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 and n2 =	indexes of refraction of the two media
θ₁ and 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 θ_c =	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

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© 1998–2012 Glenn Elert