exploitation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TP Réfraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Consignes:**\n",
    "* Modifier le code ci-dessous en ajoutant les valeurs relevées au bon endroit\n",
    "* Modifier le code afin d'indiquer ce qui est en abscisses et ce qui est en ordonnées sur vos courbes\n",
    "* Exécuter les différentes cellules (cliquer dedans puis faire ctrl+entree ou cliquez sur le bouton \"exécuter\" dans la barred 'outils en haut) afin d'afficher votre courbe et les modèles proposés\n",
    "* Ajouter vos commentaires et réponses (une cellule de texte peut être verrouillée en l'exécutant comme une cellule de code avec ctrl + entrée et déverrouillée en double cliquant dessus) Vous avez la possibilité d'ajouter des cellules de code ou de texte avec le bouton \"+\" de la barre d'outils.\n",
    "* Sauvegarder votre document régulièrement (ctrl + s ou cliquez sur l'icone en forme de disquette)\n",
    "* Télécharger le résultat (bouton \"download\" de la barre d'outils)\n",
    "* Déposer le document téléchargé sur moodle pour correction et conserver une copie comme compte rendu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indiquer votre NOM ici"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indiquer votre Prénom ici"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Utiliser votre cours ou vos souvenirs et rappeler la première loi de Snell-Descartes ci-dessous."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Répondre à la question 1 ici"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. A quoi correspond le plan d’incidence dans la vidéo présentée ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Répondre à la question 2 ici"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans le passé, plusieurs savants ont proposé un modèle mathématique de la réfraction à partir de leurs propres mesures. Le tableau ci-dessous en présente trois.\n",
    "\n",
    "| Grosseteste ($XIII^e$ Siècle) | Kepler ($XVII^e$ siècle) | Snell-Descartes ($XVII^e$ siècle) |\n",
    "| :---: | :---: | :---: |\n",
    "| $i_2$ est égal à la moitié de $i_1$: $$ \\ $$ $$i_2 = \\frac{i_1}{2}$$ | $i_1$ est proportionnel à $i_2$ mais seulement pour de faibles valeurs d'angles: $$ \\ $$ $$i_1 = k \\times i_2$$ | $sin(i_1)$ est proportionnel à $sin(i_2)$: $$ \\ $$ $$sin(i_1) = n \\times sin(i_2)$$ |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Bibliothèques nécessaires\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit\n",
    "from math import pi, sin, asin\n",
    "\n",
    "# Liste de valeurs expérimentales:\n",
    "i1 = [30.2, 30.4, 30.5, 30.8, 30.9 ] # remplacer les valeurs par vos mesures \n",
    "                                     # vous pouvez en rajouter au besoin en les séparants par des virgules\n",
    "i2 = [10.1 ,10.2 ,10.3 ,10.4 ,10.5 ] # remplacer les valeurs par vos mesures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "def modele1(x):\n",
    "    return 0.5*x\n",
    "\n",
    "ymodele = []\n",
    "for val in i1:\n",
    "    ymodele.append(modele1(val))\n",
    "\n",
    "plt.plot(i1, i2, \"+\",label=\"Données expérimentales\")\n",
    "plt.plot(i1, ymodele,label=\"Modèle\")\n",
    "plt.title(\"Modele de Grosseteste\")\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.xlim([0,90])\n",
    "plt.ylim([0,90])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k =  2.966770332950573\n"
     ]
    }
   ],
   "source": [
    "def modele2(x, k):\n",
    "    return k*x\n",
    "\n",
    "params, cov = curve_fit(modele2,i2,i1)\n",
    "k = params[0]\n",
    "\n",
    "ymodele2 = []\n",
    "for val in i2:\n",
    "    ymodele2.append(modele2(val,k))\n",
    "\n",
    "plt.plot(i2, i1, \"+\",label=\"Données expérimentales\")\n",
    "plt.plot(i2, ymodele2,label=\"Modèle\")\n",
    "plt.title(\"Modele de Kepler\")\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.xlim([0,90])\n",
    "plt.ylim([0,90])\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print(\"k = \",k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEWCAYAAAB42tAoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAfJ0lEQVR4nO3dfXhU5bnv8e9NgKIU0Uo82xIguHcQAiQg4U1EKQgisuEUQUl1K6CitGjVFl+OukGsrRW1FcUinlYUBAS1NFfRI9QtKigewlE5vCgC8hLUEiKoyGvk3n/MECYhWQkhKzNJfp/rynXNWuuZZ+55GOY3az1r1pi7IyIiUpZ68S5AREQSm4JCREQCKShERCSQgkJERAIpKEREJJCCQkREAikopFYys1QzczOrX4G2o8xsWRU97iQzm10VfVUVM1tqZtfHuw6puRQUEndmtsXMDplZsxLrP4i+2afGp7LqFR2Hi2OWR5rZbjO7KJ51iSgoJFF8BmQfXTCzjsCp8SsnvszsWmAacJm7vxWnGsrdG5O6QUEhiWIWcE3M8rXA87ENzKypmT1vZvlmttXM7jWzetFtSWb2iJntMrPNwGWl3PfPZvaFme0ws9+YWVJphZhZWzNbYmZfmdknZnZFWUWbWWsze8vMvjWzJUDJvaIeZvaume0xs4/MrE95A2FmNwKPApe4+7vl1R89dLbczJ40s6/N7GMz6xfQ/xgzWx/dW3ndzFrFbHMz+4WZfQp8Wl6tUjcoKCRRrABOM7N20TfAkUDJY/1PAE2Bc4CLiATL6Oi2G4DBQGcgCxhe4r4zgULg36JtBgDHHbc3s8bAEmAOcFa0jqfMLL2MuucAq4gExANEAu5oX82BRcBvgB8BvwZeNrPksoeBccBkoJ+7555A/d2BTdE6JgKvmNmPSnl+Q4H/BQwDkoF3gLklmv3PaH9lPWepa9xdf/qL6x+wBbgYuBf4HTCQyJt1fcCBVCAJOASkx9zvRmBp9PZ/ATfFbBsQvW994H8AB4FTYrZnA29Gb48ClkVvXwm8U6K+p4GJpdTdksibd+OYdXOA2dHbdwKzStzndeDagHH4BvgbUC9mfUXq/xywmO3/F/iP6O2lwPXR268B18W0qwfsA1pFlx3oG+/XhP4S60/HICWRzALeBlpT4rATkU/KDYCtMeu2As2jt38MbC+x7ahW0ft+YWZH19Ur0T62bXcz2xOzrn60tpJ+DOx29+9KPG6LmL5GmNm/x2xvALxZSl9HjSMSmP/bzK5zd69g/TuibWPr+HEZz+9xM3s0Zp0RGcejY1bauEgdpqCQhOHuW83sM2AQcF2JzbuAw0Te6NZF17UEdkRvf8GxN+ij247aTuQTeTN3LyynjO3AW+7evwIlfwGcYWaNY8KiJZFP5Uf7muXuN1Sgr6P+CfQD3gKeIhIcFam/uZlZTFi0BHJKabcdeNDdXwioQZeUlmI0RyGJ5joihz5iP6Xj7t8D84EHzaxJdAL2do7NY8wHbjGzFDM7A7gr5r5fAIuBR83sNDOrZ2b/WsZpp38H2pjZf5hZg+hfVzNrV7Khu28FcoH7zayhmV0AxO49zAb+3cwuiU62NzKzPmaWEjQA7v45kbAYaGZ/qGD9Z0WffwMzGwG0A14tpfvpwN1m1h6KJslHBNUjoqCQhOLum7z4JG6sm4HvgM3AMiLzAX+JbnuGyPH/j4D/B7xS4r7XAA2J7I3sBl4Czi7l8b8lMr8xkshx/y+B3wM/KKOmnxGZ+P2KyCRy0SEzd98OHJ08zifyaX4CFfh/5+7bgL7AcDP7XQXqfx9II7Ln9SAw3N0LSun3r9HnM8/MvgHWAJeWV4/UbVb8sKaI1DRmNorIZPUF8a5FaiftUYiISKDQgsLM/mJmO81sTRnbzcymmtlGM1ttZueFVYuIiFRemHsUM4mcD1+WS4kcU00DxgJ/CrEWkVrL3WfqsJOEKbSgcPe3iUzwlWUo8LxHrABON7PjJhdFRCS+4vk9iuYU/2JPXnTdFyUbmtlYInsdNG7cuEvbtm2rpUARkdpi1apVu9w96PIxZaoRX7hz9xnADICsrCzPzS3r7EkRESmNmW0tv1Xp4nnW0w6Kf5M2hWPfshURkQQRz6DIAa6Jnv3UA/g6+g1UERFJIKEdejKzuUAfoJmZ5RH51moDAHefTuTyAoOAjUSuXjm69J5ERCSeQgsKd88uZ7sDvwjr8UXi5fDhw+Tl5XHgwIF4lyJ1UKNGjUhJSaFBgwZV1meNmMwWqUny8vJo0qQJqampxFwWXCR07k5BQQF5eXm0bt26yvrVJTxEqtiBAwc488wzFRJS7cyMM888s8r3ZhUUIiFQSEi8hPHaU1CIiEggBYWInLTCwkKefPJJDh48GO9SjvP5558za1Zpv2QrFaWgEEkQf1iyocr6SkpKolOnTrRv357MzEweffRRjhw5UmX9x3J3br31VjIyMvjBD8r6faf42LNnD7fffjv9+vUrs8306dN5/vmSP9FetRYuXMi6devKbTdp0iQeeeSRUGupDJ31JJIgHn/jU27r36ZK+jrllFP48MMPAdi5cyc/+9nP+Oabb7j//vurpP9YZsaTTz5Z5f1WhdNPP5158+aVub2wsJCbbrop9DoWLlzI4MGDSU9PD/2xwqA9CpFa7qyzzmLGjBk8+eSTuDsHDhxg9OjRdOzYkc6dO/Pmm28CMHPmTIYNG8bAgQNJS0vjjjvuKOrjhz/8Iffccw+ZmZn06NGDf/7znwDk5+dz+eWX07VrV7p27cry5csB+O677xgzZgzdunWjc+fO/O1vfwNg7dq1dOvWjU6dOpGRkcGnn356XL2LFy+mZ8+enHfeeYwYMYK9e/eydetW0tLS2LVrF0eOHKF3794sXryYLVu20LZtW6666iratWvH8OHD2bdvHwCrVq3ioosuokuXLlxyySV88UXkwg99+vTh1ltvJSsri8cff7zYp/g+ffpw2223kZWVRbt27Vi5ciXDhg0jLS2Ne++9t6jG2bNnFz2PG2+8ke+//77McXr33XfJyclhwoQJdOrUiU2bNvHMM8/QtWtXMjMzufzyy4tqjrVp0yYGDhxIly5d6N27Nx9//DEACxYsoEOHDmRmZnLhhReexCvjBLh7jfrr0qWLiySydevWVbjtY4s/8VZ3/v24v8cWf3JSNTRu3Pi4dU2bNvUvv/zSH3nkER89erS7u69fv95btGjh+/fv92effdZbt27te/bs8f3793vLli1927Zt7u4OeE5Ojru7T5gwwR944AF3d8/OzvZ33nnH3d23bt3qbdu2dXf3u+++22fNmuXu7rt37/a0tDTfu3evjx8/3mfPnu3u7gcPHvR9+/YVqzE/P9979+7te/fudXf3hx56yO+//353d3/mmWd8+PDh/vDDD/vYsWPd3f2zzz5zwJctW+bu7qNHj/YpU6b4oUOHvGfPnr5z5053d583b17Rc77ooot83LhxRY85ceJEnzJlStG2O+64w93d//jHP/rZZ5/tn3/+uR84cMCbN2/uu3bt8nXr1vngwYP90KFD7u4+btw4f+655wLH6dprr/UFCxYUPeauXbuKbt9zzz0+derU42rp27evb9iwwd3dV6xY4T/5yU/c3b1Dhw6el5dXNLalKe01COR6Jd93dehJJI5u69+m6HBT6l2L2PLQZaE/5rJly7j55psBaNu2La1atWLDhsj8SL9+/WjatCkA6enpbN26lRYtWtCwYUMGDx4MQJcuXViyZAkA//jHP4ode//mm2/Yu3cvixcvJicnp+iT+oEDB9i2bRs9e/bkwQcfJC8vr+iTeqwVK1awbt06evXqBcChQ4fo2bMnANdffz0LFixg+vTpRYfVAFq0aFHU/uqrr2bq1KkMHDiQNWvW0L9/fwC+//57zj772M/dXHnllWWOz5AhQwDo2LEj7du3L7rfOeecw/bt21m2bBmrVq2ia9euAOzfv5+zzjoLoMxxKmnNmjXce++97Nmzh71793LJJZcU2753717effddRowYUbTu6IkCvXr1YtSoUVxxxRUMGzaszOdRlRQUInXA5s2bSUpKKnpDK0vsZHRSUhKFhYUANGjQoOj8/Nj1R44cYcWKFTRq1KhYP+7Oyy+/zLnnnltsfbt27ejevTuLFi1i0KBBPP300/Tt27fY/fr378/cuXOPq23fvn3k5eUBkTfSJk2aAMd/b8DMcHfat2/Pe++9V+rzbNy4cbljUK9evWLjUa9ePQoLC3F3rr32Wn73u98dd9+yxqmkUaNGsXDhQjIzM5k5cyZLly4ttv3IkSOcfvrpxQLxqOnTp/P++++zaNEiunTpwqpVqzjzzDPLfD5VQXMUIgnil/3Sym9UCfn5+dx0002MHz8eM6N379688MILAGzYsIFt27Yd94ZeUQMGDOCJJ54oWj76xnbJJZfwxBNPEDniAR988AEQCaxzzjmHW265haFDh7J69epi/fXo0YPly5ezceNGIDLXcXRv58477+Sqq65i8uTJ3HDDDUX32bZtW1EgzJkzhwsuuIBzzz2X/Pz8ovWHDx9m7dq1lXqOJfXr14+XXnqJnTt3AvDVV1+xdWvwTz00adKEb7/9tmj522+/5eyzz+bw4cNF/xaxTjvtNFq3bs2CBQuASIB+9NFHQGTuonv37kyePJnk5GS2b99+3P2rmoJCJEFU1RlPEDkccvT02IsvvpgBAwYwceJEAH7+859z5MgROnbsyJVXXsnMmTMrfVrr1KlTyc3NJSMjg/T0dKZPnw7Afffdx+HDh8nIyKB9+/bcd999AMyfP58OHTrQqVMn1qxZwzXXXFOsv+TkZGbOnEl2djYZGRn07NmTjz/+mLfeeouVK1cWhUXDhg159tlnATj33HOZNm0a7dq1Y/fu3YwbN46GDRvy0ksvceedd5KZmUmnTp149913KzucxaSnp/Ob3/yGAQMGkJGRQf/+/YsmyssycuRIpkyZQufOndm0aRMPPPAA3bt3p1evXpT1i50vvPACf/7zn8nMzKR9+/ZFJwRMmDCBjh070qFDB84//3wyMzOr5HkFsaOJX1PoF+4k0a1fv5527drFu4w6YcuWLQwePJg1a9bEu5SEUtpr0MxWuXtWZfrTHoWIiARSUIhIjZWamqq9iWqgoBARkUAKChERCaSgEBGRQAoKEamQDRs2FJ2iKXWLgkKkFjIzrr766qLlwsJCkpOTiy4vUVGpqans2rULgDZt2vDBBx/w17/+tcw2UjvpEh4itVDjxo1Zs2YN+/fv55RTTmHJkiU0b978pPudNGnSyRcnNY6CQiRMr90FX/7/qu3zXzrCpQ+V22zQoEEsWrSI4cOHM3fuXLKzs3nnnXeAyGUnxowZw+bNmzn11FOZMWMGGRkZFBQUkJ2dzY4dO+jZsyexX8idPXs2U6dO5eDBg/To0YOnnnqKpKSkYo95tM2hQ4fo3r17qW2k5tGhJ5FaauTIkcybN48DBw6wevVqunfvXrRt4sSJdO7cmdWrV/Pb3/626FIa999/PxdccAFr167lpz/9Kdu2bQMi3/SdN28ey5cvL7rm0OzZs4s93vr163nxxRdZvnw5H374IUlJSaVex0hqHu1RiISpAp/8w5KRkcGWLVuYO3cugwYNKrZt2bJlvPzyywD07duXgoICvvnmG95++21eeeUVAC677DLOOOMMAN544w3Wr19fdNnuvXv30qJFi2J9vvHGG2VefltqNgWFSC02ZMgQfv3rX7N06VIKCgoq3Y+7M2LECB56qOzgC7r8ttRsOvQkUouNGTOGiRMn0rFjx2LrYy81vnTpUpo1a8Zpp53GhRdeyJw5cwB47bXX2L17NxC5tPbLL79cdGntgoICtmzZUqzPylx+W2oG7VGI1GIpKSnccsstx62fNGkSY8aMISMjg1NPPZXnnnsOiMxdZGdn0759e84//3xatmwJFL+09pEjR2jQoAHTpk0jNTW1qM+y2rRq1apanquER5cZF6liusy4xJsuMy4iItVKQSEiIoEUFCIhqGmHdKX2COO1p6AQqWKNGjWioKBAYSHVzt0pKCigUaNGVdqvznoSqWIpKSnk5eWRn58f71KkDmrUqBEpKSlV2qeCQqSKNWjQgNatW8e7DJEqE+qhJzMbaGafmNlGM7urlO0tzexNM/vAzFab2aDS+hERkfgJLSjMLAmYBlwKpAPZZpZeotm9wHx37wyMBJ4Kqx4REamcMPcougEb3X2zux8C5gFDS7Rx4LTo7abA5yHWIyIilRBmUDQHtscs50XXxZoEXG1mecCrwM2ldWRmY80s18xyNUEoIlK94n16bDYw091TgEHALDM7riZ3n+HuWe6elZycXO1FiojUZWEGxQ4g9oL1KdF1sa4D5gO4+3tAI6BZiDWJiMgJCjMoVgJpZtbazBoSmazOKdFmG9APwMzaEQkKHVsSEUkgoQWFuxcC44HXgfVEzm5aa2aTzWxItNmvgBvM7CNgLjDK9XVWEZGEEuoX7tz9VSKT1LHr/jPm9jqgV5g1iIjIyYn3ZLaIiCQ4BYWIiARSUIiISCAFhYiIBFJQiIhIIAWFiIgEUlCIiEggBYWIiARSUIiISCAFhYiIBFJQiIhIIAWFiIgEUlCIiEggBYWIiARSUIiISCAFhYiIBFJQiIhIIAWFiIgEUlCIiEggBYWIiARSUIiISCAFhYiIBFJQiIhIIAWFiIgEUlCIiEggBYWIiARSUIiISCAFhYiIBFJQiIhIIAWFiIgEUlCIiEggBYWIiARSUIiISCAFhYiIBAo1KMxsoJl9YmYbzeyuMtpcYWbrzGytmc0Jsx4RETlx9cPq2MySgGlAfyAPWGlmOe6+LqZNGnA30Mvdd5vZWWHVIyIilRPmHkU3YKO7b3b3Q8A8YGiJNjcA09x9N4C77wyxHhERqYQwg6I5sD1mOS+6LlYboI2ZLTezFWY2sLSOzGysmeWaWW5+fn5I5YqISGniPZldH0gD+gDZwDNmdnrJRu4+w92z3D0rOTm5mksUEanbwgyKHUCLmOWU6LpYeUCOux9298+ADUSCQ0REEkSYQbESSDOz1mbWEBgJ5JRos5DI3gRm1ozIoajNIdYkIiInKLSgcPdCYDzwOrAemO/ua81sspkNiTZ7HSgws3XAm8AEdy8IqyYRETlx5u7xruGEZGVleW5ubrzLEBGpUcxslbtnVea+8Z7MFhGRBKegEBGRQAoKEREJpKAQEZFACgoREQmkoBARkUAKChERCaSgEBGRQAoKEREJpKAQEZFACooa4Mqn34t3CSJSh4X2U6hSNZbMepie29fD910hSf9cIlL99M6TwEb96R88+uVUGlsLqJcU73JEpI5SUCSoK59+j147ZnFm/W95qDCb1Xe/CkD31j/ixRt7xrk6EalLypyjMLNXzSy1+kqRo/6wZAObP9vE9Umv8ffve7Da/xWAX/ZLU0iISLUL2qN4FlhsZs8BD7v74WqqqU678un3eP+zr3iw/is0oJAphVcAkT2J2/q3iXN1IlIXlRkU7r7AzF4D7gNyzWwWcCRm+2PVUF+d8+KNPWH/bvjDWGbu68dW/xcdbhKRuCrv9NhDwHfAD4AmJf4kLKecAb94n8cLh+lwk4jEXZl7FGY2EHgMyAHOc/d91VaVQNMU2rRO1eEmEYm7oDmKe4AR7r62uoqR4rQnISKJIGiOond1FiIiIolJl/AQEZFACgoREQmkoBARkUAKChERCaSgEBGRQAoKEREJpKAQEZFACgoREQmkoBARkUAKChERCaSgEBGRQAoKEREJpKAQEZFACgoREQkUalCY2UAz+8TMNprZXQHtLjczN7OsMOsREZETF1pQmFkSMA24FEgHss0svZR2TYBfAu+HVYuIiFRemHsU3YCN7r7Z3Q8B84ChpbR7APg9cCDEWkREpJLCDIrmwPaY5bzouiJmdh7Qwt0XBXVkZmPNLNfMcvPz86u+UhERKVPcJrPNrB7wGPCr8tq6+wx3z3L3rOTk5PCLExGRImEGxQ6gRcxySnTdUU2ADsBSM9sC9AByNKEtIpJYwgyKlUCambU2s4bASCDn6EZ3/9rdm7l7qrunAiuAIe6eG2JNIiJygkILCncvBMYDrwPrgfnuvtbMJpvZkLAeV0REqlb9MDt391eBV0us+88y2vYJsxYREakcfTNbREQCKShERCSQgkJERAIpKEREJJCCQkREAikoREQkkIJCREQCKShERCSQgkJERAIpKEREJJCCQkREAikoREQkkIJCREQCKShERCSQgkJERAIpKEREJJCCQkREAikoREQkkIJCREQCKShERCSQgkJERAIpKEREJJCCQkREAikoREQkkIJCREQCKShERCSQgkJERAIpKEREJJCCQkREAikoREQkkIJCREQCKShERCSQgkJERAIpKEREJFCoQWFmA83sEzPbaGZ3lbL9djNbZ2arzewNM2sVZj0iInLiQgsKM0sCpgGXAulAtpmll2j2AZDl7hnAS8DDYdUjIiKVE+YeRTdgo7tvdvdDwDxgaGwDd3/T3fdFF1cAKSHWIyIilRBmUDQHtscs50XXleU64LXSNpjZWDPLNbPc/Pz8KixRRETKkxCT2WZ2NZAFTCltu7vPcPcsd89KTk6u3uJEROq4+iH2vQNoEbOcEl1XjJldDNwDXOTuB0OsR0REKiHMPYqVQJqZtTazhsBIICe2gZl1Bp4Ghrj7zhBrERGRSgotKNy9EBgPvA6sB+a7+1ozm2xmQ6LNpgA/BBaY2YdmllNGdyIiEidhHnrC3V8FXi2x7j9jbl8c5uOLiMjJS4jJbBERSVwKChERCaSgEBGRQAoKEREJpKAQEZFACgoREQmkoBARkUAKChERCaSgEBGRQAoKEREJpKAQEZFACgoREQmkoBARkUAKChERCaSgEBGRQAoKEREJpKAQEZFACgoREQmkoBARkUAKChERCaSgEBGRQAoKEREJpKAQEZFACgoREQmkoBARkUAKChERCaSgEBGRQAoKEREJpKAQEZFACgoREQmkoBARkUAKChERCaSgEBGRQAoKEREJpKAQEZFAoQaFmQ00s0/MbKOZ3VXK9h+Y2YvR7e+bWWqY9YiIyIkLLSjMLAmYBlwKpAPZZpZeotl1wG53/zfgD8Dvw6pHREQqJ8w9im7ARnff7O6HgHnA0BJthgLPRW+/BPQzMwuxJhEROUH1Q+y7ObA9ZjkP6F5WG3cvNLOvgTOBXbGNzGwsMDa6eNDM1oRScc3TjBJjVYdpLI7RWByjsTjm3MreMcygqDLuPgOYAWBmue6eFeeSEoLG4hiNxTEai2M0FseYWW5l7xvmoacdQIuY5ZToulLbmFl9oClQEGJNIiJygsIMipVAmpm1NrOGwEggp0SbHODa6O3hwH+5u4dYk4iInKDQDj1F5xzGA68DScBf3H2tmU0Gct09B/gzMMvMNgJfEQmT8swIq+YaSGNxjMbiGI3FMRqLYyo9FqYP8CIiEkTfzBYRkUAKChERCZSwQaHLfxxTgbG43czWmdlqM3vDzFrFo87qUN5YxLS73MzczGrtqZEVGQszuyL62lhrZnOqu8bqUoH/Iy3N7E0z+yD6/2RQPOoMm5n9xcx2lvVdM4uYGh2n1WZ2XoU6dveE+yMy+b0JOAdoCHwEpJdo83NgevT2SODFeNcdx7H4CXBq9Pa4ujwW0XZNgLeBFUBWvOuO4+siDfgAOCO6fFa8647jWMwAxkVvpwNb4l13SGNxIXAesKaM7YOA1wADegDvV6TfRN2j0OU/jil3LNz9TXffF11cQeQ7K7VRRV4XAA8QuW7YgeosrppVZCxuAKa5+24Ad99ZzTVWl4qMhQOnRW83BT6vxvqqjbu/TeQM0rIMBZ73iBXA6WZ2dnn9JmpQlHb5j+ZltXH3QuDo5T9qm4qMRazriHxiqI3KHYvornQLd19UnYXFQUVeF22ANma23MxWmNnAaquuelVkLCYBV5tZHvAqcHP1lJZwTvT9BKghl/CQijGzq4Es4KJ41xIPZlYPeAwYFedSEkV9Ioef+hDZy3zbzDq6+564VhUf2cBMd3/UzHoS+f5WB3c/Eu/CaoJE3aPQ5T+OqchYYGYXA/cAQ9z9YDXVVt3KG4smQAdgqZltIXIMNqeWTmhX5HWRB+S4+2F3/wzYQCQ4apuKjMV1wHwAd38PaETkgoF1TYXeT0pK1KDQ5T+OKXcszKwz8DSRkKitx6GhnLFw96/dvZm7p7p7KpH5miHuXumLoSWwivwfWUhkbwIza0bkUNTm6iyymlRkLLYB/QDMrB2RoMiv1ioTQw5wTfTspx7A1+7+RXl3SshDTx7e5T9qnAqOxRTgh8CC6Hz+NncfEreiQ1LBsagTKjgWrwMDzGwd8D0wwd1r3V53BcfiV8AzZnYbkYntUbXxg6WZzSXy4aBZdD5mItAAwN2nE5mfGQRsBPYBoyvUby0cKxERqUKJeuhJREQShIJCREQCKShERCSQgkJERAIpKEREJJCCQuQkmFkLM/vMzH4UXT4jupwa38pEqo6CQuQkuPt24E/AQ9FVDwEz3H1L3IoSqWL6HoXISTKzBsAq4C9Ertjayd0Px7cqkaqTkN/MFqlJ3P2wmU0A/g8wQCEhtY0OPYlUjUuBL4hclFCkVlFQiJwkM+sE9CdytdrbKvJDMCI1iYJC5CREf1XxT8Ct7r6NyAUaH4lvVSJVS0EhcnJuIHK13iXR5aeAdmZWJ388SmonnfUkIiKBtEchIiKBFBQiIhJIQSEiIoEUFCIiEkhBISIigRQUIiISSEEhIiKB/huP3Ur8n9rGSwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n =  2.8433370530484465\n"
     ]
    }
   ],
   "source": [
    "def modele3(x, n):\n",
    "    return n*x\n",
    "\n",
    "sini1 = []\n",
    "sini2 = []\n",
    "for i in range(len(i1)):\n",
    "    sini1.append(sin(i1[i]*pi/180)) # angles en radian\n",
    "    sini2.append(sin(i2[i]*pi/180)) # angles en radian\n",
    "    \n",
    "params, cov = curve_fit(modele3,sini2,sini1)\n",
    "n = params[0]\n",
    "\n",
    "ymodele3 = []\n",
    "for val in sini2:\n",
    "    ymodele3.append(modele3(val,n))\n",
    "\n",
    "plt.plot(sini2, sini1, \"+\",label=\"Données expérimentales\")\n",
    "plt.plot(sini2, ymodele3,label=\"Modèle\")\n",
    "plt.title(\"Modele de Snell-Descartes\")\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.xlim([0,1])\n",
    "plt.ylim([0,1])\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print(\"n = \",n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Quel modèle vous semble le plus adapté aux valeurs relevées ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Répondre à la question 3 ici"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. L'indice de réfraction est une caractéristique des matériaux. Elle est liée à la vitesse de propagation de la lumière dans le milieu considéré. On sait que pour le plexiglas, elle est de 1,42 de 1,33 pour l'eau et 1,6 pour le verre. Indiquer si vous avez utilisé la simulation ou si vous étiez en salle de TP puis préciser en justifiant le matériau correspondant à votre expérience."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Répondre à la question 4 ici"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5. Utiliser maintenant le modèle obtenu afin de prévoir la valeur de l’angle de réfraction $i_2$ que l’on obtiendrait pour un angle d'incidence $i_1$ = 30°. Vérifier ensuite expérimentalement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Valeur attendue pour l'angle $i_2$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Valeur obtenue lors de la vérification expérimentale $i_2$ = "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conclusion:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons maintenant observer ce qui se passe lorsque le rayon lumineux passe du plexiglas à l'air. Vous pouvez cliquer sur le lien ci-contre afin de passer à la <a href = '../apps/refraction3.ipynb'> manipulation suivante </a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6. Utiliser votre cours ou vos souvenirs et indiquer les conditions expérimentales nécessaires pour observer une réflexion totale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Répondre à la question 6 ici"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7. Quelle valeur d'angle limite avez-vous obtenu expérimentalement ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Répondre à la question 7 ici"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:red;\"> **Vous êtes au bout du TP** </span>\n",
    "* Sauvegarder votre document final (ctrl + s ou cliquer sur l'icone en forme de disquette)\n",
    "* Télécharger le résultat (bouton \"download\" de la barre d'outils)\n",
    "* Déposer le document téléchargé sur moodle pour correction\n",
    "* Vous pouvez conserver ce document et l'utiliser <a href=\"https://mybinder.org/v2/gh/jcamponovo/formation2020/master?urlpath=apps/environnement.ipynb\">ici</a> ou en conserver une copie lisible dans un navigateur (mais non modifiable) en utilisant **\"File\"** => **\"Download as\"** => **\"HTML\"** "
   ]
  }
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