<iframe 
    src="http://jsxgraph.uni-bayreuth.de/share/iframe/snells-law" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Snell's law" 
    allowfullscreen
></iframe>

<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-5, 5, 5, -5], axis: false, keepaspectratio: true });
    
    // Line l1 as an interface between two environments, green, with the index of refraction 
    // n_1, and the blue, with the index of refraction n_2.
    
    var M = board.create('point', [-4, 0], { name: 'M', visible: false, fixed: true });
    var I = board.create('point', [0, 0], { name: 'I', size: 1, fixed: true });
    var l1 = board.create('line', [M, I]);
    var ineq1 = board.create('inequality', [l1], { fillColor: 'green' });
    var ineq2 = board.create('inequality', [l1], { inverse: true, fillColor: 'blue' });
    
    // Normal line n with auxiliary points N and O that allows us to determine 
    // the angles of incidence (α) and refraction (β), respectively
    var n = board.create('perpendicular', [l1, I], { name: 'n', color: 'black', dash: "2", strokeWidth: 1 });
    var N = board.create('glider', [0, 4, n], { name: 'N', visible: false });
    var O = board.create('glider', [0, -4, n], { name: 'O', visible: false });
    // a light source L
    var L = board.create('point', [-3, 4], { name: 'L', color: 'red', size: 3 });
    
    // Position of the light source L is limited to the green environment
    var xL, yL;
    L.on('drag', function() {
        if (L.Y() < 0) {
            L.moveTo([xL, yL], 0);
        }
        xL = L.X();
        yL = L.Y();
    });
    
    // r1, the incident light ray
    var r1 = board.create('segment', [L, I], { strokeColor: 'orange', strokeWidth: 4 });
    
    // Sliders to control indexes of refraction
    var n_1 = board.create('slider', [[-4, -3], [-2, -3], [1, 1, 3]], { name: 'n_1', snapWidth: 0.01 });
    var n_2 = board.create('slider', [[-4, -4], [-2, -4], [1, 1, 3]], { name: 'n_2', snapWidth: 0.01 });
    
    // The value of s controls the kind of refraction/reflection, if s > 1 the total reflection occurs
    // (numerically it is the absolute value of the sine of the angle of refraction)
    var s = () => (n_1.Value() / n_2.Value()) * Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))).toFixed(6);
    
    // Two possible points through which the modified ray passes, B for the reflected ray and C for the refracted one
    var B = board.create('point', [
                   () => -L.X(),
                   () => L.Y()
                ], {
        visible: () => (s() > 1 || Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) == 1) ? true : false,
        name: 'R_1',
        face: 'o',
        size: 1
    });
    var C = board.create('point', [
                   () => 5 * (n_1.Value() / n_2.Value()) * Math.sin(JXG.Math.Geometry.angle(N, I, L)),
                   () => -5 * Math.cos(Math.asin((n_1.Value() / n_2.Value()) * Math.sin(JXG.Math.Geometry.angle(N, I, L))))
                ], {
        visible: () => (s() <= 1 && Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) != 1) ? true : false,
        name: 'R_2',
        face: 'o',
        size: 1
    });
    
    // Reflected (r2) and refracted (r3) ray
    var r2 = board.create('segment', [I, B], {
        visible: () => (s() > 1 || Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) == 1) ? true : false,
        strokeColor: 'orange',
        strokeWidth: 4,
        lastArrow: { type: 1, size: 3 }
    });
    var r3 = board.create('segment', [I, C], {
        visible: () => (s() <= 1 && Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) != 1) ? true : false,
        strokeColor: 'orange',
        strokeWidth: 4,
        lastArrow: { type: 1, size: 3 }
    });
    
    // Angles of impact (angle 1), refraction (angle2) and reflection (angle3), respectively
    var angle1 = board.create('nonreflexangle', [N, I, L], { radius: 1, color: 'orange', fillOpacity: 0, name: 'α' });
    var angle2 = board.create('nonreflexangle', [O, I, C], {
        visible: () => (s() <= 1 && Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) != 1) ? true : false,
        radius: 1,
        color: 'orange',
        fillOpacity: 0,
        name: 'β'
    });
    var angle3 = board.create('nonreflexangle', [B, I, N], {
        visible: () => (s() > 1 || Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) == 1) ? true : false,
        radius: 1,
        color: 'orange',
        fillOpacity: 0,
        name: 'β'
    });
 </script> 

<jsxgraph width="100%" aspect-ratio="1 / 1" title="Snell's law" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-5, 5, 5, -5], axis: false, keepaspectratio: true });
   
   // Line l1 as an interface between two environments, green, with the index of refraction 
   // n_1, and the blue, with the index of refraction n_2.
   
   var M = board.create('point', [-4, 0], { name: 'M', visible: false, fixed: true });
   var I = board.create('point', [0, 0], { name: 'I', size: 1, fixed: true });
   var l1 = board.create('line', [M, I]);
   var ineq1 = board.create('inequality', [l1], { fillColor: 'green' });
   var ineq2 = board.create('inequality', [l1], { inverse: true, fillColor: 'blue' });
   
   // Normal line n with auxiliary points N and O that allows us to determine 
   // the angles of incidence (α) and refraction (β), respectively
   var n = board.create('perpendicular', [l1, I], { name: 'n', color: 'black', dash: "2", strokeWidth: 1 });
   var N = board.create('glider', [0, 4, n], { name: 'N', visible: false });
   var O = board.create('glider', [0, -4, n], { name: 'O', visible: false });
   // a light source L
   var L = board.create('point', [-3, 4], { name: 'L', color: 'red', size: 3 });
   
   // Position of the light source L is limited to the green environment
   var xL, yL;
   L.on('drag', function() {
       if (L.Y() < 0) {
           L.moveTo([xL, yL], 0);
       }
       xL = L.X();
       yL = L.Y();
   });
   
   // r1, the incident light ray
   var r1 = board.create('segment', [L, I], { strokeColor: 'orange', strokeWidth: 4 });
   
   // Sliders to control indexes of refraction
   var n_1 = board.create('slider', [[-4, -3], [-2, -3], [1, 1, 3]], { name: 'n_1', snapWidth: 0.01 });
   var n_2 = board.create('slider', [[-4, -4], [-2, -4], [1, 1, 3]], { name: 'n_2', snapWidth: 0.01 });
   
   // The value of s controls the kind of refraction/reflection, if s > 1 the total reflection occurs
   // (numerically it is the absolute value of the sine of the angle of refraction)
   var s = () => (n_1.Value() / n_2.Value()) * Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))).toFixed(6);
   
   // Two possible points through which the modified ray passes, B for the reflected ray and C for the refracted one
   var B = board.create('point', [
                  () => -L.X(),
                  () => L.Y()
               ], {
       visible: () => (s() > 1 || Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) == 1) ? true : false,
       name: 'R_1',
       face: 'o',
       size: 1
   });
   var C = board.create('point', [
                  () => 5 * (n_1.Value() / n_2.Value()) * Math.sin(JXG.Math.Geometry.angle(N, I, L)),
                  () => -5 * Math.cos(Math.asin((n_1.Value() / n_2.Value()) * Math.sin(JXG.Math.Geometry.angle(N, I, L))))
               ], {
       visible: () => (s() <= 1 && Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) != 1) ? true : false,
       name: 'R_2',
       face: 'o',
       size: 1
   });
   
   // Reflected (r2) and refracted (r3) ray
   var r2 = board.create('segment', [I, B], {
       visible: () => (s() > 1 || Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) == 1) ? true : false,
       strokeColor: 'orange',
       strokeWidth: 4,
       lastArrow: { type: 1, size: 3 }
   });
   var r3 = board.create('segment', [I, C], {
       visible: () => (s() <= 1 && Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) != 1) ? true : false,
       strokeColor: 'orange',
       strokeWidth: 4,
       lastArrow: { type: 1, size: 3 }
   });
   
   // Angles of impact (angle 1), refraction (angle2) and reflection (angle3), respectively
   var angle1 = board.create('nonreflexangle', [N, I, L], { radius: 1, color: 'orange', fillOpacity: 0, name: 'α' });
   var angle2 = board.create('nonreflexangle', [O, I, C], {
       visible: () => (s() <= 1 && Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) != 1) ? true : false,
       radius: 1,
       color: 'orange',
       fillOpacity: 0,
       name: 'β'
   });
   var angle3 = board.create('nonreflexangle', [B, I, N], {
       visible: () => (s() > 1 || Math.abs(Math.sin(JXG.Math.Geometry.angle(N, I, L))) == 1) ? true : false,
       radius: 1,
       color: 'orange',
       fillOpacity: 0,
       name: 'β'
   });
</jsxgraph>