (Hint: in the photoelectric effect, the y intercept is the work function of the metal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5. Consider the dotted lines you produced in the graph in section 5.3.4. Does the uncertainty in the fit to the data seem reasonable?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5.5 Extra credit analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This analysis is optional but worth 10 extra points.\n",
    "\n",
    "You can use python (will need to write a small amount of code) or this can be done with excel or any other computer software or program that allows plotting (or even a graphing calculator).\n",
    "You are welcome to use any plotting software i.e. excel, mathematica, python, to do so.  Insert an image of your graph below or upload a separate image to Canvas.\n",
    "\n",
    "If you are using Python feel free to use the example code above we have given for a comparison model fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Replot the turn-on voltage $V_x$ versus the frequency $\\nu$ using software. Now instead of Tyalor equations use a least-squares model fit or a linear regression to fit a linear curve of the form $y=A+b*x$ to the data, including error bars to y values. \n",
    "\n",
    "**What values do you get for the fitting coefficients A and B?** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
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    "**Are these equal to the values you computed above using Taylor Chapter 8 equations? Why or why not?**"
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