{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Curve fitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "RMSE=\\sqrt{\\frac{1}{n}\\sum{(y-\\hat{y})^2}}\\\\\n",
    "R^2=1-\\frac{\\sum{(y-\\hat{y})^2}}{\\sum{(y-\\bar{y})^2}}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.Fit gas equation\n",
    "\\begin{equation}\n",
    "PV^\\gamma=constant(K)\\\\\n",
    "logP=logK-\\gamma logV\\\\\n",
    "y=a+bx\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>volume(cm3)</th>\n",
       "      <th>pressure(gm/cm2)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>54.3</td>\n",
       "      <td>61.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>61.8</td>\n",
       "      <td>49.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>72.4</td>\n",
       "      <td>37.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>88.7</td>\n",
       "      <td>28.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>118.6</td>\n",
       "      <td>19.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>194.0</td>\n",
       "      <td>10.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   volume(cm3)  pressure(gm/cm2)\n",
       "0         54.3              61.2\n",
       "1         61.8              49.2\n",
       "2         72.4              37.6\n",
       "3         88.7              28.4\n",
       "4        118.6              19.2\n",
       "5        194.0              10.1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_excel('data/gas.xlsx')\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "plt.figure(figsize = [6,6])\n",
    "plt.scatter(df['volume(cm3)'],df['pressure(gm/cm2)'])\n",
    "plt.xlabel('volume(cm3)')\n",
    "plt.ylabel('pressure(gm/cm2)')\n",
    "plt.title('Gas')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma = 1.4\n",
      "K= 1.6e+04\n"
     ]
    }
   ],
   "source": [
    "n=6\n",
    "x=np.log(df['volume(cm3)'])\n",
    "y=np.log(df['pressure(gm/cm2)'])\n",
    "z=np.polyfit(x, y, 1) # linear  fit =y=a+bx\n",
    "p=np.poly1d(z)  #  [a,b]\n",
    "ey=p(x) # expected value\n",
    "a=\"{:.3}\".format(p[0])\n",
    "b=\"{:.3}\".format(p[1])\n",
    "K=np.exp(p[0])\n",
    "gamma=p[1]\n",
    "\n",
    "RMSE=np.sqrt(np.sum((y-ey)**2)/n)\n",
    "R_square=1-(np.sum(np.sum(np.sum((y-ey)**2))/np.sum((y-np.mean(y))**2)))\n",
    "rmse=\"{:.2}\".format(RMSE)\n",
    "r2=\"{:.2}\".format(R_square)\n",
    "\n",
    "\n",
    "plt.figure(figsize = [6,6])\n",
    "plt.plot(x, y, 'ro',label='observed')\n",
    "plt.plot(x, ey, 'b-',label='fitted, a= '+str(a)+', b='+str(b))\n",
    "plt.xlabel('log(V)')\n",
    "plt.ylabel('log(P)')\n",
    "plt.figtext(0.2, 0.3, 'RMSE = '+str(rmse)+',r2='+str(r2))\n",
    "plt.legend()\n",
    "plt.title('Fitted curve')\n",
    "plt.show()\n",
    "print('gamma =',\"{:.2}\".format(-gamma))\n",
    "print('K=',\"{:.2}\".format(K))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.Fit \n",
    "\\begin{equation}\n",
    "f(\\theta)=A+B\\cos\\theta+C\\cos^2\\theta\\\\\n",
    "y=A+Bx+Cx^2\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>theta(degree)</th>\n",
       "      <th>f(theta)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>30</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>45</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>90</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>120</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>150</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   theta(degree)  f(theta)\n",
       "0             30        11\n",
       "1             45        13\n",
       "2             90        16\n",
       "3            120        17\n",
       "4            150        14"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.read_excel('data/scattering.xlsx')\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": [
    "plt.figure(figsize = [6,6])\n",
    "plt.scatter(df1['theta(degree)'],df1['f(theta)'])\n",
    "plt.xlabel(r'$\\theta$(degree)')\n",
    "plt.ylabel(r'f($\\theta$)')\n",
    "plt.title('Scattering')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "n1=5\n",
    "x1=np.cos(df1['theta(degree)']*np.pi/180)\n",
    "y1=df1['f(theta)']\n",
    "z1=np.polyfit(x1, y1, 2) # second order  fit y=a+bx+cx2\n",
    "p1=np.poly1d(z1)  #  [c,b,a]\n",
    "ey1=p1(x1) #expected value\n",
    "A=\"{:.3}\".format(p1[0])\n",
    "B=\"{:.3}\".format(p1[1])\n",
    "C=\"{:.3}\".format(p1[2])\n",
    "\n",
    "\n",
    "RMSE1=np.sqrt(np.sum((y1-ey1)**2)/n1)\n",
    "R_square1=1-(np.sum(np.sum(np.sum((y1-ey1)**2))/np.sum((y1-np.mean(y1))**2)))\n",
    "rmse1=\"{:.2}\".format(RMSE1)\n",
    "r21=\"{:.2}\".format(R_square1)\n",
    "\n",
    "\n",
    "plt.figure(figsize = [6,6])\n",
    "plt.plot(x1, y1, 'ro',label='observed')\n",
    "plt.plot(x1, ey1, 'b-',label='fitted, A= '+str(A)+', B='+str(B)+',C='+str(C))\n",
    "plt.xlabel(r'cos($\\theta$)')\n",
    "plt.ylabel(r'f($\\theta$)')\n",
    "plt.figtext(0.2, 0.3, 'RMSE = '+str(rmse1)+',r2='+str(r21))\n",
    "plt.legend()\n",
    "plt.title('Fitted curve')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.Determination of decay conctant and half life\n",
    "\\begin{equation}\n",
    "N=N_0~e^{-\\lambda~t}\\\\\n",
    "logN=logN_0-\\lambda~t\\\\\n",
    "y=A+BX\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t [s]</th>\n",
       "      <th>N [s-1]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>390</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>395</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>400</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>405</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>410</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>83 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    t [s]  N [s-1]\n",
       "0       0       32\n",
       "1       5       28\n",
       "2      10       29\n",
       "3      15       28\n",
       "4      20       25\n",
       "..    ...      ...\n",
       "78    390        1\n",
       "79    395        1\n",
       "80    400        2\n",
       "81    405        2\n",
       "82    410        1\n",
       "\n",
       "[83 rows x 2 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = pd.read_excel('data/env-dec.xlsx')\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "plt.figure(figsize = [6,6])\n",
    "plt.scatter(df2['t [s]'],df2['N [s-1]'])\n",
    "plt.xlabel('time(s)')\n",
    "plt.ylabel('Count($s^{-1}$)')\n",
    "plt.title('Decay curve')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "n2=83\n",
    "x2=df2['t [s]']\n",
    "y2=np.log(df2['N [s-1]'])\n",
    "z2=np.polyfit(x2, y2, 1) # second order  fit y=a+bx\n",
    "p2=np.poly1d(z2)  #  [c,b,a]\n",
    "ey2=p2(x2) #expected value\n",
    "A1=\"{:.3}\".format(p2[0])\n",
    "B1=\"{:.3}\".format(-p2[1])\n",
    "\n",
    "\n",
    "RMSE2=np.sqrt(np.sum((y2-ey2)**2)/n2)\n",
    "R_square2=1-(np.sum(np.sum(np.sum((y2-ey2)**2))/np.sum((y2-np.mean(y2))**2)))\n",
    "rmse2=\"{:.2}\".format(RMSE2)\n",
    "r22=\"{:.2}\".format(R_square2)\n",
    "\n",
    "\n",
    "plt.figure(figsize = [6,6])\n",
    "plt.plot(x2, y2, 'ro',label='observed')\n",
    "plt.plot(x2, ey2, 'b-',label='fitted, A= '+str(A1)+', B='+str(B1))\n",
    "plt.xlabel('time(sec)')\n",
    "plt.ylabel('ln(A)')\n",
    "plt.figtext(0.2, 0.3, 'RMSE = '+str(rmse2)+',r2='+str(r22))\n",
    "plt.legend()\n",
    "plt.title('Fitted curve')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "decay constant =0.008246 /sec\n"
     ]
    }
   ],
   "source": [
    "print('decay constant =%0.6f /sec'%-p2[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "half life = 84.04 sec\n"
     ]
    }
   ],
   "source": [
    "T=-0.693/p2[1]\n",
    "print('half life = %0.2f sec'%T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.Absorption of coefficient\n",
    "\\begin{equation}\n",
    "N=N_0~e^{-\\mu~x}\\\\\n",
    "logN=logN_0-\\mu~x\\\\\n",
    "y=A+BX\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>n</th>\n",
       "      <th>N [s-1]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>12</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>13</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>14</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>15</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>16</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>17</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>18</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>19</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>20</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     n  N [s-1]\n",
       "0    0      8.0\n",
       "1    1      6.0\n",
       "2    2      5.0\n",
       "3    3      4.0\n",
       "4    4      3.0\n",
       "5    5      2.0\n",
       "6    6      2.0\n",
       "7    7      2.0\n",
       "8    8      2.0\n",
       "9    9      1.0\n",
       "10  10      1.0\n",
       "11  11      1.0\n",
       "12  12      0.5\n",
       "13  13      0.5\n",
       "14  14      0.5\n",
       "15  15      0.5\n",
       "16  16      1.0\n",
       "17  17      0.5\n",
       "18  18      0.4\n",
       "19  19      0.3\n",
       "20  20      0.1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = pd.read_excel('data/env-beta.xlsx')\n",
    "df3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": [
    "plt.figure(figsize = [6,6])\n",
    "plt.scatter(0.03*df3['n'],df3['N [s-1]'])# one sheet of Al is 0.03 mm thick\n",
    "plt.xlabel('Thickness(mm)')\n",
    "plt.ylabel('Count($s^{-1}$)')\n",
    "plt.title('Absorption curve')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ttVSrVi2XP41dJcUYwNCh0L07XHUVbN4cdTQiiadixYpZk7rs/Py4445j1apVWQlg8+bNfP755xxwwAFUqlSJmTNnAmSVcgb49ttvOfnkk3dp57nnnmPAgAEsXbqUJUuW8M0333DUUUcxc+bMrDOAnB55efMHqF69Ou+//z4bNmzA3XnzzTepXbs2Xbp04fvvv2fJkiUsWbKElJSUrDf/CRMmcM011+x13zNnzuSYY44ByDoD2Pmx/c1//fr1WT/P9evXM2XKlByvmDr11FOZMWNG1njFBx98kFXYbfsVR8uWLeOFF17g9NNPz9PPJLukSADDh8MFF8Add0C7dvDtt3FuqPmEJUmcdtpp3HnnnTRo0ICvv/6as88+m/PPP5/09HS2bt3Kc889x1VXXUX9+vVJT0/PemN78sknufDCC2nevPkOE8SsWLEixy6K0aNH06NHjx2W9erVi2effTbXMU+YMIFq1aoxa9YsunTpQseOHQH47rvv6Nw53FLUtGlTevfuTcOGDTnhhBPYtm1bjn3v2X399dfsv//+Ob62fQygfv36PPPMM9x9991xxfrDDz/QsmVL6tevT5MmTejSpQudOnUCwtjM9pLatWvXplOnTqSlpdGkSRPOPffcrETRq1cv6tSpQ7du3XjooYcKZgA6p0uDEvWR38tAR41yr1DBvXJl9ylT9rKy5hOWApYIl4EWlQceeMAnTZoUdRh50r9/f1+5cmXUYeRZbi4DjWw+gLzI03wAO1mwAHr3hvnz4frr4brroHTpHFZMTc15Sr4aNWDJknzFIMlJ8wFIUcjNfABJ0QWU3fHHwwcfwJlnwr/+BZ06QY4382k+YREp4ZIuAQBUqAAjRsDjj8PMmdCgAcyYsdNKmk9YREq4pEwAEKZZPecceP/9kBBOOikMEm/bFltB8wlLIShOXa5S/OT27ytpE8B29etDZib07BkuE/3zn+Gnnyi0SbkleZUrV47Vq1crCUihcHdWr15NuXLl4t4m6QaBd8cdHnoI/vEPqFoVxo2DJk0KpSlJUps3b2b58uW7VKMUKSjlypWjWrVqlC1bdoflCTcpfKIxg4suCm/6fftCy5Zw991hWS5vdhTJUdmyZTnqqKOiDkMkS9J3Ae2sSROYMwc6doRLLoF+/eDXXWYqFhEp/pQAcnDQQTBpEtx+O7zwAmRkwCefRB2ViEjBUgLYjVKl4Mor4a23YN06aNYsXDZajIZMRET2SAlgL1q1CnXbW7SAc8+FgQNh/fo4N1YtIRFJYEoAcahSBV5/HW64AZ5+Gpo2DSUl9mjUKBg0KJSTcA9fBw1SEhCRhKEEEKfSpeHGG+G11+CHH8K4wOjRe9hgyBDYsGHHZRs2hOUiIglACSCXOnQIXULp6fCXv8Df/w45XtatWkIikuCUAPLgiCPC4PDgwfDII2F8YNGinVZSLSERSXBKAHlUtmyoHTRpUnjzb9gQJk7MtoJqCYlIglMCyKfu3cONY8ceCz16wD//GZt2UrWERCTBqRZQAfn99/Dm/9BD0Lw5jB0LRx4ZdVQiIpoQptDtuy88+CCMGQOffRbmGHj99aijEhHZPSWAAtavH8yeHSqK/ulPYcrJrVujjkpEZFdKAIWgVq0w0czAgXDzzdC+PXz/fdRRiYjsSAmgkKSkhNpBTz4ZkkGDBvD221FHJSLyByWAQnb22WES+kqVoF07uPXWbNNOiohESAmgCJxwAnz0UZho5tproVs3WL066qhEJNkpARSRihXh2Wfh4Ydh6tRw49gHH0QdlYgkMyWAImQGF1wA774bKkS3agX33bebOQZUSlpECpkSQAQyMsLdw507w2WXQZ8+8Msv2VZQKWkRKQJKABE58ECYMAHuvDPUEMrICFVGAZWSFpEioQQQITO44opweejGjWHayf/8B3ypSkmLSOFTAkgALVrAxx9D69ahp+esCuNZT8quK6qUtIgUICWABFG5Mrz6KvzrXzByQ0+a2EfMp/YfK6iUtIgUMCWABFK6NFx/PbzxhvFjxaNobJmMor9KSYtIoVACSEAnnwwff1GeRi1TOIOR/K3jEn7rpTd/ESlYSgAJqmpVmDYNrroqfPhv3hy+/jrqqESkJFECSGBlysBtt8GLL4ZbARo2hBdeiDoqESkplACKga5dw41jxx0HvXrB5ZfDpk1RRyUixZ0SQDGRmgozZ8LFF8O990KbNrotQETyRwmgGNlnH7j/fhg3Dj7/PMwx8OqrUUclIsWVEkAx1KcPZGZCtWqhntCQIbBlS9RRiUhxowRQTG2fdvLcc+GWW8K0kytWRB2ViBQnSgDFWPnyoXbQiBFhboEGDeCtt6KOSkSKCyWAEuCss+DDD0OF0VNOCRPRa9pJEdkbJYASol69MO1kv35w3XVhbODHH6OOSkQSmRJACbLffmHOmEceCV1BDRrAe+9FHZWIJColgBLGDM4/H2bNgrJlw/0C99yzm2knRSSpKQGURKNG0bBnKnMWH0jXsq/zz39Cz57w889RByYiiUQJoKTJNp/wAfzMCxs7cXfZq3npxW00bAizZ0cdoIgkCiWAkman+YQN+Mfm23n7kN5s3gwnngiPPqouIRFRAih5dlMg6MSVE/n4YzjpJLjgAjjjDFi3rohjE5GEogRQ0uxu3uDq1TnkEHjlFbjpJhgzBho3hnnzijY8EUkcSgAlzdChYf7g7LLNJ1yqFPzf/8Ebb8CaNdCkCTz9dARxikjkIk0AZvaEma00M30OLSj9+4cpxGrUCNeE7mY+4Xbt4OOPQwI46yw47zzYuDGimEUkElGfAYwAOkUcQ8nTvz8sWRLqQSxZstvJ5A8/HKZOhWuvhf/+N0w7+b//FWmkIhKhSBOAu78D/BRlDMmuTJnQO/Tyy/DNN9CoETz3XNRRiUhRiPoMQBJE586hS6hu3TDfwKWXatpJkZIu4ROAmQ0ys0wzy1y1alXU4ZRo1avD22/DZZeFmcdatQqT0YtIyZTwCcDdh7t7hrtnVK5cOepwSrx99oFhw+D552HBglBQ7qWXoo5KRApDwicAiUbPnjBnTpiMvls3uPpqTTspUtJEfRnoaGAWcJyZLTezv0YZj+zomGNCOem//Q1uvz1cOvrdd1FHJSIFJeqrgE5398Pdvay7V3P3x6OMR3ZVrlyoHfTMM6GQXHp6uHRURIo/dQFJXM44I8w4VrkydOgA//43bN0adVQikh9KABK3OnXC3MP9+8MNN4RLR3VhlkjxpQQguVKhQqgdNHx4uGS0QQOYOTPqqEQkL5QAJNfMQu2g998PYwRt28Jdd2mOAZHiRglA8iw9PQwM//nPMHhw+LpmTdRRiUi8lAAkXypVgvHj4d57w1wDDRtCZmbUUYlIPJQAJN/MQu2gGTPClUEtWsBDD6lLSCTRKQFIgWnWLBSUO+UUuOgi+MtfYO3aqKMSkd1RApACdfDB8OKLcMstMG4cZGTAZ59FHZWI5EQJQApcqVJwzTUwbRr8+is0bQojRkQdlYjsTAlACk2bNjB3bphpbOBAOOcc2LAh6qhEZDslAClUhx4KU6bAddeFs4BmzWDhwqijEhFQApCdjRoVakCXKhW+jhqV721Llw61g159FVasCOMCY8cWTdsisgfuXmwejRo1cilEI0e6p6S4hys4wyMlJSwvoG2/+cb9xBPDyxde6P7bb0XXtkiyAjI9h/dU82J0sXZGRoZn6i6jwpOamvMckDVqwJIlBbbt5s1hkPjuu8PZwLhxcNRJRdO2SDIys9nunrHzcnUByR+WLcvd8jxuW7ZsqB00cSL873/h7uHJS+sXSdsi8gclAPlD9eq5W57PbU89NUw7ecwxcCqTuJLb2UyZImlbRJQAJLuhQyElZcdlKSlheSFte/TRoZz030/5kju5knZM41uqFknbIkkvp4GBRH1oELgIjBzpXqOGu1n4mpuB1Pxs6+6jL5zh+9laP4SVPqVK/yJtW6QkQ4PAUhwsWAB9+sDnn8P114f7B0qXjjoqkeJNg8BSLBx/PHzwAQwYAP/6F3TqBCtXRh2VSMmkBCAJJyUl3DX8+ONhfCA9PZSaFpGCpQQgCeucc8LZwH77wUknwR13wLZtUUclUnIoAUhCS0sLM4z17AlXXRUuHf3pp6ijEikZlAAk4e2/f6gd9MAD8Prr4caxDz+MOiqR4k8JQIoFszDL2LvvhuctW4aEUIwuYhNJOEoAUqw0bhzuHu7YES65BPr1C5POiEjuKQFIsXPQQTBpUhgUfuGFUFDuk0+ijkqk+FECkGKpVCkYPBjeegvWrw8TzTz+uLqERHJDCUCKtVat4OOPw5jAuefC2WeHhCAie6cEIMVelSrw2mtwww3wzDNhEvoFC6KOSiTxKQFIiVC6NNx4Y7hMdOXKMC7w7LNRRyWS2JQApERp3z50CTVoAP37wwUXwG+/RR2VSGJSApAS54gjYNo0uPJKePRRaNECFi2KOiqRxKMEICVS2bJw++3hctFFi8LdwxMmRB2VSGJRApASrXv30CV07LGhntA//xkmpRcRJQBJAqmpoaz0RRfBPfdAmzbwzTdRRyUSPSUASQr77htqB40ZA599FgaJX3st6qhEoqUEIEmlXz+YPRuqVoXOncOUk1u3Rh2VSDSUACTp1KoF778PAwfCzTeHS0e//z7qqESKnhKAJKWUlFA76MknQzJo0ACmT486KpGipQQgSe3ss8O0k5Uqwcknwy23aNpJSR5KAJL0TjgBPvoI+vaFIUOga1dYvTrqqEQKnxKACFCxYqgd9PDD8OaboUvo/fejjkqkcCkBiMSYhdpB774bisu1agX33qs5BqTkUgIQ2UlGRph2sksXuPxy6N0bfvkl6qhECp4SgEgODjww1A66665QT6hRo1BSQqQkUQIQ2Q2zUDvo7bdDSenmzeGxx9QlJCWHEoDIXrRoET79t2kD558PZ54J69ZFHZVI/ikBiMShcmV45RX497/D1UJNmsD8+VFHJZI/SgAicSpdOtQOeuONcJ9A48ZhDmKR4koJQCSXTj45dAllZMCAATBoEGzcGHVUIrmnBCCSB1WrhhvGrr4a/vMfOPFE+OqrqKMSyR0lAJE8KlMGbr0VXnoJli4N004+/3zUUYnETwlAJJ+6dAldQrVrh5vGLrsMNm2KOiqRvVMCECkANWrAjBlwySVw333QujUsWxZ1VCJ7pgQgUkD22Se8+Y8fHy4RbdAAXn456qhEdk8JQKSA9e4dpp088shQWvraa2HLlqijEtmVEoBIITj2WJg1C849NwwUn3IKrFgRdVQiO4o0AZhZJzNbaGZfmdnVUcYiSWzUKEhNhVKlwtdRowpk2/LlwyWiTz0VJpxJT4dp0wqw7WSkn1fBcvdIHkBp4GvgaGAf4BOgzp62adSokYsUqJEj3VNS3EONt/BISQnLC3DbefPca9d2L1XK/aab3LduzWfbyUg/rzwDMj2H91TzOEobmlk5oCvQCqgKbATmAS+7++d5STxm1hy40d07xp5fE0tIt+5um4yMDM/MzMxLcyI5S00NF/HvrEYNWLKkQLddty4Ukxs1Cjp2hJGfN+CQ5XPz1nYyys/vKsmZ2Wx3z9h5+V67gMzsRuBdoDnwAfAYMA7YAtxmZm+YWVoeYjoC+Cbb8+WxZTu3P8jMMs0sc9WqVXloRmQPdnetZjzXcOZy2/32C7WDHnsMpk+HBssn8x7N89Z2MsrP70pyFM8YwEfu3sjd/+nuz7r7VHd/yd3vcfduQH9CF05uWQ7Ldjkdcffh7p7h7hmVK1fOQzMie1C9eu6W53Nbs1A76L33YJ8y22jD29zD5Tv+4cfTdjLKz+9KcrTXBODue7yS2d1Xunte+mWWA0dme14N+C4P+xHJu6FDISVlx2UpKWF5IW7bsCHMefgDupV+hX9yDz15gZ+pFH/bySg/vyvJWU4DA9kfwJPAE7t5PL637few3zLAIuAo/hgErrunbTQILIVi5Ej3GjXczcLX3Awq5mdbd9/2zEi/58B/exk2+VFllnrmTa/kavukk8+fd7Iir4PAZtYrh8XVgcuA0u5eLa/Jx8w6A/cSrgh6wt33mMo1CCwl1axZ0LcvrFwZ7ib+299Cd5FIQdjdIHCZvW3o7ln1DcPb5JQAABvCSURBVM3saOBaoDVwG/B4foJy91eAV/KzD5GSoHnzUFBuwAC44IJQV+ixx8LAsUhhietGMDOrbWYjgReBmYTr9R9xd9U8FCkghxwSSksPHQpjxoQZx+bNizoqKcniuQx0POFT+iygLTAZ2N/MDjKzgwo3PJHkUqpUqB00dSqsWRPmHn766aijkpIqnjOAxrGvVxDuA8gEZsce6pAXKQQnnQRz50LTpnDWWaGmkKadlIIWzxhAahHEISI7OeywMAH9DTfALbeEekLPPRcKzYkUhHi6gFL38rqZWZ6vBBKR3StTJowJvPIKLF8OjRqF+QZECkI8XUB3mtnzZjbAzOqaWRUzq25m7czsJkKZiNqFHKdIUvvTn8JVQnXrhstFL7lE005K/sVzJ3Af4DrgOOAhYAZhIPg8YCHQzt3fKMwgRSRUPHj77TDn8AMPQKtWOddGE4lXXNVAE4VuBBMJXngBBg6E0qXDVUJdu0YdkSSyPFcD3WknJ5rZX2LdQQPMbEDBhSgi8erZE+bMCRWSu3WDq6/WtJOSe3EnADN7BrgLaEm4NLQxsEtGEZGiccwxoaro3/4Gt98O7drBdyqnKLmw18tAs8kg3AFcfPqMREq4cuXg0UehZcuQCNLT4dlnwxzEInuTmy6gecBhhRWIiOTdGWeE+wQqV4YOHeDf/4atW6OOShJdbhLAIcB8M3vdzCZvfxRWYCKSO3XqwIcfhmRwww3QuTNoEj3Zk9x0Ad1YWEGISMGoUAGeegpat4aLLoIGDUJhuZYto45MElHcZwDu/nZOj8IMTkRyzyzUDnr/fShfHtq2hbvuAo3eyc7iKQWx1sx+zeGx1sx+LYogRST30tMhMxP+/GcYPBhOPTVUGBXZLp47gSu6+/45PCq6+/5FEaSI5E2lSqF20H33wWuvhbmIP/oo6qgkUeTqRjARKX7MQu2gGTNg27YwHvDQQ+oSEiUAkaTRtGm4e/iUU8IA8emnw9q1UUclUVICEEkiBx8ML74It94auoYyMuDTT6OOSqKiBCCSZEqVCrWDpk0LZwBNm8KTT0YdlURBCUAkSbVpE+YYOPFEOOecUF10w4aoo5KipAQgksQOPRSmTIHrrgs3kDVtCgsXRh2VFBUlAJEkV7p0qB306qvw/fdhXGDs2KijkqKgBCAiAHTsGLqE0tLgtNPgwgvh99+jjkoKkxKAiGSpVg2mT4d//hMefhhatIDFi6OOSgqLEoCI7KBs2VA7aOJE+OqrcPfwZNX9LZGUAEQkR6eeGm4cO+aY8P3gwbB5c9RRSUFSAhCR3Tr6aJg5E/7+93BWcNJJsHx51FFJQVECEJE9Klcu1A4aPRo++STMMTBlStRRSUFQAhCRuJx2Wigvfdhh0KkTXH+9pp0s7pQARCRuxx0HH3wAZ50FN90ULh394Yeoo5K8UgIQkVxJSQm1g554At59N3QJvfNO1FFJXigBiEieDBwYzgYqVoR27eD228N8A1J8KAGISJ6lpYUZxnr1ChVGTz0Vfvop6qgkXkoAIpIv++8PY8bAgw/C66+HLqEPP4w6KomHEoCI5JtZqB307rthvoGWLeGBBzTtZKJTAhCRAtO4cbh7uFOnMA9xv37w669RRyW7owQgUlyNGgWpqeEjd2pqeJ4A2x54IEyaBHfcAS+8AI0ahRvI8t1ufkXZdqJy92LzaNSokYuIu48c6Z6S4h56WcIjJSUsT6BtZ8xwr1rVvVw59/+eO8u3lc9ju/mVn2MuAYBMz+E91bwYddJlZGR4ZmZm1GGIRC81FZYu3XV5jRqwZElCbbtyJfTvD1OnwgCe4mH+TgU2xLVtgcnPMZcAZjbb3TN2Wa4EIFIMlSqV8wir2d4vxo9g261b4eYyN/IvrqcO8xlPH2qzIP528ys/x1wC7C4BaAxApDiqXj13yyPetnRpuKHGCKbQgZVUoTEf8Synx99ufuXnmEswJQCR4mjo0FCTIbuUlLA8gbc9JWUWH9OAhsyhP89yQZnh/HbDrXvfNr/yE3dJltPAQKI+NAgsks3Ike41aribha+5GdCMeNvNlPGr9n/Ywb1hQ/evv45/F3mWn7iLOTQILCKJ5sUXQ2XRbdtCgbkePaKOqGTSGICIJJxu3cKNY7VqQc+eYTJ6TTtZdJQARCRSqakwYwZcfDHccw+0aQPffBN1VMlBCUBEIrfvvnD//TB2LMybFwrKvfZa1FGVfEoAIpIw+vYN004ecQR07gz/93+wZUvUUZVcSgAiklBq1YL334dzzglXabZvD99/H3VUJZMSgIgknPLl4b//hREjwqxj6ekwfXrUUZU8SgAikrDOOitMLnPAAXDyyXDLLUlRuaHIKAGISEKrVy9MO9m3LwwZAl26wI8/FnEQJbSUtBKAiCS8ihXh2WfhkUdg2jRo2BBmzSqixkeNgkGDQjVR9/B10KASkQSUAESkWDCD88+H996DMmWgdWu4994imHZyyBDYsGHHZRs2hOXFnBKAiBQrjRrB7NmhK+jyy6F3b/jll0JscNmy3C0vRpQARKTYOfBAmDAB7r4bJk8OXUIff1xIjZXgUtKRJAAz62Nmn5vZNjPbpUCRiMjemME//hEuD/39d2jeHB57rBC6hEpwKemozgDmAT2BdyJqX0RKiBYtwqf/tm3DGMGZZ8K6dQXYQP/+MHx4mD7SLHwdPjwsL+YiSQDu/oW7L4yibREpeSpXhldegZtugtGjoUkTmD+/ABvo3z/MHbxtW/haAt78QWMAIlJClCoVage98QasXg2NG8Mzz0QdVWIrtARgZlPNbF4Oj1NzuZ9BZpZpZpmrVq0qrHBFpIRo1w7mzoWMDBgwIFyyv3Fj1FElpjKFtWN3P6WA9jMcGA5hRrCC2KeIlGyHHw5vvgnXXw+33hruJB4/HmrWjDqyxKIuIBEpkcqUCbWDXnop3LzbsCE8/3zUUSWWqC4D7WFmy4HmwMtm9noUcYhIydelS7hKqE6dcNPYpZfCpk1RR5UYoroKaIK7V3P3fd39UHfvGEUcIpIcatSAd96BSy4JM4+1ahXOCpKduoBEJCnssw/cd18YC/jiizDt5MsvRx1VtJQARCSp9O4Nc+aESg5du8I11yTvtJNKACKSdGrWDOWkzzsPbrstTDbz3XdRR1X0lABEJCmVLx8qOjz9dJiIvkGDcOloMlECEJGkduaZYdrJgw8OE9DfdFPyTDupBCAiSa9u3ZAE/vKXcPPYn/4EyVB4QAlARATYb79QO+ixx+Dtt0OX0LvvFsCOE3g+YSUAEZEYs1A76L33YN99oU2bMOlMnucYSPD5hJUARER20rBhuFS0e3e44gro0QPWrMnDjhJ8PmElABGRHFSqFGoHDRsWbhhr1ChcLZQrCT6fsBKAiMhumMFll8GMGeFmsRYt4OGHc9EllODzCSsBiIjsRbNmoaDcySfDhReGq4XWro1jwwSfT1gJQEQkDgcfHEpL33ILjBsXZhz77LO9bJTg8wmb53l4u+hlZGR4Zq474URECtb06XD66fDLL6FL6Oyzo45oz8xstrtn7LxcZwAiIrnUtm3oEmrWDAYOhL/+ddeLfYoDJYBcKl26NOnp6dSrV49u3brx888/A7BkyRLMjOuuuy5r3R9//JGyZcty0UUXAbBw4ULatm1Leno6tWvXZtCgQQBMnz6dSpUqkZ6envWYOnVqvuJ0dy655BJq1qxJWloac+bMyXG9Tp06Ub9+ferWrcv555/P1q1bd3j9rrvuwsz48ccf99rm3Llzad68OXXr1iUtLY2xY8cWeLxjx44lLS2NunXrcuWVV2Ytv/zyy7N+drVq1eKAAw6Iu22RvDjssDAB/f/9HzzxREgGX34ZdVS55O7F5tGoUSOPWoUKFbK+HzBggN98883u7r548WI/+uijPT09Pev1hx9+2OvXr+8XXnihu7t36NDBJ06cmPX6p59+6u7ub731lnfp0qVA43z55Ze9U6dOvm3bNp81a5Y3adIkx/V++eUXd3fftm2b9+zZ00ePHp312rJly7xDhw5evXp1X7Vq1R7b27x5sy9cuNC//PJLd3f/9ttv/bDDDvM1a9YUWLw//vijH3nkkb5y5Up3Dz//qVOn7rLe/fff7wMHDoyrXZGC8Oqr7gcf7F6xovu4cVFHsysg03N4T9UZQD40b96cb7/9Nut5+fLlqV27NtvHKcaOHUvfvn2zXl+xYgXVqlXLen7CCScUWmyTJk1iwIABmBnNmjXj559/ZsWKFbust//++wOwZcsWNm3ahJllvXb55Zdzxx137LAsuxEjRtCnTx+6detGhw4dqFWrFsceeywAVatWpUqVKqyKs6BKPPEuWrSIWrVqUblyZQBOOeUUns9hktfRo0dz+umnx9WuSEHo1Cl0CdWrB337wsUXw++/Rx3V3ikB5NHWrVt588036d69+w7LTzvtNMaMGcPy5cspXbo0VatWzXrt8ssvp127dvzpT39i2LBhWd1HADNmzNihC+jrr7/epc1+/frtsM72x9NPP73Lut9++y1HHnlk1vNq1artkKyy69ixI1WqVKFixYr07t0bgMmTJ3PEEUdQv379Pf4cZs2axVNPPcW0adN2WP7hhx+yadMmjjnmmKxjzyn22267Le54a9asyYIFC1iyZAlbtmxh4sSJfPPNNzuss3TpUhYvXky7du32GLdIQTvyyFBD6B//gAcfDNNOLlkSdVR7VibqAIqbjRs3kp6ezpIlS2jUqBHt27ff4fVOnTpx3XXXceihh9KvX78dXhs4cCAdO3bktddeY9KkSTz22GN88sknALRq1YqXXnppj23ntk99Z7v7JP/666/z22+/0b9/f6ZNm0aLFi0YOnQoU6ZM2Ws77du356CDDtph2YoVKzjzzDN56qmnKFUqfMYYNmxYvuM98MADeeSRR+jXrx+lSpXixBNPZNGiRTusM2bMGHr37k3p0qX3GrtIQStbNtQOatkyDA43bBjmG+jaNerIcqYzgFwqX748c+fOZenSpWzatImHHnpoh9f32WcfGjVqxN13302vXr122b5q1aqcc845TJo0iTJlyjBv3ry4287NGUC1atV2+HS8fPnyHc5GdlauXDm6d+/OpEmT+Prrr1m8eDH169cnNTWV5cuX07BhQ77//vtdtqtQocIOz3/99Ve6dOnCzTffTLNmzbKW7+0MIN54u3XrxgcffMCsWbM47rjjsrqcthszZoy6fyRyPXrA7Nmh+Ge3bnDVVQk67WROAwOJ+ki0QeA5c+b4kUce6Zs2bfLFixd73bp13d193rx5PmLECHd3f/LJJ7MGgV999VXftGmTu7uvWLHCDzvsMF+xYkWhDAK/9NJLOwyqNm7ceJd11q5d69999527h0Hcvn37+gMPPLDLejVq1MgaBP7ggw/8zDPP3OXY3N1///13b9eunQ8bNqxQ4nV3/+GHH9zd/aeffvL69ev7woULs15bsGCB16hRw7dt25br9kUKw8aN7uef7w7urVq5L18eTRxoELjgNWjQgPr16zNmzJgdltetW5ezzjprl/WnTJlCvXr1qF+/Ph07duTOO+/ksMMOA3YdA3juuefyFVvnzp05+uijqVmzJueddx4PP/xw1mvp6ekArF+/nu7du5OWlkb9+vWpUqUK559//h73u2zZMsqXL5/ja+PGjeOdd95hxIgRWccxd+7cAosX4NJLL6VOnTq0aNGCq6++mlq1amW9Nnr0aE477bTddnWJFLVy5eCRR0L15zlzwhwD+bzCu0DpTmDJlcGDB3PmmWeSlpYWdSgixcoXX0CfPjB/PtxwQ7h/oKiGqnZ3J7ASgIhIEVm/Hv7+9zAw3L49jBwJVaoUfrsqBSEiErEKFWDECPjvf0OJ6QYNYObM6OJRAhARKUJmoXbQ+++HytBt28Kdd+Zj2sl8UAIQEYlA/frhUtEePeDKK+HUU/M47WQ+KAGIiERk//3D3AL33w+vvRZuHPvoo6JrXwlARCRCZqF20IwZsG1buIv4oYeKpktICUBEJAE0bRoKyrVvDxddBKedBr/+WrhtKgGIiCSIgw6CyZPhttvg+echIwM+/bTw2lMCEBFJIKVKhdpB06bBunXhzOCJJwqprcLZrYiI5Efr1qFLqEWLcNnouHEF34bKQYuIJKhDD4XXXw9nAD16FPz+lQBERBJY6dJw3nmFs291AYmIJCklABGRJKUEICKSpJQARESSlBKAiEiSUgIQEUlSSgAiIklKCUBEJEkpAYiIJCklABGRJKUEICKSpJQARESSlBKAiEiSUgIQEUlSSgAiIklKCUBEJEkpAYiIJCklABGRJKUEICKSpJQARESSlBKAiEiSUgIQEUlSSgAiIkkqkgRgZnea2QIz+9TMJpjZAVHEISKSzKI6A3gDqOfuacCXwDURxSEikrQiSQDuPsXdt8Sevg9UiyIOEZFklghjAOcAr0YdhIhIsilTWDs2s6nAYTm8NMTdJ8XWGQJsAUbtYT+DgEEA1atXL4RIRUSSU6ElAHc/ZU+vm9lZQFfgZHf3PexnODAcICMjY7friYhI7hRaAtgTM+sEXAW0cfcNUcQgIpLsohoDeBCoCLxhZnPN7NGI4hARSVqRnAG4e80o2hURkT8kwlVAIiISASUAEZEkpQQgIpKklABERJKUEoCISJJSAhARSVJKACIiSUoJQEQkSSkBiIgkKSUAEZEkpQQgIpKklABERJKUEoCISCIbNQpSU6FUqfB11G7nz8q1SKqBiohIHEaNgkGDYENs2pSlS8NzgP798717nQGIiCSqIUP+ePPfbsOGsLwAKAGIiCSqZctytzyXlABERBJV9eq5W55LSgAiIolq6FBISdlxWUpKWF4AlABERBJV//4wfDjUqAFm4evw4QUyAAy6CkhEJLH1719gb/g70xmAiEiSUgIQEUlSSgAiIklKCUBEJEkpAYiIJCklABGRJKUEICKSpJQARESSlBKAiEiSUgIQEUlS5u5RxxA3M1sFLM3j5ocAPxZgOFHSsSSeknIcoGNJVPk5lhruXnnnhcUqAeSHmWW6e0bUcRQEHUviKSnHATqWRFUYx6IuIBGRJKUEICKSpJIpAQyPOoACpGNJPCXlOEDHkqgK/FiSZgxARER2lExnACIikk2JSwBm1snMFprZV2Z2dQ6v72tmY2Ovf2BmqUUfZXziOJbWZjbHzLaYWe8oYoxHHMfxDzObb2afmtmbZlYjijjjEcexnG9mn5nZXDObaWZ1oogzHns7lmzr9TYzN7OEvJomjt/J2Wa2KvY7mWtm50YRZzzi+Z2YWd/Y/8vnZvZsvhp09xLzAEoDXwNHA/sAnwB1dlrn78Cjse9PA8ZGHXc+jiUVSAOeBnpHHXM+juMkICX2/QXF/Heyf7bvuwOvRR13Xo8ltl5F4B3gfSAj6rjz+Ds5G3gw6lgL6FiOBT4GDow9r5KfNkvaGUAT4Ct3X+Tum4AxwKk7rXMq8FTs++eAk83MijDGeO31WNx9ibt/CmyLIsA4xXMcb7n7htjT94FqRRxjvOI5ll+zPa0AJOogWzz/KwA3AXcAvxVlcLkQ73EUB/Ecy3nAQ+6+BsDdV+anwZKWAI4Avsn2fHlsWY7ruPsW4Bfg4CKJLnfiOZbiILfH8Vfg1UKNKO/iOhYzu9DMvia8cV5SRLHl1l6PxcwaAEe6+0tFGVguxfv31SvWxficmR1ZNKHlWjzHUguoZWbvmtn7ZtYpPw2WtASQ0yf5nT+BxbNOIiguce5N3MdhZmcAGcCdhRpR3sV1LO7+kLsfA1wF/F+hR5U3ezwWMysFDAP+WWQR5U08v5MXgVR3TwOm8kcPQKKJ51jKELqB2gKnA/81swPy2mBJSwDLgezZvRrw3e7WMbMyQCXgpyKJLnfiOZbiIK7jMLNTgCFAd3f/vYhiy63c/k7GAH8u1Ijybm/HUhGoB0w3syVAM2ByAg4E7/V34u6rs/1N/QdoVESx5Va871+T3H2zuy8GFhISQt5EPfBRwIMoZYBFwFH8MYhSd6d1LmTHQeBxUced12PJtu4IEncQOJ7fSQPC4NexUcdbAMdybLbvuwGZUced37+v2PrTScxB4Hh+J4dn+74H8H7UcefjWDoBT8W+P4TQZXRwntuM+qAL4YfYGfgy9oYyJLbs34RPlgDlgPHAV8CHwNFRx5yPY2lM+ESwHlgNfB51zHk8jqnAD8Dc2GNy1DHn41juAz6PHcdbe3pTjfqxt2PZad2ETABx/k5ujf1OPon9To6POuZ8HIsB9wDzgc+A0/LTnu4EFhFJUiVtDEBEROKkBCAikqSUAEREkpQSgIhIklICEBFJUkoAIiJJSglAihUzOzhbWd/vzezb2Pc/m9n83Wzz79idxrvb59lm9mDhRb3bdi8zswGFsN+uZvavgt6vlDy6D0CKLTO7EVjn7nfF5nV4yd3r5WE/ZxNucrqoQAPcc5tlgDlAQw9FCQty3xbbdwv/o8qqyC50BiAlSWkz+09soowpZlYewMxGbJ8wx8wam9l7ZvaJmX1oZhWz78DMupjZLDM7JLbd/bH1F2WfdMfMBpvZR7EKk/+KLatgZi/H9j3PzPrFlt+WbcKbu2K7aAfM2f7mb2bTzWyYmb1jZl/E4nzBzP5nZjfH1kk1swVm9t/Y/keZ2SmxypD/M7MmAB4+1U0Huhbiz1pKgDJRByBSgI4FTnf388xsHNALGLn9RTPbBxgL9HP3j8xsf2Bjttd7AP8AOrv7mtg0EYcDLYHjgcnAc2bWIdZWE8Kt+ZPNrDVQGfjO3bvE9lfJzA4i1J853t09W+XGFsDsneLf5O6tzexSYBKhaNlPwNdmNiy2Tk2gDzAI+Aj4Syy+7sC1/FF8LhNoBYzLw89RkoTOAKQkWezuc2PfzybMmJbdccAKd/8IwuQt2bpfTiKUb+7isck2Yia6+zZ3nw8cGlvWIfb4mNDVcjwhIXwGnGJmt5tZK3f/BfiVMJnKf82sJ7C9S+ZwYNVO8U2Off2MUNdphYcqlov4o0rkYnf/zN23EerbvBn7xP/ZTse7Eqi6h5+ViBKAlCjZy0hvZdczXGP3cyosIpRArrWHfVq2r7e6e3rsUdPdH3f3Lwmf2j8DbjWz62MJpgnwPOHT+WuxfWwkFCbMqa1tO7W7Ldux7Lz89xzWIbbvjYjsgRKAJJMFQFUzawxgZhVjg7EAS4GewNNmVncv+3kdOMfM9ovt5wgzq2JmVYEN7j4SuAtoGFunkru/AlwGpMf28QWhO6ew1ALmFeL+pQTQGIAkDXffFBuYfSA2QLwROCXb6wvNrD8w3sy67WE/U8ysNjArNk6wDjiD8IZ+p5ltAzYTJrivCEwys3KEM4fLY7t5FXimoI8xm5OAawpx/1IC6DJQkYiY2QTgSnf/XwHv91DgWXc/uSD3KyWPEoBIRMzsOOBQd3+ngPfbGNicbUBcJEdKACIiSUqDwCIiSUoJQEQkSSkBiIgkKSUAEZEkpQQgIpKk/h+FaU5dOTmb+QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n3=20\n",
    "x3=0.03*df3['n']\n",
    "y3=np.log(df3['N [s-1]'])\n",
    "z3=np.polyfit(x3, y3, 1) # second order  fit y=a+bx\n",
    "p3=np.poly1d(z3)  #  [c,b,a]\n",
    "ey3=p3(x3) #expected value\n",
    "A2=\"{:.3}\".format(p3[0])\n",
    "B2=\"{:.3}\".format(-p3[1])\n",
    "\n",
    "\n",
    "RMSE3=np.sqrt(np.sum((y3-ey3)**2)/n3)\n",
    "R_square3=1-(np.sum(np.sum(np.sum((y3-ey3)**2))/np.sum((y3-np.mean(y2))**2)))\n",
    "rmse3=\"{:.2}\".format(RMSE3)\n",
    "r23=\"{:.2}\".format(R_square3)\n",
    "\n",
    "\n",
    "plt.figure(figsize = [6,6])\n",
    "plt.plot(x3, y3, 'ro',label='observed')\n",
    "plt.plot(x3, ey3, 'b-',label='fitted, A= '+str(A2)+', B='+str(B2))\n",
    "plt.xlabel('Thickness(mm)')\n",
    "plt.ylabel('ln(N)')\n",
    "plt.figtext(0.2, 0.3, 'RMSE = '+str(rmse3)+',r2='+str(r23))\n",
    "plt.legend()\n",
    "plt.title('Fitted curve')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "absorption coefficient =5.695 /mm\n"
     ]
    }
   ],
   "source": [
    "print('absorption coefficient =%0.3f /mm'%-p3[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mass absorption coefficient =21.091 sq.cm/gm\n"
     ]
    }
   ],
   "source": [
    "density=2.7 # in cgs\n",
    "mu_m=-10*p3[1]/density # in cgs\n",
    "print('mass absorption coefficient =%0.3f sq.cm/gm'%mu_m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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