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
• If a ray of light travels from…
  • a medium with a low index to a medium with a high index (n₁ < n₂)…
    • it slows down
    • it refracts toward the normal
  • a medium with a high index to a medium with low index (n₁ > n₂)…
    • it speeds up
    • it refracts away from the normal
• 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
  • occurs when the speed of light in a medium (and thus the index of refraction) is a function of frequency and medium
    • Informally, this can be summarized as different colors travel at different speeds in some media.
  • can be used to produce a spectrum
    • violet refracts the most (n is "large", v is "slow" for violet light)
    • red refracts the least (n is "small", v is "fast" for red light)
  • is the cause of the colors seen in…
    • rainbows (sunlight passing through raindrops)
    • halos (sunlight passing through ice crystals)

  

• Birefringence