124 Physics Spring 2012 Document #19: Cycle 4 Review Sheet Part 2
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PHYS 124: Cycle 4 Review Sheet Part 2: Physical Optics
Geometric vs. Physical Optics:
The study of Optics divides neatly into two regimes, depending on the size of the wave compared to the optical elements of the system:
If the wavelength of the light is small compared to the any dimension of the system, we can
ignore the details of the wave itself, and treat the light as a simple ray that moves in a straight
line from one position to another. We call this regime Geometrical Optics. In this case, we
use the technique of ray tracing to follow the path of the light ray as it reects and refracts
through optical components. item If the wavelength of the light is comparable to or larger
than any dimension of the system, we cannot ignore the details of the wave. In this case
phenomena the light may diffract and/or interfere. This regime is called Physical Optics.
To deal with this, we usually apply Huygenss Principle.
Principle of Superposition and Interference
When two waves encounter each other in a medium, they simply add together at each point
in the medium. This summing results in the effect we call interference. If one wave overlaps a
second wave, and both waves are displacements in the same direction, then the increased amplitude
is called constructive interference. If on the other hand the displacements are opposite, the waves
cancel each other out at just the point of overlap, and we have destructive interference.
Note that the property of interference is unique to waves.
Huygenss Principle and Diffraction
Make sure you have a clear understanding of Huygenss Principle. Basically any point on
a wave front can be considered as a point source of that wave. This results in the interesting
effect called diffraction which is the property that waves tend to bend around sharp corners. Like
interference, diffraction is a physical property that is unique to waves.
Youngs Double Slit experiment:
Be sure that you understand this experiment and what it means. Here is a diagram showing
how the experiment works.
Physics Spring 124 2012 Document #19: Cycle 4 Review Sheet Part 2
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wave
crests
Wall
Constructive
interference
at circles:
maxima
(bright)
minima
(dark)
Study Figure 24.7 on page 1107 of Reese which can be used to derive the positions of maxima
(bright fringes) and minima (dark fringes) on a target:
m = d sin
1
(m + ) = d sin
2
(maxima)
(minima)
Single Slit Diffraction
A single slit will also result in a diffraction interference pattern, due to the sharp edges on
either side of the slit. However, this will not be as distinct as the patter for a double slit. For subtle
reasons the single slit equation gives the position of the minima not the rst maxima according to
m = d sin
Physics 124 Spring 2012 Document #19: Cycle 4 Review Sheet Part 2
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Diffraction Grating
By going to multiple slits we set up a diffraction grating. The maxima are much more tightly
positioned. The position of the maxima are given by the same equation as for the double slit:
m = d sin
(maxima)
Since the angle to the maxima is wavelength dependent, the grating gives a nice dispersion
effect which is to say it breaks white light up into the rainbow of colors.
For either Double Slit or a Diffraction Grating, you should be able to determine the position of
maxima on a target at a given distance, when a source of light of a given wavelength is imposed.
Polarization
Since light is a transverse wave, the electric eld may oscillate in any plane perpendicular to
the direction of propagation. If we dene a reference angle for this, then the plane angle relative
to the reference is called the polarization angle for a single coherent wave. We say the wave is
polarized in a particular plane.
Most sources of light are unpolarized. This corresponds to generating waves at a variety of
polarization angles.
A polaroid lter allows only the component of an electromagnetic wave that is aligned with the
direction of the lter. Since the intensity of the light is proportional to the square of the amplitude,
we can write an expression for the transmission of polarized light through a polaroid lter:
I = I0 cos2