go_01_real_virtual_image.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": [
        "#### Real and virtual image"
      ],
      "metadata": {
        "id": "XemF8eivOshZ"
      }
    },
    {
      "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",
        "# color: https://matplotlib.org/stable/gallery/color/named_colors.html"
      ],
      "metadata": {
        "id": "c6ktEOVahKD-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def convex_lens_imaging_real(ax, title=None, title_loc='center', fontsize=12, annotation=True):\n",
        "    # Optical axis\n",
        "    ax.plot([-1.2, 1.2], [0, 0], 'w', linewidth=2)\n",
        "\n",
        "    # Distances\n",
        "    d = 0.05\n",
        "    f = 0.4\n",
        "\n",
        "    # y1 and arrows\n",
        "    y1 = 0.4\n",
        "    ax.plot([-2.5*f, -2.5*f], [0, y1], 'c', linewidth=2)\n",
        "    ax.arrow(-2.5*f, y1-0.1, 0, 0,  head_width=0.07, head_length=0.1, fc='c', ec='none')\n",
        "\n",
        "    # Angles\n",
        "    theta_1 = 0\n",
        "    theta_2 = np.arctan2(y1, f-d/2)\n",
        "\n",
        "    # Ray 1\n",
        "    ax.plot([-2.5*f, -d/2], [y1, y1], 'r', linewidth=2)\n",
        "    ax.plot([d/2, 2.5*f], [y1, y1-(2.5*f-d/2)*np.tan(theta_2)], 'r', linewidth=2)\n",
        "    ax.arrow(-f, y1, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "    ax.arrow(d/2+f/2, y1-f/2*np.tan(theta_2), 0.001*np.cos(theta_2), -0.001*np.sin(theta_2),  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "\n",
        "    # Ray1 2\n",
        "    ax.plot([-2.5*f, 2.5*f], [y1, -y1], 'r', linewidth=2)\n",
        "    ax.arrow(-f, y1/2.5, 0.0025, -0.001,  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "\n",
        "    # Ray 3\n",
        "    ax.plot([-2.5*f, -d/2], [y1, y1-(2.5*f-d/2)/1.5], 'r', linewidth=2)\n",
        "    ax.plot([d/2, 2.5*f], [y1-(2.5*f-d/2)/1.5, y1-(2.5*f-d/2)/1.5], 'r', linewidth=2)\n",
        "    ax.arrow(0.5*f, y1-(2.5*f-d/2)/1.5, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "\n",
        "    # y2 and arrows\n",
        "    y2 = 0.4\n",
        "    ax.plot([(f-d/2)/y1*(2.5*f-d/2)/1.5+d/2, (f-d/2)/y1*(2.5*f-d/2)/1.5+d/2], [0, y1-(2.5*f-d/2)/1.5], 'lime', linewidth=2, zorder=5)\n",
        "    ax.arrow((f-d/2)/y1*(2.5*f-d/2)/1.5+d/2+0.005, y1-(2.5*f-d/2)/1.5+0.08, 0, -0.001,  head_width=0.07, head_length=0.1, fc='lime', ec='none')\n",
        "\n",
        "    # f distance\n",
        "    ax.plot([0, 0], [0, -0.1], 'w-', linewidth=1)\n",
        "    ax.plot([0, f], [-0.05, -0.05], 'w-', linewidth=1)\n",
        "    ax.plot([f, f], [0, -0.1], 'w-', linewidth=1)\n",
        "    ax.plot([0, -f], [-0.05, -0.05], 'w-', linewidth=1)\n",
        "    ax.plot([-f, -f], [0, -0.1], 'w-', linewidth=1)\n",
        "    ax.text(f/2, -0.15, r'$f$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "    ax.text(-f/2, -0.15, r'$f$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "    ax.arrow(0.06, -0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(f-0.06, -0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(-0.06, -0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(-f+0.06, -0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "\n",
        "    if annotation:\n",
        "        # s distance\n",
        "        ax.plot([0, 0], [y1-(2.5*f-d/2)/1.5, y1-(2.5*f-d/2)/1.5-0.1], 'w-', linewidth=1)\n",
        "        ax.plot([0, (f-d/2)/y1*(2.5*f-d/2)/1.5+d/2], [y1-(2.5*f-d/2)/1.5-0.05, y1-(2.5*f-d/2)/1.5-0.05], 'w-', linewidth=1)\n",
        "        ax.plot([(f-d/2)/y1*(2.5*f-d/2)/1.5+d/2, (f-d/2)/y1*(2.5*f-d/2)/1.5+d/2], [y1-(2.5*f-d/2)/1.5, y1-(2.5*f-d/2)/1.5-0.1], 'w-', linewidth=1)\n",
        "        ax.plot([0, -2.5*f], [y1-(2.5*f-d/2)/1.5-0.05, y1-(2.5*f-d/2)/1.5-0.05], 'w-', linewidth=1)\n",
        "        ax.plot([-2.5*f, -2.5*f], [y1-(2.5*f-d/2)/1.5, y1-(2.5*f-d/2)/1.5-0.1], 'w-', linewidth=1)\n",
        "        ax.text(((f-d/2)/y1*(2.5*f-d/2)/1.5+d/2)/2, y1-(2.5*f-d/2)/1.5-0.15, r'$s_i$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "        ax.text(-2.5*f/2, y1-(2.5*f-d/2)/1.5-0.15, r'$s_o$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "        ax.arrow(0.06, y1-(2.5*f-d/2)/1.5-0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "        ax.arrow((f-d/2)/y1*(2.5*f-d/2)/1.5+d/2-0.06, y1-(2.5*f-d/2)/1.5-0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "        ax.arrow(-0.06, y1-(2.5*f-d/2)/1.5-0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "        ax.arrow(-2.5*f+0.06, y1-(2.5*f-d/2)/1.5-0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "\n",
        "    # Lens\n",
        "    lens = Ellipse((0,0), d, 1.2, edgecolor='none', facecolor='skyblue', zorder=-5)\n",
        "    ax.add_patch(lens)\n",
        "\n",
        "    # Set limits and aspect ratio\n",
        "    ax.set_xlim(-1.2, 1.2)\n",
        "    ax.set_ylim(-0.7, 0.7)\n",
        "    ax.set_aspect('equal')\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 convex_lens_imaging_virtual(ax, title=None, title_loc='center', fontsize=12, annotation=True):\n",
        "    # Optical axis\n",
        "    ax.plot([-1.2, 1.2], [0, 0], 'w', linewidth=2)\n",
        "\n",
        "    # Distances\n",
        "    d = 0.05\n",
        "    f = 0.4\n",
        "\n",
        "    # y2 and arrows\n",
        "    y2 = 0.4\n",
        "    ax.plot([-2.5*f, -2.5*f], [0, y2], 'lime', linewidth=2)\n",
        "    ax.arrow(-2.5*f, y2-0.1, 0, 0,  head_width=0.07, head_length=0.1, fc='lime', ec='none')\n",
        "\n",
        "    # # Angles\n",
        "    # theta_1 = 0\n",
        "    # theta_2 = np.arctan2(y2, f-d/2)\n",
        "\n",
        "    # Ray 1\n",
        "    ax.plot([-2.5*f, -d/2], [y2, y2], 'r--', linewidth=2)\n",
        "    ax.plot([d/2, 2.5*f], [y2, y2], 'r', linewidth=2)\n",
        "    ax.arrow(f, y2, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "\n",
        "    # Ray 2\n",
        "    ax.plot([-2.5*f, 0], [y2, y2-y2/(3.5*f)*2.5*f], 'r--', linewidth=2)\n",
        "    ax.plot([0, 2.5*f], [y2-y2/(3.5*f)*2.5*f, y2-2*y2/(3.5*f)*2.5*f], 'r', linewidth=2)\n",
        "    ax.plot([-2.5*f+2.5*f/(2*y2-y2/(3.5*f)*2.5*f)*y2-0.05, 0], [y2-y2/(3.5*f)*2.5*f, y2-y2/(3.5*f)*2.5*f], 'r', linewidth=2)\n",
        "    ax.arrow(f, 0, 0.001*2.5*f, -0.001*y2/(3.5*f)*2.5*f,  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "\n",
        "    # y1 and arrows\n",
        "    ax.plot([-2.5*f+2.5*f/(2*y2-y2/(3.5*f)*2.5*f)*y2-0.05, -2.5*f+2.5*f/(2*y2-y2/(3.5*f)*2.5*f)*y2-0.05], [0, y2-y2/(3.5*f)*2.5*f], 'c', linewidth=2, zorder=5)\n",
        "    ax.arrow(-2.5*f+2.5*f/(2*y2-y2/(3.5*f)*2.5*f)*y2-0.05, y2-y2/(3.5*f)*2.5*f-0.1, 0, 0,  head_width=0.07, head_length=0.1, fc='c', ec='none')\n",
        "\n",
        "    # # Ray 3\n",
        "    ax.plot([-2.5*f, -2.5*f+2.5*f/(2*y2-y2/(3.5*f)*2.5*f)*y2-0.05],[y2, y2-y2/(3.5*f)*2.5*f], 'r--', linewidth=2)\n",
        "    ax.plot([-2.5*f+2.5*f/(2*y2-y2/(3.5*f)*2.5*f)*y2-0.05, 2.5*f],[y2-y2/(3.5*f)*2.5*f,-y2], 'r', linewidth=2)\n",
        "    ax.arrow(f, -y2/2.5, 0.0025, -0.001,  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "\n",
        "    # # Ray 4\n",
        "    ax.plot([-2.5*f+2.5*f/(2*y2-y2/(3.5*f)*2.5*f)*y2-0.05, d/2],[y2-y2/(3.5*f)*2.5*f+d/5,y2], 'r', linewidth=2)\n",
        "    ax.plot([-2.5*f+2.5*f/(2*y2-y2/(3.5*f)*2.5*f)*y2-0.05, -f],[y2-y2/(3.5*f)*2.5*f+d/5,0], 'r--', linewidth=2)\n",
        "\n",
        "    # f distance\n",
        "    ax.plot([0, 0], [0, -0.1], 'w-', linewidth=1)\n",
        "    ax.plot([0, f], [-0.05, -0.05], 'w-', linewidth=1)\n",
        "    ax.plot([f, f], [0, -0.1], 'w-', linewidth=1)\n",
        "    ax.plot([0, -f], [-0.05, -0.05], 'w-', linewidth=1)\n",
        "    ax.plot([-f, -f], [0, -0.1], 'w-', linewidth=1)\n",
        "    ax.text(f/2, -0.15, r'$f$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "    ax.text(-f/2, -0.15, r'$f$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "    ax.arrow(0.06, -0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(f-0.06, -0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(-0.06, -0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(-f+0.06, -0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "\n",
        "    if annotation:\n",
        "        # s distance\n",
        "        ax.plot([0, 0], [y2-(2.5*f-d/2)/1.5, y2-(2.5*f-d/2)/1.5-0.1], 'w-', linewidth=1)\n",
        "        ax.plot([0, (f-d/2)/y2*(2.5*f-d/2)/1.5+d/2], [y2-(2.5*f-d/2)/1.5-0.05, y2-(2.5*f-d/2)/1.5-0.05], 'w-', linewidth=1)\n",
        "        ax.plot([(f-d/2)/y2*(2.5*f-d/2)/1.5+d/2, (f-d/2)/y2*(2.5*f-d/2)/1.5+d/2], [y2-(2.5*f-d/2)/1.5, y2-(2.5*f-d/2)/1.5-0.1], 'w-', linewidth=1)\n",
        "        ax.plot([0, -2.5*f], [y2-(2.5*f-d/2)/1.5-0.05, y2-(2.5*f-d/2)/1.5-0.05], 'w-', linewidth=1)\n",
        "        ax.plot([-2.5*f, -2.5*f], [y2-(2.5*f-d/2)/1.5, y2-(2.5*f-d/2)/1.5-0.1], 'w-', linewidth=1)\n",
        "        ax.text(((f-d/2)/y2*(2.5*f-d/2)/1.5+d/2)/2, y2-(2.5*f-d/2)/1.5-0.15, r'$s_i$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "        ax.text(-2.5*f/2, y2-(2.5*f-d/2)/1.5-0.15, r'$s_o$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "        ax.arrow(0.06, y2-(2.5*f-d/2)/1.5-0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "        ax.arrow((f-d/2)/y2*(2.5*f-d/2)/1.5+d/2-0.06, y2-(2.5*f-d/2)/1.5-0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "        ax.arrow(-0.06, y2-(2.5*f-d/2)/1.5-0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "        ax.arrow(-2.5*f+0.06, y2-(2.5*f-d/2)/1.5-0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "\n",
        "    # Lens\n",
        "    lens = Ellipse((0,0), d, 1.2, edgecolor='none', facecolor='skyblue', zorder=-5)\n",
        "    ax.add_patch(lens)\n",
        "\n",
        "    # Set limits and aspect ratio\n",
        "    ax.set_xlim(-1.2, 1.2)\n",
        "    ax.set_ylim(-0.7, 0.7)\n",
        "    ax.set_aspect('equal')\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 concave_lens_imaging_virtual(ax, title=None, title_loc='center', fontsize=12, annotation=True):\n",
        "    # Optical axis\n",
        "    ax.plot([-1.2, 1.2], [0, 0], 'w', linewidth=2)\n",
        "\n",
        "    # Distances\n",
        "    d = 0.05\n",
        "    f = 0.4\n",
        "\n",
        "    # y1 and arrows\n",
        "    y1 = 0.4\n",
        "    ax.plot([-2.5*f, -2.5*f], [0, y1], 'c', linewidth=2)\n",
        "    ax.arrow(-2.5*f, y1-0.1, 0, 0,  head_width=0.07, head_length=0.1, fc='c', ec='none')\n",
        "\n",
        "    # # Angles\n",
        "    # theta_1 = 0\n",
        "    # theta_2 = np.arctan2(y1, f-d/2)\n",
        "\n",
        "    # Ray 1 (horizontal to lens)\n",
        "    ax.plot([-2.5*f, -d/2], [y1, y1], 'r', linewidth=2)\n",
        "\n",
        "    # Ray 2 (horizontal after lens)\n",
        "    ax.plot([-2.5*f, 0], [y1, y1-y1/(3.5*f)*2.5*f], 'r', linewidth=2)\n",
        "    ax.plot([0, f], [y1-y1/(3.5*f)*2.5*f, 0], 'r--', linewidth=2)\n",
        "    ax.plot([0, 2.5*f], [y1-y1/(3.5*f)*2.5*f, y1-y1/(3.5*f)*2.5*f], 'r', linewidth=2)\n",
        "    ax.plot([-2.5*f+2.5*f/(2*y1-y1/(3.5*f)*2.5*f)*y1-0.05, 0], [y1-y1/(3.5*f)*2.5*f, y1-y1/(3.5*f)*2.5*f], 'r--', linewidth=2)\n",
        "    ax.arrow(f, y1-y1/(3.5*f)*2.5*f, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "\n",
        "    # y2 and arrows\n",
        "    ax.plot([-2.5*f+2.5*f/(2*y1-y1/(3.5*f)*2.5*f)*y1-0.05, -2.5*f+2.5*f/(2*y1-y1/(3.5*f)*2.5*f)*y1-0.05], [0, y1-y1/(3.5*f)*2.5*f], 'lime', linewidth=2, zorder=5)\n",
        "    ax.arrow(-2.5*f+2.5*f/(2*y1-y1/(3.5*f)*2.5*f)*y1-0.05, y1-y1/(3.5*f)*2.5*f-0.1, 0, 0,  head_width=0.07, head_length=0.1, fc='lime', ec='none')\n",
        "\n",
        "    # # Ray 3 (passing through lens center)\n",
        "    ax.plot([-2.5*f, 0],[y1, 0], 'r', linewidth=2)\n",
        "    ax.plot([0, 2.5*f],[0,-y1], 'r', linewidth=2)\n",
        "    ax.arrow(f, -y1/2.5, 0.0025, -0.001,  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "\n",
        "    # # Ray 4 (virtual ray from front focal point)\n",
        "    ax.plot([-2.5*f+2.5*f/(2*y1-y1/(3.5*f)*2.5*f)*y1-0.05, d/2],[y1-y1/(3.5*f)*2.5*f+d/5,y1], 'r--', linewidth=2)\n",
        "    ax.plot([-2.5*f+2.5*f/(2*y1-y1/(3.5*f)*2.5*f)*y1-0.05, -f],[y1-y1/(3.5*f)*2.5*f+d/5,0], 'r--', linewidth=2)\n",
        "    ax.plot([d/2, f],[y1,2*y1], 'r', linewidth=2)\n",
        "    ax.arrow(f/2+d/4, y1+y1/2, 0.001*f/2, 0.001*y1/2,  head_width=0.04, head_length=0.06, fc='w', ec='none', zorder=5)\n",
        "\n",
        "    # f distance\n",
        "    ax.plot([0, 0], [0, -0.1], 'w-', linewidth=1)\n",
        "    ax.plot([0, f], [-0.05, -0.05], 'w-', linewidth=1)\n",
        "    ax.plot([f, f], [0, -0.1], 'w-', linewidth=1)\n",
        "    ax.plot([0, -f], [-0.05, -0.05], 'w-', linewidth=1)\n",
        "    ax.plot([-f, -f], [0, -0.1], 'w-', linewidth=1)\n",
        "    ax.text(f/2, -0.15, r'$f$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "    ax.text(-f/2, -0.15, r'$f$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "    ax.arrow(0.06, -0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(f-0.06, -0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(-0.06, -0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(-f+0.06, -0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "\n",
        "    if annotation:\n",
        "        # s distance\n",
        "        ax.plot([0, 0], [y1-(2.5*f-d/2)/1.5, y1-(2.5*f-d/2)/1.5-0.1], 'w-', linewidth=1)\n",
        "        ax.plot([0, (f-d/2)/y1*(2.5*f-d/2)/1.5+d/2], [y1-(2.5*f-d/2)/1.5-0.05, y1-(2.5*f-d/2)/1.5-0.05], 'w-', linewidth=1)\n",
        "        ax.plot([(f-d/2)/y1*(2.5*f-d/2)/1.5+d/2, (f-d/2)/y1*(2.5*f-d/2)/1.5+d/2], [y1-(2.5*f-d/2)/1.5, y1-(2.5*f-d/2)/1.5-0.1], 'w-', linewidth=1)\n",
        "        ax.plot([0, -2.5*f], [y1-(2.5*f-d/2)/1.5-0.05, y1-(2.5*f-d/2)/1.5-0.05], 'w-', linewidth=1)\n",
        "        ax.plot([-2.5*f, -2.5*f], [y1-(2.5*f-d/2)/1.5, y1-(2.5*f-d/2)/1.5-0.1], 'w-', linewidth=1)\n",
        "        ax.text(((f-d/2)/y1*(2.5*f-d/2)/1.5+d/2)/2, y1-(2.5*f-d/2)/1.5-0.15, r'$s_i$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "        ax.text(-2.5*f/2, y1-(2.5*f-d/2)/1.5-0.15, r'$s_o$', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "        ax.arrow(0.06, y1-(2.5*f-d/2)/1.5-0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "        ax.arrow((f-d/2)/y1*(2.5*f-d/2)/1.5+d/2-0.06, y1-(2.5*f-d/2)/1.5-0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "        ax.arrow(-0.06, y1-(2.5*f-d/2)/1.5-0.05, 0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "        ax.arrow(-2.5*f+0.06, y1-(2.5*f-d/2)/1.5-0.05, -0.001, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "\n",
        "    # # Lens\n",
        "    # lens = Ellipse((0,0), d, 1.2, edgecolor='none', facecolor='skyblue', zorder=-5)\n",
        "    # ax.add_patch(lens)\n",
        "\n",
        "    # Set limits and aspect ratio\n",
        "    ax.set_xlim(-1.2, 1.2)\n",
        "    ax.set_ylim(-0.7, 0.7)\n",
        "    ax.set_aspect('equal')\n",
        "    # ax.grid(True)\n",
        "    ax.axis('off')\n",
        "\n",
        "    r=5\n",
        "    y_concave = np.linspace(-0.6, 0.6, 50)\n",
        "    x1_concave = -np.sqrt((r-d/2)**2-y_concave**2)+r\n",
        "    x2_concave = -x1_concave\n",
        "    plt.fill_betweenx(y_concave, x1_concave, x2_concave, color='skyblue')\n",
        "\n",
        "    if title:\n",
        "        ax.set_title(title, loc=title_loc, fontsize=fontsize)\n",
        "\n",
        "fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(12, 5))\n",
        "\n",
        "convex_lens_imaging_real(axes[0], title='Convex Lens, Real Image', annotation=False)\n",
        "convex_lens_imaging_virtual(axes[1], title='Convex Lens, Virtual Image', annotation=False)\n",
        "concave_lens_imaging_virtual(axes[2], title='Concave Lens, Virtual Image', annotation=False)\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "BPNatGj0hp5K",
        "outputId": "97710855-99f6-4648-c03f-ab7709b5cd05"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x500 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}