Reflection and Refraction
Consider a light ray which encounters a surface separating two regions with different indices of refraction, as shown below.
The reflected and transmitted ray directions are given by the law of reflection:
and the law of refraction (Snells law):
where qi and qt are defined in the figure above, and ni and nt are the indices of refraction in the incident and transmitted regions. The index of refraction is defined by
Note that since the velocity decreases when the region is not a vacuum, the product fl must also decrease. It is interesting that the frequency remains unchanged (frequency determines color); it is the wavelength that changes:
where l0 is the vacuum wavelength and ln is the wavelength in the medium with index of refraction n.
Total Internal Reflection
This occurs when a ray traveling in a medium with higher index of refraction is completely reflected at the boundary of a medium with lower index of refraction. This will occur for any incident angles that is greater than the critical angle:
sin(θc) = nt/ni
For example, for an air-glass interface,
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