{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# parabolic reflector\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\nimport matplotlib.pyplot as plt\n\nfig, ax = plt.subplots(1,1)\n\n\ndef y(x):\n    return x**2/2\n\ndef df(x,y):\n    return np.array([-x, 1])\n\n#x0 = 1.5\nfor x0 in np.linspace(-1.5,1.5,10):\n    y0 = 2\n    i = np.array([0,-0.2])\n    n = df(x0, y(x0))\n    pn = -np.dot(i, n)/np.dot(n, n) * n\n    o = i + 2*pn\n    sample = 2\n    line = [np.array([x0]*sample), np.linspace(y(x0),2,sample)]\n    if x0 < 0:\n        x = np.linspace(x0,0,2)\n    else:\n        x = np.linspace(0,x0, 2)\n    z  = o[1]/o[0]*(x-x0) + y(x0)\n    l, = ax.plot(line[0], line[1], '-')\n    ax.quiver(x0, y0, i[0], i[1], angles='xy', scale_units='xy', scale=1)\n    ax.quiver(x0, y(x0), o[0], o[1], angles='xy', scale_units='xy', scale=1)\n    ax.plot(x, z, '-',c=l.get_color())\n\nx = np.linspace(-2,2,100)\nax.plot(x, y(x), '-k',lw=3)\nax.plot(0, 0.5, 'ok')\n\nax.set_ylim(0,2)\nax.set_xlim(-2,2)\nplt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.15"
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  "nbformat": 4,
  "nbformat_minor": 0
}