Chapter 35: The Nature of Light and the Laws of Geometric Optics
Learning Goals
- Understand the properties of light.
- Understand the assumptions of ray optics.
- Understand reflection and refraction.
- Understand Huygen's principle.
- Understand dispersion and total internal reflection.
Geometric Optics
In geometric optics, light beams are characterized by
light rays which point in the direction of energy flow.
This is in contrast with physical optics where light is
characterized by its wave properties.
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:
qi = qt
and the law of refraction (Snells law):
nisin(qi) = ntsin(qt)
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
where c is the speed of light in vacuum, and v is the speed of light
in the region.
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
Total internal reflection occurs when the incident medium
has the higher index of refraction (e.g. incident region is glass,
transmitted region is air), hence the name internal.
In this case, there is no transmitted ray and the incident beam is
totally (100%) reflected. For a given incident medium, this occurs
for all incident angles greater than a
critical angle qc
given by
where n is the relative index of refraction
ni/nt. For internal incidence, n > 1 always.
Huygen’s Principle
states that all points on a wave front can be
considered as point sources for the production of
secondary wavelets.
Fermat’s Principle
states that when light travels between any two points,
the path taken is the one that requires the least time.