Refraction

Summary

• Refraction is the change in direction of a wave caused by a change in wave speed.
  • An interface is the boundary between two different media…
    • or two regions of a medium with different characteristics such as…
      • density (which is often related to temperature)
      • concentration of solute (salinity, for example)
      • mechanical stress
  • In geometric optics, when an incident ray meets an interface it will be partially
    • reflected
      • Reflected rays obey the law of reflection described in a previous section of this book.
      • Materials that reflect a significant portion of incident light appear shiny or lustrous.
    • transmitted
      • Transmitted rays obey Snell's law of refraction, which is described in this section of this book.
      • Materials that transmit a significant portion of incident light appear clear or transparent.
      • Materials that do not transmit any incident light are said to be opaque.
    • absorbed
      • The energy of absorbed rays is not destroyed, but changes form.
      • Materials that absorb a significant portion of incident light appear dark.
  • Angles are measured with respect to the line normal to the surface.
    • The angle of incidence is the angle between the incident ray and the normal.
    • The angle of reflection is the angle between the reflected ray and the normal.
    • The angle of refraction is the angle between the transmitted ray and the normal.
• Refraction is described mathematically by Snell's law.

  n₁ sin θ₁ = n₂ sin θ₂

  where

  n1 n2 =	indexes of refraction of the two media
  θ1 θ2 =	angles between the ray and the line normal to the surface in the two media

  • Snell's law describes the path of least action between two points in different media
• The index of refraction…
  • is a property of a medium
  • is a measure of the "slowness" of a wave
  • is defined mathematically by the formula

    n =	c
    	v

    where

    n =	index of refraction
    c =	speed of light in a vacuum
    v =	speed of light in a medium

  • is always greater than 1 (since the speed of light in a medium is always slower than the speed of light in a vacuum)
  • has no units (since it is the ratio of two speeds)
  • generally increases with the density of the medium (and is sometimes referred to informally as the optical density)
• Total internal reflection occurs when
  • Snell's law has no real solution
  • light travels from a "slow medium" to a "fast medium" (n₁ > n₂)
  • the incident angle is greater than the critical angle

    sin θc =	n2
    	n1

    • The critical angle is the incident angle that corresponds to a refracted angle of 90° (that is, the transmitted ray travels parallel to the interface)
• Dispersion
  • the speed of light in a medium (and thus the index of refraction) is a function of frequency and medium
• Birefringence