The Physics
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Opus in profectus

# Refraction

## Summary

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• 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