Why does a straw look bent in a glass of water? Why does a diamond sparkle? Why can a thin glass fibre carry your internet connection across an ocean? All three answers come from one equation.
Reflection and Refraction
Snell's law and total internal reflectionSnell’s law
When light crosses from one transparent material into another, it changes speed — and because it changes speed, it changes direction. The relationship is:
n₁ sin θ₁ = n₂ sin θ₂
Here n is the refractive index (a measure of how much the material slows light down) and θ is measured from the normal — an imaginary line at right angles to the surface, not from the surface itself. That detail trips up almost everyone at first.
Light going from a low index to a high index (air into water) bends toward the normal. Light going the other way bends away from it.
The surprise: total internal reflection
Now try the “Water → Air” preset and press Sweep angle. As the angle grows, the refracted ray bends further and further from the normal — until at one specific angle it disappears completely.
That angle is the critical angle, and it only exists when light travels from a higher index into a lower one:
θc = arcsin(n₂ / n₁)
Past it, no light escapes at all. Every bit of it reflects back inside. This is total internal reflection, and it is exactly how fibre-optic cables trap light and carry it for kilometres with almost no loss — and a large part of why cut diamonds return so much light to your eye.
Try this
- Set n₁ = 1.00 and n₂ = 1.50 (air to glass). Sweep and watch the refracted ray always stay closer to the normal than the incoming one.
- Flip it to glass into air. Find the angle where the refracted ray vanishes — it should match the critical angle readout, about 41.8°.
- Set both indices equal. The ray goes straight through, unbent.
Why it matters
Refraction is why lenses work, which means it is why glasses, cameras, microscopes and telescopes exist. It is why the sky reddens at sunset and why a swimming pool looks shallower than it is. And total internal reflection is the backbone of modern communications.