What if light reflected differently?

Shine a light down into water. Some light bounces off the top. Most light goes in.

Now put the light inside the water and shine it out toward the air. Will it always get out?

When light meets the surface of water or glass, two things happen at once. Some of it bounces off, like a ball off a wall: that's reflection. The rest goes through, but changes direction as it crosses: that's refraction, the bending that makes a fish in a tank seem to be in the wrong place.

In this lab, a laser inside the water shines at the surface, toward the air on the other side. What if you tilt it more and more? Does light always get out, or can the reflection take over completely?

At a boundary between two transparent materials, an incoming ray splits into a reflected ray, at the same angle as it arrived, and a refracted ray, bent according to Snell's law. How the light divides between them depends on the angle and the two refractive indices.

This lab starts with a laser in water (n = 1.333) aimed at the surface at 30° from the normal, then tilts it to 60°. The question: is there an angle beyond which none of the light can escape into the air?

The laser is in the water. It points at the air, a little tilted.

The light comes out into the air. It bends as it comes out. A tiny bit bounces back into the water.

In the model, the laser is in the water, tilted 30 degrees from the dashed line that runs straight through the surface. When the beam crosses into the air, it bends away from the dashed line and leaves at about 42 degrees.

At the same time, a weak reflected beam bounces back into the water at 30 degrees, exactly the angle it arrived at. Only about 2.6 percent of the light is reflected; about 97 percent gets out into the air.

With n₁ = 1.333 and n₂ = 1.000, a ray at θ₁ = 30° refracts to θ₂ = asin(1.333 × sin 30°) ≈ 41.8°, bending by 11.8°. The reflected ray leaves at 30°, by the law of reflection.

The unpolarized Fresnel reflectance at this angle is about 2.6%, so 97.4% of the light is transmitted. Even straight on (0°), about 2.0% reflects: some reflection always accompanies a change of refractive index.

Olly tilts the laser more. The light bends more and more as it comes out.

Then, at a big tilt, no light comes out at all! It all bounces back into the water.

Tilt the laser farther and the bent beam swings closer and closer to the water's surface. At 45 degrees it leaves at about 70 degrees, and the reflection grows to about 14 percent. At 48 degrees the beam leaving the water almost skims the surface, and 43 percent reflects.

Then, just past about 48.6 degrees, the outgoing beam vanishes. At 60 degrees, every bit of the light bounces back inside the water. This is called total internal reflection.

As θ₁ rises, θ₂ approaches 90° and the reflectance climbs steeply: 13.9% at 45°, 43.3% at 48°. At θ_c = asin(n₂/n₁) = asin(1/1.333) ≈ 48.6°, the refracted ray grazes the surface.

Beyond θ_c, Snell's law would require sin θ₂ > 1, so there is no transmitted ray and the reflectance is 100%. At the lab's what-if angle of 60°, the model reports total internal reflection, with the reflected beam leaving at 60°.

Light goes faster in air than in water. That change makes it bend.

At a big tilt, the light would have to bend too far. So it cannot get out.

Light travels faster in air than in water. When a tilted beam crosses from water into air, the change of speed makes it bend away from the dashed line, and the more tilted the beam, the more it bends.

At about 48.6 degrees, the outgoing beam would already be running along the surface. Any more tilt and it would have to bend past flat, which it can't. So instead, all the light reflects. Our model treats the surface as perfectly flat and smooth, and the laser as one color.

The refractive index n = c/v compares light's speed in a vacuum with its speed in the material. Matching wavefronts across the boundary gives Snell's law; when n₁ > n₂ the refracted angle exceeds the incident one, reaching 90° at θ_c. Fresnel's equations give how the light divides, rising to 100% reflection at and beyond θ_c.

Model limits: one refractive index per material (real water varies from about 1.331 to 1.343 across visible colors), a flat, clean, non-absorbing boundary, unpolarized light and pure ray optics. Weak beams are drawn brighter than their true strength; the percentages are the modeled values.

Thin glass threads can trap light inside. The light bounces along the thread.

Threads like these carry phone calls and the internet.

Total internal reflection is put to work every day. Optical fibers are thin threads of glass or plastic. Light inside them keeps hitting the wall at a steep slant, so it reflects again and again and stays trapped inside. Fibers like these carry telephone, internet and cable TV signals.

You can see it in a swimming pool too. Look up at the surface from underwater, at a slant, and it acts like a mirror, reflecting the pool below.

OpenStax describes fiber optics as a widely used application of total internal reflection, carrying telephone, internet and cable TV signals: in a thin fiber, light is likely to strike the wall beyond the critical angle and be totally reflected. Prisms using total internal reflection serve as perfect mirrors in binoculars and periscopes.

Critical angles depend on the pair of materials: 48.6° for water to air, about 41.8° for glass (n = 1.5) to air in the model, and only 24.4° for diamond to air. OpenStax uses that small angle to explain the sparkle of diamonds.