go_02_reflection_refraction.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "#### Reflection and refraction"
      ],
      "metadata": {
        "id": "XOEDyDz58y3u"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.patches import Arc, Rectangle, Ellipse, Circle\n",
        "import numpy as np\n",
        "\n",
        "plt.style.use('dark_background')\n",
        "\n",
        "# color: https://matplotlib.org/stable/gallery/color/named_colors.html"
      ],
      "metadata": {
        "id": "Df9mNXbHY9xm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Constants for styling\n",
        "ARROW_HEAD_WIDTH = 0.07\n",
        "ARROW_HEAD_LENGTH = 0.1\n",
        "LINE_WIDTH = 3\n",
        "\n",
        "def reflection(ax, title=None, title_loc='center', fontsize=12, incident_angle=45, len=2, arc_d=0.3, arrow2origin=0.7, theta2origin=0.3, origin=[0,0]):\n",
        "    \"\"\"\n",
        "    Draw a reflection diagram on the provided axes.\n",
        "\n",
        "    Parameters:\n",
        "        ax (matplotlib.axes.Axes): The axes to draw the diagram on.\n",
        "        title (str, optional): The title of the subplot.\n",
        "        title_loc (str, optional): The location of the title ('center', 'left', 'right').\n",
        "        fontsize (int, optional): The font size of the title and labels.\n",
        "        incident_angle (float, optional): The angle of the incident ray in radians.\n",
        "        len (float, optional): Length of rays.\n",
        "        arc_d (float, optional): Diameter of circle underying of arc.\n",
        "        arrow2origin (float, optional): Distance from arrow base to origin.\n",
        "        theta2origin (float, optional): Distance from annotation (theta) to angle origin.\n",
        "        origin (list, optional): Point of reflection.\n",
        "    \"\"\"\n",
        "    # Geometry of medium (hardcoded)\n",
        "    rect = Rectangle((origin[0]-1, origin[1]-0.2), 2, 0.2, linewidth=1, edgecolor='none', facecolor='dodgerblue')\n",
        "    ax.add_patch(rect)\n",
        "\n",
        "    incident_angle=np.deg2rad(incident_angle)\n",
        "    incident_x = [origin[0]-len*np.sin(incident_angle), origin[0]]\n",
        "    incident_y = [origin[1]+len*np.cos(incident_angle), origin[1]]\n",
        "    ax.plot(incident_x, incident_y, 'r', linewidth=LINE_WIDTH, zorder=0)\n",
        "\n",
        "    reflected_x = [origin[0], origin[0]+len*np.sin(incident_angle)]\n",
        "    reflected_y = [origin[1], origin[1]+len*np.cos(incident_angle)]\n",
        "    ax.plot(reflected_x, reflected_y, 'r', linewidth=LINE_WIDTH, zorder=0)\n",
        "\n",
        "    normal_x = [origin[0], origin[0]]\n",
        "    normal_y = [origin[1]-len, origin[1]+len]\n",
        "    ax.plot(normal_x, normal_y, 'w--', linewidth=LINE_WIDTH)\n",
        "\n",
        "    angle_arc_i = Arc(origin, arc_d, arc_d, theta1=90, theta2=90+np.rad2deg(incident_angle), color='w')\n",
        "    angle_arc_r = Arc(origin, arc_d, arc_d, theta1=90-np.rad2deg(incident_angle), theta2=90, color='w')\n",
        "    ax.add_patch(angle_arc_i)\n",
        "    ax.add_patch(angle_arc_r)\n",
        "\n",
        "    # Theta labels\n",
        "    ax.text(origin[0]-theta2origin*np.sin(incident_angle/2), origin[1]+theta2origin*np.cos(incident_angle/2), r'$\\theta_i$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize)\n",
        "    ax.text(origin[0]+theta2origin*np.sin(incident_angle/2), origin[1]+theta2origin*np.cos(incident_angle/2), r'$\\theta_r$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize)\n",
        "\n",
        "    # Other labels\n",
        "    ax.text(origin[0]-0.75, origin[1]+0.1, '$n_1$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize)\n",
        "    ax.text(origin[0]-0.75, origin[1]-0.1, '$n_2$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize)\n",
        "\n",
        "    # Arrows\n",
        "    ax.arrow(\n",
        "        origin[0]-arrow2origin*np.sin(incident_angle),\n",
        "        origin[1]+arrow2origin*np.cos(incident_angle),\n",
        "        0.001*np.sin(incident_angle),\n",
        "        -0.001*np.cos(incident_angle),\n",
        "        head_width=ARROW_HEAD_WIDTH, head_length=ARROW_HEAD_LENGTH, fc='w', ec='none')\n",
        "    ax.arrow(\n",
        "        origin[0]+arrow2origin*np.sin(incident_angle),\n",
        "        origin[1]+arrow2origin*np.cos(incident_angle),\n",
        "        0.001*np.sin(incident_angle),\n",
        "        0.001*np.cos(incident_angle),\n",
        "        head_width=ARROW_HEAD_WIDTH, head_length=ARROW_HEAD_LENGTH, fc='w', ec='none')\n",
        "\n",
        "    ax.set_xlim(origin[0]-1, origin[0]+1)\n",
        "    ax.set_ylim(origin[1]-0.2, origin[1]+1)\n",
        "    ax.set_aspect('equal')\n",
        "\n",
        "    # ax.grid(True)\n",
        "    ax.axis('off')\n",
        "\n",
        "    if title:\n",
        "        ax.set_title(title, loc=title_loc, fontsize=fontsize)\n",
        "\n",
        "def refraction(ax, title=None, title_loc='center', fontsize=12, n_1=1, n_2=1.5, incident_angle_deg=45, len=2, arc_d=0.3, arrow2origin=0.5, theta2origin=0.3, origin=[0,0]):\n",
        "    \"\"\"\n",
        "    Draw a refraction diagram on the provided axes.\n",
        "\n",
        "    Parameters:\n",
        "        ax (matplotlib.axes.Axes): The axes to draw the diagram on.\n",
        "        title (str, optional): The title of the subplot.\n",
        "        title_loc (str, optional): The location of the title ('center', 'left', 'right').\n",
        "        fontsize (int, optional): The font size of the title and labels.\n",
        "        n_1, n_2 (float, optional): Refractive indices of medium.\n",
        "        incident_angle_deg (float, optional): The angle of the incident ray in radians.\n",
        "        len (float, optional): Length of rays.\n",
        "        arc_d (float, optional): Diameter of circle underying of arc.\n",
        "        arrow2origin (float, optional): Distance from arrow base to origin.\n",
        "        theta2origin (float, optional): Distance from annotation (theta) to angle origin.\n",
        "        origin (list, optional): Point of refraction.\n",
        "    \"\"\"\n",
        "    # Geometry of medium (hardcoded)\n",
        "    rect = Rectangle((origin[0]-1, origin[1]-0.6), 2, 0.6, linewidth=1, edgecolor='none', facecolor='dodgerblue', zorder=-1)\n",
        "    ax.add_patch(rect)\n",
        "\n",
        "    incident_angle=np.deg2rad(incident_angle_deg)\n",
        "    incident_x = [origin[0]-len*np.sin(incident_angle), origin[0]]\n",
        "    incident_y = [origin[1]+len*np.cos(incident_angle), origin[1]]\n",
        "    ax.plot(incident_x, incident_y, 'r', linewidth=LINE_WIDTH, zorder=0)\n",
        "\n",
        "    refracted_angle = np.arcsin(n_1 * np.sin(incident_angle) / n_2)\n",
        "    refracted_x = [origin[0], origin[0]+len * np.sin(refracted_angle)]\n",
        "    refracted_y = [origin[1], origin[1]-len * np.cos(refracted_angle)]\n",
        "    ax.plot(refracted_x, refracted_y, 'r', linewidth=LINE_WIDTH, zorder=0)\n",
        "\n",
        "    normal_x = [origin[0], origin[0]]\n",
        "    normal_y = [origin[1]-len, origin[1]+len]\n",
        "    ax.plot(normal_x, normal_y, 'w--', linewidth=LINE_WIDTH)\n",
        "\n",
        "    angle_arc_i = Arc(origin, arc_d, arc_d, theta1=90, theta2=90+np.rad2deg(incident_angle), color='w')\n",
        "    angle_arc_r = Arc(origin, arc_d, arc_d, theta1=-90, theta2=np.rad2deg(refracted_angle) - 90, color='w')\n",
        "    ax.add_patch(angle_arc_i)\n",
        "    ax.add_patch(angle_arc_r)\n",
        "\n",
        "    # Theta labels\n",
        "    ax.text(origin[0]-theta2origin*np.sin(incident_angle/2), origin[1]+theta2origin*np.cos(incident_angle/2), r'$\\theta_i$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize)\n",
        "    ax.text(origin[0]+theta2origin*np.sin(refracted_angle/2), origin[1]-theta2origin*np.cos(refracted_angle/2), r'$\\theta_t$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize)\n",
        "\n",
        "    # Other labels\n",
        "    ax.text(origin[0]-0.75, origin[1]+0.1, f'$n_1={n_1}$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize)\n",
        "    ax.text(origin[0]-0.75, origin[1]-0.1, f'$n_2={n_2}$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize)\n",
        "    ax.text(origin[0]+0.5, origin[1]+0.4, rf'$\\theta_1={incident_angle_deg}, \\theta_2={np.rad2deg(refracted_angle):.1f}$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize)\n",
        "\n",
        "    # Arrows\n",
        "    ax.arrow(\n",
        "        origin[0]-arrow2origin * np.sin(incident_angle),\n",
        "        origin[1]+arrow2origin * np.cos(incident_angle),\n",
        "        0.001 * np.sin(incident_angle),\n",
        "        -0.001 * np.cos(incident_angle),  head_width=ARROW_HEAD_WIDTH, head_length=ARROW_HEAD_LENGTH, fc='w', ec='none')\n",
        "    # ax.quiver(\n",
        "    #     origin[0]-arrow2origin * np.sin(incident_angle),\n",
        "    #     origin[1]+arrow2origin * np.cos(incident_angle),\n",
        "    #     0.001 * np.sin(incident_angle),\n",
        "    #     -0.001 * np.cos(incident_angle))\n",
        "    ax.arrow(\n",
        "        origin[0]+arrow2origin * np.sin(refracted_angle),\n",
        "        origin[1]-arrow2origin * np.cos(refracted_angle),\n",
        "        0.001 * np.sin(refracted_angle),\n",
        "        -0.001 * np.cos(refracted_angle),\n",
        "        head_width=ARROW_HEAD_WIDTH, head_length=ARROW_HEAD_LENGTH, fc='w', ec='none')\n",
        "\n",
        "    ax.set_xlim(origin[0]-1, origin[0]+1)\n",
        "    ax.set_ylim(origin[1]-0.6, origin[1]+0.6)\n",
        "    ax.set_aspect('equal')\n",
        "\n",
        "    ax.grid(True)\n",
        "    ax.axis('off')\n",
        "\n",
        "    if title:\n",
        "        ax.set_title(title, loc=title_loc, fontsize=fontsize)"
      ],
      "metadata": {
        "id": "VZ3NsYWsUPL9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(8, 3))\n",
        "\n",
        "reflection(axes[0], title='Reflection', incident_angle=60)\n",
        "refraction(axes[1], title='Refraction', n_1=1, n_2=1.3, incident_angle_deg=60)\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "wsNLjqlO1c5e",
        "outputId": "1b4a7135-69b9-404c-b91d-db2e8fbe3a5c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x300 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Reflection**\n",
        "\n",
        "$$\\theta_i=\\theta_r$$\n",
        "\n",
        "**Refraction**\n",
        "\n",
        "$$\\boxed{n_1\\sin(\\theta_i)=n_2\\sin(\\theta_t)}$$\n",
        "\n",
        "$i$: incident, $r$: reflected, $t$: transmitted, $n$: refractive index\n",
        "\n",
        "$$c_{k}=\\frac{c}{n_{k}}$$\n",
        "\n",
        "$$\\lambda_{k}=\\frac{\\lambda}{n_{k}}$$"
      ],
      "metadata": {
        "id": "8CMwXZs92qUQ"
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}