Week 11: Light
- The speed of light in a medium is:
vmedium=
c
n
(904)
nis called theindex of refractionof the medium. You need to know the following
approximateindices of refraction to work problems: Air:na≈1. Water:nw≈ 4 /3.
Glass:ng≈ 3 /2. Any others needed will be given in the problem in context.
- The index of refraction is not constant – it varies with thefrequencyof the light:
n(ω), a phenomena known asdispersion.
- In the visible range, for most common transparent materials (e.g. normal glass,
water, plastic)n(red)< n(violet, that is, the index of refractionincreases with
frequencyacross the visible spectrum. One can, however, engineer glasses where
the opposite is true. Dispersion curves in general have distinct ranges where the
index of refraction increasesordecreases with frequency across the entire range of
electromagnetic radiation frequencies.
- The Law of Reflection:
The angle of incidence equals the angle of reflection,
θi=θℓ (905)
- Snell’s Law:
n 1 sin(θ 1 ) =n 2 sin(θ 2 ) (906)
- Fermat’s Principle:
Light takes the path that minimizes the time of flight between any twopoints. Both
the law of reflection and Snell’s law can be derived from Fermat’s principle.
- Critical Angle, Total Internal Reflection:
Light passing from a dense mediumn 2 to a less dense mediumn 1 < n 2 istotally
internally reflectedif the angle of incidence is greater than:
θc= sin−^1
(
n 1
n 2
)
(907)
- Polarization:
We describe the orientation and phase of the two components of theelectricfield
component for a given fixed harmonic frequency as thepolarizationof the harmonic
wave.
- Unpolarized Light:
Unpolarized light is light for which the polarization vector is constantlyshifting its
direction around. On average, unpolarized light has its energy/intensity equally
distributed between the two independent directions of polarization.
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