Waves: Snell's Law

Waves: Snell’s Law

  • Snell’s Law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
  • The law is named after the Dutch astronomer Willebrord Snellius, who formulated it in 1621.
  • The formula for Snell’s law is n1sinθ1 = n2sinθ2.
    • n1 and n2 represent the refractive indices of the two media.
    • θ1 is the angle between the incident ray and the normal (perpendicular line to the boundary) in the first medium.
    • θ2 is the angle between the refracted ray and the normal in the second medium.
  • Refractive index of a medium is a measure of how much the speed of light (or another wave) is reduced inside the medium, compared to the speed of light in a vacuum.
  • Snell’s Law allows the calculation or prediction of the angle of a refracted ray if the angle of incidence is known and the mediums’ refractive indices are known.
  • If a light wave travels from a medium with a high refractive index to one with a lower refractive index, it bends away from the normal. Conversely, if it goes from a low to a high refractive index, it bends towards the normal.
  • Total Internal Reflection (TIR) occurs when the light travels from a denser medium to a less dense medium at an angle larger than the critical angle. In this case, Snell’s Law still applies as the refracted angle would be 90 degrees.
  • Applications of Snell’s Law extend to optics (like lenses and prisms), fibre optic cables (which use TIR), and understanding certain visual phenomena like mirages and rainbows.
  • When revising Snell’s Law, make sure to practise drawing ray diagrams to understand the behaviour of waves. It’s also important to be comfortable with solving problems using the Snell’s Law formula.