Fix section describing total internal reflection

With a sphere of index of refraction greater than the surrounding
medium, there is no incoming ray that can be chosen to show total
internal reflection. An incoming ray will be bent to a smaller angle
relative to the surface normal, and then bent back to the original angle
on exit.

To illustrate total reflection, this change renders a bubble of air
inside water. Glancing rays are then reflected off the surface instead
of refracted.

In the service of this change, I've also moved the center sphere back
a bit from the left and right spheres so you can see the affected side
more clearly. This will invalidate all of the other three-sphere images,
which will be fixed up in #1358 (Alpha.2 milestone verify Book 1
progression).

Resolves #900

Author: hollasch

books/RayTracingInOneWeekend.html

@@ -3067,7 +3067,7 @@
         auto material_right  = make_shared<metal>(color(0.8, 0.6, 0.2));
 
         world.add(make_shared<sphere>(point3( 0.0, -100.5, -1.0), 100.0, material_ground));
-        world.add(make_shared<sphere>(point3( 0.0,    0.0, -1.0),   0.5, material_center));
+        world.add(make_shared<sphere>(point3( 0.0,    0.0, -1.2),   0.5, material_center));
         world.add(make_shared<sphere>(point3(-1.0,    0.0, -1.0),   0.5, material_left));
         world.add(make_shared<sphere>(point3( 1.0,    0.0, -1.0),   0.5, material_right));
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
@@ -3309,17 +3309,18 @@
 </div>
 
 <div class='together'>
-Now we'll update the scene to change the left and center spheres to glass:
+Now we'll update the scene to illustrate refraction by changing the left sphere to glass, which has
+an index of refraction of approximately 1.5.
 
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
     auto material_ground = make_shared<lambertian>(color(0.8, 0.8, 0.0));
+    auto material_center = make_shared<lambertian>(color(0.1, 0.2, 0.5));
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
-    auto material_center = make_shared<dielectric>(1.5);
     auto material_left   = make_shared<dielectric>(1.5);
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
     auto material_right  = make_shared<metal>(color(0.8, 0.6, 0.2), 1.0);
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [two-glass]: <kbd>[main.cc]</kbd> Changing left and center spheres to glass]
+    [Listing [two-glass]: <kbd>[main.cc]</kbd> Changing the left sphere to glass]
 
 </div>
 
@@ -3334,9 +3335,10 @@
 
 Total Internal Reflection
 --------------------------
-That definitely doesn't look right. One troublesome practical issue is that when the ray is in the
-material with the higher refractive index, there is no real solution to Snell’s law, and thus there
-is no refraction possible. If we refer back to Snell's law and the derivation of $\sin\theta'$:
+One troublesome practical issue with refraction is that there are ray angles for which no solution
+is possible using Snell's law. When a ray enters a medium of lower index of refraction at a
+sufficiently glancing angle, it can refract with an angle greater than 90&deg;. If we refer back to
+Snell's law and the derivation of $\sin\theta'$:
 
   $$ \sin\theta' = \frac{\eta}{\eta'} \cdot \sin\theta $$
 
@@ -3366,8 +3368,10 @@
 </div>
 
 Here all the light is reflected, and because in practice that is usually inside solid objects, it is
-called “total internal reflection”. This is why sometimes the water-air boundary acts as a perfect
-mirror when you are submerged.
+called _total internal reflection_. This is why sometimes the water-to-air boundary acts as a
+perfect mirror when you are submerged -- if you're under water looking up, you can see things above
+the water, but when you are close to the surface and looking sideways, the water surface looks like
+a mirror.
 
 We can solve for `sin_theta` using the trigonometric qualities:
 
@@ -3434,25 +3438,42 @@
 
 </div>
 
-<div class='together'>
-Attenuation is always 1 -- the glass surface absorbs nothing. If we try that out with these
-parameters:
+Attenuation is always 1 -- the glass surface absorbs nothing.
 
-    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ Highlight
+If we render the prior scene with the new `dielectric::scatter()` function, we see … no change. Huh?
+
+Well, it turns out that given a sphere of material with an index of refraction greater than air,
+there's no incident angle that will yield total internal reflection -- neither at the ray-sphere
+entrance point nor at the ray exit. This is due to the geometry of spheres, as a grazing incoming
+ray will always be bent to a smaller angle, and then bent back to the original angle on exit.
+
+So how can we illustrate total internal reflection? Well, if the sphere has an index of refraction
+_less_ than the medium it's in, then we can hit it with shallow grazing angles, getting total
+_external_ reflection. That should be good enough to observe the effect.
+
+We'll model a world filled with water (index of refraction approximately 1.33), and change the
+sphere material to air (index of refraction 1.00) -- an air bubble! To do this, change the left
+sphere material's index of refraction to
+
+  $$\frac{\text{index of refraction of air}}{\text{index of refraction of water}}$$
+
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
     auto material_ground = make_shared<lambertian>(color(0.8, 0.8, 0.0));
     auto material_center = make_shared<lambertian>(color(0.1, 0.2, 0.5));
-    auto material_left   = make_shared<dielectric>(1.5);
-    auto material_right  = make_shared<metal>(color(0.8, 0.6, 0.2), 0.0);
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
+    auto material_left   = make_shared<dielectric>(1.00 / 1.33);
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
+    auto material_right  = make_shared<metal>(color(0.8, 0.6, 0.2), 1.0);
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [scene-dielectric]: <kbd>[main.cc]</kbd> Scene with dielectric and shiny sphere]
-
-</div>
+    [Listing [two-glass]: <kbd>[main.cc]</kbd> Left sphere is an air bubble in water]
 
 <div class='together'>
-We get:
+This change yields the following render:
+
+  ![<span class='num'>Image 17:</span> Air bubble sometimes refracts, sometimes reflects
+  ](../images/img-1.17-air-bubble-total-reflection.png class='pixel')
 
-  ![<span class='num'>Image 17:</span> Glass sphere that sometimes refracts
-  ](../images/img-1.17-glass-sometimes-refract.png class='pixel')
+Here you can see that more-or-less direct rays refract, while glancing rays reflect.
 
 </div>
 
@@ -3544,7 +3565,7 @@
     auto material_right  = make_shared<metal>(color(0.8, 0.6, 0.2), 0.0);
 
     world.add(make_shared<sphere>(point3( 0.0, -100.5, -1.0), 100.0, material_ground));
-    world.add(make_shared<sphere>(point3( 0.0,    0.0, -1.0),   0.5, material_center));
+    world.add(make_shared<sphere>(point3( 0.0,    0.0, -1.2),   0.5, material_center));
     world.add(make_shared<sphere>(point3(-1.0,    0.0, -1.0),   0.5, material_left));
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
     world.add(make_shared<sphere>(point3(-1.0,    0.0, -1.0),   0.4, material_bubble));
@@ -3812,7 +3833,7 @@
         auto material_right  = make_shared<metal>(color(0.8, 0.6, 0.2), 0.0);
 
         world.add(make_shared<sphere>(point3( 0.0, -100.5, -1.0), 100.0, material_ground));
-        world.add(make_shared<sphere>(point3( 0.0,    0.0, -1.0),   0.5, material_center));
+        world.add(make_shared<sphere>(point3( 0.0,    0.0, -1.2),   0.5, material_center));
         world.add(make_shared<sphere>(point3(-1.0,    0.0, -1.0),   0.5, material_left));
         world.add(make_shared<sphere>(point3(-1.0,    0.0, -1.0),   0.4, material_bubble));
         world.add(make_shared<sphere>(point3( 1.0,    0.0, -1.0),   0.5, material_right));