Snell's Law of Refraction

When light passes from one transparent material into another, it bends at the boundary — this is called refraction. Light bends toward the normal (an imaginary line perpendicular to the surface) when entering a denser material, and away from the normal when entering a less dense one.

n₁ · sin θ₁ = n₂ · sin θ₂

  • n₁ — refractive index (unitless): how much the first material slows down light
  • θ₁ — angle of incidence (°): the angle of the incoming ray, measured from the normal
  • n₂ — refractive index (unitless): how much the second material slows down light
  • θ₂ — angle of refraction (°): the angle of the bent ray inside the second material, measured from the normal

A ray of light grazes along the surface of an unknown liquid, entering at ninety degrees from the normal, and bends to thirty degrees from the normal inside the liquid. What is the liquid's refractive index?

  • n₁ = 1 (air)
  • θ₁ = 90°
  • θ₂ = 30°
  1. n₂ = (n₁ · sin θ₁) / sin θ₂
  2. n₂ = (1 · sin 90°) / sin 30° = (1 × 1) / 0.5

n₂ = 2

This liquid has a refractive index of 2. Light traveling inside it hits the surface, trying to escape back into air. What is the sine of the critical angle for total internal reflection?

  • 0.5
  • 2
  • 1

Now suppose the liquid is even denser, with a refractive index of 4 instead of 2. Light again grazes in at ninety degrees. Compared to before, does the refracted ray bend closer to or further from the normal?

  • Further from the normal
  • Closer to the normal
  • No change