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HTML

              
                <div id="controls">
  <div>
    <input type="range" id="rays" min="2" max="50" step="1">
    <label for="rays">Num rays</label>
    <input type="checkbox" id="en1" checked="true">
    <label for="en1">Lens 1</label>
    <input type="checkbox" id="en2" checked="true">
    <label for="en2">Lens 2</label>
    <input type="checkbox" id="en3" checked="true">
    <label for="en3">Lens 3</label>
  </div>
  <div>
    <input type="range" id="bnd1" min="100" max="2000" step="10">
    <label for="bnd1">Boundary 1</label>
    <input type="range" id="dist1" min="1" max="500" step="1">
    <label for="dist1">Dist before lens 1</label>
  </div>
  <div>
    <input type="range" id="bnd2" min="100" max="2000" step="10">
    <label for="bnd2">Boundary 2</label>
    <input type="range" id="thk1" min="2" max="50" step="1">
    <label for="thk1">Thickness 1</label>
  </div>
  <div>
    <input type="range" id="bnd3" min="100" max="2000" step="10">
    <label for="bnd3">Boundary 3</label>
          <input type="range" id="dist2" min="1" max="500" step="1">
    <label for="dist2">Dist before lens 2</label>
  </div>
  <div>
    <input type="range" id="bnd4" min="100" max="2000" step="10">
    <label for="bnd4">Boundary 4</label>
      <input type="range" id="thk2" min="2" max="50" step="1">
    <label for="thk2">Thickness 2</label>
  </div>
  <div>
    <input type="range" id="bnd5" min="100" max="2000" step="10">
    <label for="bnd5">Boundary 5</label>
          <input type="range" id="dist3" min="1" max="500" step="1">
    <label for="dist3">Dist before lens 3</label>
  </div>
  <div>
    <input type="range" id="bnd6" min="100" max="2000" step="10">
    <label for="bnd6">Boundary 6</label>
      <input type="range" id="thk3" min="2" max="50" step="1">
    <label for="thk3">Thickness 3</label>
  </div>
  <div>
    <input type="range" id="sensor" min="100" max="1000" step="1">
    <label for="sensor">Sensor location</label>
  </div>
</div>
<div>
  <canvas id="canvas" width="1000" height="300"></canvas>
</div>
<div>
  <p>Measurements</p>
  <p>Effective focal length: <span id="focal_l">...</span></p>
  <p>Highlight height (must be zero for EFL to be valid): <span id="hlht">...</span></p>
  <p>Back focal distance: <span id="bfd">...</span></p>
</div>
              
            
!

CSS

              
                div {
  /* border: solid 1px; */
}
              
            
!

JS

              
                const draw_axis = (ctx) => {
  ctx.beginPath();
  ctx.strokeStyle = "black"
  ctx.moveTo(0, 150);
  ctx.lineTo(1000, 150);
  ctx.closePath();
  ctx.stroke();
}

const draw_aligned_vertical_boundary = (ctx, pos) => {
  ctx.beginPath();
  ctx.strokeStyle = "black"
  ctx.moveTo(pos, 0);
  ctx.lineTo(pos, 300);
  ctx.closePath();
  ctx.stroke();
}

const draw_aligned_circular_boundary = (ctx, origin, center) => {
  const x = origin + center;
  const y = 150;
  const radius = Math.abs(center);
  ctx.beginPath();
  ctx.strokeStyle = "black"
  ctx.arc(x, y, radius, Math.PI/2, Math.PI*3/2, center < 0 );
  ctx.stroke();
}

const draw_raylike = (ctx, start, direction, color, scale=50) => {
  ctx.beginPath();
  ctx.fillStyle = color;
  ctx.arc(start.x, 150-start.y, 3, 0, 2 * Math.PI);
  ctx.fill();
  
  const rx = direction.x;
  const ry = -direction.y;
  const mag = Math.sqrt((rx*rx)+(ry*ry))
  const nx = rx / mag * scale;
  const ny = ry / mag * scale;
  ctx.beginPath();
  ctx.strokeStyle = color;
  ctx.moveTo(start.x, 150-start.y);
  ctx.lineTo(start.x + nx, 150-start.y + ny);
  ctx.stroke();
}

const draw_ray = (ctx, start, direction) => draw_raylike(ctx, start, direction, 'red', 25)
const draw_normal = (ctx, start, direction) => draw_raylike(ctx, start, direction, 'green', 10)
const draw_highlight_ray = (ctx, start, direction) => draw_raylike(ctx, start, direction, 'grey', 50)

const intersect_ray_circle = (ray, circle) => {
  const sqrt = Math.sqrt;
  const abs = Math.abs
  const sq = (x) => Math.pow(x,2)
  // move circle to origin
  const x1 = ray.start.x - circle.x
  const x2 = x1 + ray.direction.x
  const y1 = ray.start.y - circle.y
  const y2 = y1 + ray.direction.y
  const r = circle.r
  
  // intersection of circle at origin and line defined by two points
  // https://mathworld.wolfram.com/Circle-LineIntersection.html
  const dx = x2 - x1
  const dy = y2 - y1
  const dr = sqrt(sq(dx) + sq(dy))
  const D = x1*y2 - x2*y1
  const desc = sq(r) * sq(dr) - sq(D);
  // console.log("desc ", desc)
  if( desc < 0 )
    return "no intersection"
  const s = dy < 0 ? -1 : 1
  const x = (D*dy+s*dx*sqrt(desc)) / sq(dr)
  const x_ = (D*dy-s*dx*sqrt(desc)) / sq(dr)
  const y = (-1*D*dx+abs(dy)*sqrt(desc)) / sq(dr)
  const y_ = (-1*D*dx-abs(dy)*sqrt(desc)) / sq(dr)
  //console.log(`y = [ -1*${D}*${dx}+abs(${dy})*sqrt(${desc}) ] / ${dr}^2`) 
  //   console.log(`[${-1*D*dx}+${abs(dy)*sqrt(desc)}]/${sq(dr)}`)
              
  // move back from origin
  return [
    {x: x + circle.x, y: y + circle.y},
    {x: x_ + circle.x, y: y_ + circle.y},
  ]
}

const intersect_ray_line = (ray, line) => {
  return intersect_ray_ray( ray, { start: {x: line.x, y:0}, direction: {x:0, y:100} })
}

const intersect_ray_ray = (rayA, rayB) => {
  const x1 = rayA.start.x, y1 = rayA.start.y;
  const x2 = x1 + rayA.direction.x, y2 = y1 + rayA.direction.y;
  const x3 = rayB.start.x, y3 = rayB.start.y;
  const x4 = x3 + rayB.direction.x, y4 = y3 + rayB.direction.y;
  const D = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4)
  const x = ((x1*y2 - y1*x2)*(x3-x4) - (x1-x2)*(x3*y4 - y3*x4)) / D
  const y = ((x1*y2 - y1*x2)*(y3-y4) - (y1-y2)*(x3*y4 - y3*x4)) / D
  return [{x: x, y: y}]
}

const normal_at_circular_boundary = (point, circle, flip = false) => {
  // flip the normal for when we're doing concave intersections
  if(flip) {
     return {
      x: circle.x - point.x,
      y: circle.y - point.y
    }
  }
  // we assume the point is on the circle
  const normal = {
    x: point.x - circle.x,
    y: point.y - circle.y
  }
  return normal // I guess that's it... draw a line from the center of the circle to the point
}

const refracted_ray = (n1, n2, incoming, norm) => {
  // https://en.wikipedia.org/wiki/Snell's_law
  // snell's law: sin A2 / sin A1 = n1 / n2
  // n1 / n2 * sin A1 = sin A2
  // https://physics.stackexchange.com/questions/435512/snells-law-in-vector-form
  // vector form: norm x v2 = u( norm x v1), u = n1 / n2
  // moving in->out ie: n1 -> n2
  const sin = Math.sin
  const cos = Math.cos
  const asin = Math.asin
  const atan2 = Math.atan2
  const th_in = atan2(-incoming.y, -incoming.x)
  const th_norm = atan2(norm.y, norm.x)
  const th_1 = th_in - th_norm
  const th_norm_out = atan2(-norm.y, -norm.x)
  const th_2 = asin( n1 / n2 * sin(th_1))
  const th_out = th_2 + th_norm_out
  return {
    x: cos(th_out),
    y: sin(th_out)
  }
}

const dist_to = (A, B) => {
  return Math.sqrt( Math.pow(B.x - A.x, 2) + Math.pow(B.y - A.y,2))
}

const closest_intersection = (start, intrs) => {
  let ret = intrs[0]
  let shortest_distance = Infinity
  intrs.forEach((intr) => {
    const dist = dist_to(start, intr)
    if( dist < shortest_distance) {
      shortest_distance = dist
      ret = intr
    }
  })
  return ret
}

const cast_to_boundary = (ctx, cast_ray, boundary) => {
  let intrs
  if(boundary.circle) {
    intrs = intersect_ray_circle(
      cast_ray,
      boundary.circle
    )

    if( typeof(intrs) == "string")
       return intrs
  } else if( boundary.line) {
    intrs = intersect_ray_line(cast_ray, boundary.line)
  } else {
    return "Unknown boundary type"
  }
  const closest_intr = closest_intersection(cast_ray.start, intrs)
  // if( boundary.line) console.log(intrs)

  const n = boundary.normal_at(closest_intr)
  draw_normal(ctx, closest_intr, n)
  // if( boundary.line) console.log(closest_intr)

  const a = refracted_ray( boundary.n1, boundary.n2, cast_ray.direction, n)
  // draw_ray(ctx, closest_intr, a)
  
  return {
    start: closest_intr,
    direction: a
  }
}

const make_meniscus_boundaries = (index, thickness, first_face_x, first_face_r, second_face_r) => {
  const ffc = first_face_x + first_face_r
  const sfc = first_face_x + thickness + second_face_r
  const boundaries = [
    {
      n1: 1.0,
      n2: index,
      circle: {x: ffc, y: 0, r: first_face_r},
      normal_at: (p) => normal_at_circular_boundary(p, {x: ffc, y: 0, r: first_face_r}),
      x_crossing: (ffc - first_face_r)
    },
    {
      n1: index,
      n2: 1.0,
      circle: {x: sfc, y: 0, r: second_face_r},
      normal_at: (p) => normal_at_circular_boundary(p, {x: sfc, y: 0, r: second_face_r}),
      x_crossing: (sfc - second_face_r)
    }
  ]
  draw_aligned_circular_boundary(ctx, boundaries[0].x_crossing, boundaries[0].circle.r);
  draw_aligned_circular_boundary(ctx, boundaries[1].x_crossing, boundaries[1].circle.r);
  
  return boundaries
}

const make_biconvex_boundaries = (index, thickness, first_face_x, first_face_r, second_face_r) => {
  const ffc = first_face_x + first_face_r
  const sfc = first_face_x + thickness - second_face_r
  const boundaries = [
    {
      n1: 1.0,
      n2: index,
      circle: {x: ffc, y: 0, r: first_face_r},
      normal_at: (p) => normal_at_circular_boundary(p, {x: ffc, y: 0, r: first_face_r}),
      x_crossing: (ffc - first_face_r)
    },
    {
      n1: index,
      n2: 1.0,
      circle: {x: sfc, y: 0, r: second_face_r},
      normal_at: (p) => normal_at_circular_boundary(p, {x: sfc, y: 0, r: second_face_r}, true),
      x_crossing: (first_face_x + thickness)
    }
  ]
  draw_aligned_circular_boundary(ctx, boundaries[0].x_crossing, boundaries[0].circle.r);
  draw_aligned_circular_boundary(ctx, boundaries[1].x_crossing, -boundaries[1].circle.r);
  
  return boundaries
}

const make_biconcave_boundaries = (index, thickness, first_face_x, first_face_r, second_face_r) => {
  const ffc = first_face_x - first_face_r
  const sfc = first_face_x + thickness + second_face_r
  const boundaries = [
    {
      n1: 1.0,
      n2: index,
      circle: {x: ffc, y: 0, r: first_face_r},
      normal_at: (p) => normal_at_circular_boundary(p, {x: ffc, y: 0, r: first_face_r}, true),
      x_crossing: (ffc + first_face_r)
    },
    {
      n1: index,
      n2: 1.0,
      circle: {x: sfc, y: 0, r: second_face_r},
      normal_at: (p) => normal_at_circular_boundary(p, {x: sfc, y: 0, r: second_face_r}, false),
      x_crossing: (first_face_x + thickness)
    }
  ]
  draw_aligned_circular_boundary(ctx, boundaries[0].x_crossing, -boundaries[0].circle.r);
  draw_aligned_circular_boundary(ctx, boundaries[1].x_crossing, boundaries[1].circle.r);
  
  return boundaries
}

const draw_entire_diagram = (ctx) => {
  const canvas = document.getElementById('canvas')
  ctx.clearRect(0, 0, canvas.width, canvas.height);
  
  // center line and end stops
  draw_axis(ctx);
  draw_aligned_vertical_boundary(ctx, mm(0));
  draw_aligned_vertical_boundary(ctx, mm(1000));

  // an image or a target or similar
  draw_aligned_vertical_boundary(ctx, mm(10));

  const boundaries = []
  let x1 = 0
  let x2 = 0
  let x3 = 0
  let length = mm(10)
  en1(()=>{
    x1 = mm(10) + dist1();
    boundaries.push( ...make_biconvex_boundaries(1.61, thk1(), x1, bnd1(), bnd2()) )
    length += dist1() + thk1()
  })
  en2(()=>{
    x2 = length + dist2();
    boundaries.push( ...make_biconcave_boundaries(1.62, thk2(), x2, bnd3(), bnd4()) )
    length += dist2() + thk2()
  })
  en3(()=>{
    x3 = length + dist3();
    boundaries.push( ...make_biconvex_boundaries(1.61, thk3(), x3, bnd5(), bnd6()) )
    length += dist3() + thk3()
  })
  
  // target
  draw_aligned_vertical_boundary(ctx, sensor())
  boundaries.push({
    n1: 1,
    n2: 1,
    line: {x: sensor(), y: 0},
    normal_at: (p) => ({x:-1, y:0})
  })

  // all the rays
  for( let y = mm(-50); y <= mm(50); y += (mm(50) - mm(-50))/num_rays()) {
    const cast_ray = {start: {x: mm(10), y: y}, direction: {x:10, y:0}}

    let next = cast_ray
    for( let i = 0; i < boundaries.length; i += 1) {
      draw_ray(ctx, next.start, next.direction)
      if( typeof(next) == "string")
        continue;
      if( Math.abs(next.start.y) > mm(75))
        continue;
      next = cast_to_boundary(ctx, next, boundaries[i])
    }
  }
  
  // tracer ray to measure effective focal length
  const cast_ray = { start: {x:mm(0), y:mm(15)}, direction: {x:1, y:0}}
  let next = cast_ray
  draw_highlight_ray(ctx, next.start, next.direction)
  for( let i = 0; i < boundaries.length; i += 1) {
    next = cast_to_boundary(ctx, next, boundaries[i])
  }
  draw_highlight_ray(ctx, next.start, { x: -next.direction.x, y: -next.direction.y} )
  const pint = intersect_ray_ray(cast_ray, next)
  draw_highlight_ray(ctx, {x: pint[0].x, y: pint[0].y}, {x:0, y:mm(-50)})
  
  // update labels
  update_measurements(length, pint[0].x, next.start.y)
}

const update_measurements = (length, efl, highlight_height) => {
  document.querySelector("span#focal_l").innerText = efl
  document.querySelector("span#bfd").innerText = sensor() - length
  document.querySelector("span#hlht").innerText = highlight_height
}

const setupSlider = (ctx, slider, initValue) => {
  // slider.min = 0
  // slider.max = max
  // slider.step = 10
  slider.value = initValue
  slider.addEventListener('input', () => draw_entire_diagram(ctx))
  return () => {
    return Number(slider.value)
  }
}

const setupCheckbox = (ctx, checkbox) => {
  checkbox.addEventListener('click', () => draw_entire_diagram(ctx))
  return (f) => {
    if(checkbox.checked) {
      f()
    }
  }
}

const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');

// const global_scale = (x) => (x * 2)
// const reverse_global_scale = (x) => ( x / 2 )
const mm = (x) => ( x)

const num_rays = setupSlider(ctx, document.querySelector("input#rays"), 4)
const bnd1 = setupSlider(ctx, document.querySelector("input#bnd1"), mm(40.1))
const bnd2 = setupSlider(ctx, document.querySelector("input#bnd2"), mm(537))
const bnd3 = setupSlider(ctx, document.querySelector("input#bnd3"), mm(47))
const bnd4 = setupSlider(ctx, document.querySelector("input#bnd4"), mm(40))
const bnd5 = setupSlider(ctx, document.querySelector("input#bnd5"), mm(235.5))
const bnd6 = setupSlider(ctx, document.querySelector("input#bnd6"), mm(37.9))
const dist1 = setupSlider(ctx, document.querySelector("input#dist1"), mm(10+100))
const dist2 = setupSlider(ctx, document.querySelector("input#dist2"), mm(10))
const dist3 = setupSlider(ctx, document.querySelector("input#dist3"), mm(10.8))
const thk1 = setupSlider(ctx, document.querySelector("input#thk1"), mm(6))
const thk2 = setupSlider(ctx, document.querySelector("input#thk2"), mm(1))
const thk3 = setupSlider(ctx, document.querySelector("input#thk3"), mm(6))
const en1 = setupCheckbox(ctx, document.querySelector("input#en1"))
const en2 = setupCheckbox(ctx, document.querySelector("input#en2"))
const en3 = setupCheckbox(ctx, document.querySelector("input#en3"))
const sensor = setupSlider(ctx, document.querySelector("input#sensor"), //mm(396))
                           //mm(10+100+ 6+10+1+10.8+6+85.3))
                           mm(10+100+ 6+10+1+10.8+6+85.3*2))
draw_entire_diagram(ctx)
              
            
!
999px

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