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Chapter 32
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Electromagnetic Waves (cont.)
Standing electromagnetic waves
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Electromagnetic waves can be reflected by a
conductor or dielectric, which can lead to standing
waves. (See Figure 32.22 below.)
Mathematically, standing waves are a superposition
of incoming and outgoing waves.
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Q32.8
The drawing shows
a sinusoidal
electromagnetic
standing wave. The
average Poynting
vector in this wave
A. points along the x-axis.
B. points along the y-axis.
C. points along the z-axis.
D. is zero.
E. none of the above
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A32.8
The drawing shows
a sinusoidal
electromagnetic
standing wave. The
average Poynting
vector in this wave
A. points along the x-axis.
B. points along the y-axis.
C. points along the z-axis.
D. is zero.
E. none of the above
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Chapter 33
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The Nature and Propagation of Light
The nature of light

Light has properties of
both waves and particles.
The wave model is easier
for explaining
propagation, but some
other behavior requires
the particle model.

The rays are
perpendicular to the wave
fronts (cross sections of the wave
which are in phase).

This chapter will
concentrate on the ray
perspective
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Reflection and refraction
When light strikes a surface, it is (in general) both reflected and refracted.
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Specular and diffuse reflection
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Specular reflection occurs at a very smooth surface (left
figure).
Diffuse reflection occurs at a rough surface (right figure).
Our primary concern is with specular reflection.
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Laws of reflection and refraction
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The index of refraction is
n = c/v >1.
Angles are measured
with respect to the
normal.
Reflection: The angle of
reflection is equal to the
angle of incidence.
Refraction: Snell’s law
applies.
In a material  = 0/n.
Figure 33.7 (right)
illustrates the laws of
reflection and refraction.
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Reflection and refraction in three cases
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Figure 33.8 below shows three important cases:
 If nb > na, the refracted ray is bent toward the normal.
 If nb < na, the refracted ray is bent away from the normal.
 A ray oriented along the normal never bends.
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Why does the ruler appear to be bent?
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The straight ruler in Figure
33.9(a) appears to bend at
the surface of the water.
Figure 33.9(b) shows why.
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Some indexes of refraction
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Q33.2
Light passes from vacuum (index of refraction n = 1) into
water (n = 1.333).
If the incident angle qa is in the range 0° < qa < 90°,
A. the refracted angle is greater than the incident angle.
B. the refracted angle is equal to the incident angle.
C. the refracted angle is less than the incident angle.
D. the answer depends on the specific value of qa .
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A33.2
Light passes from vacuum (index of refraction n = 1) into
water (n = 1.333).
If the incident angle qa is in the range 0° < qa < 90°,
A. the refracted angle is greater than the incident angle.
B. the refracted angle is equal to the incident angle.
C. the refracted angle is less than the incident angle.
D. the answer depends on the specific value of qa .
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Q33.1
When light passes from vacuum (index of refraction n = 1)
into water (n = 1.333),
A. the wavelength increases and the frequency is unchanged.
B. the wavelength decreases and the frequency is unchanged.
C. the wavelength is unchanged and the frequency increases.
D. the wavelength is unchanged and the frequency decreases.
E. both the wavelength and the frequency change.
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A33.1
When light passes from vacuum (index of refraction n = 1)
into water (n = 1.333),
A. the wavelength increases and the frequency is unchanged.
B. the wavelength decreases and the frequency is unchanged.
C. the wavelength is unchanged and the frequency increases.
D. the wavelength is unchanged and the frequency decreases.
E. both the wavelength and the frequency change.
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Q33.3
Light passes from a medium of index of refraction na into a
second medium of index of refraction nb. The angles of
incidence and refraction are qa and qb, respectively.
If na < nb,
Aqa > qb and the light speeds up as it enters the second medium.
B. qa > qb and the light slows down as it enters the second medium.
C. qa < qb and the light speeds up as it enters the second medium.
D. qa < qb and the light slows down as it enters the second medium.
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A33.3
Light passes from a medium of index of refraction na into a
second medium of index of refraction nb. The angles of
incidence and refraction are qa and qb, respectively.
If na < nb,
Aqa > qb and the light speeds up as it enters the second medium.
B. qa > qb and the light slows down as it enters the second medium.
C. qa < qb and the light speeds up as it enters the second medium.
D. qa < qb and the light slows down as it enters the second medium.
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Total internal reflection
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Light striking at the critical angle emerges tangent to the
surface. (See Figure 33.13 below.)
If qa > qcrit, the light is undergoes total internal reflection.
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Some applications of total internal reflection
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A binocular using Porro prisms (below)
and a “light pipe” (right) make use of
total internal reflection in their design.
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A diamond and a periscope
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Diamonds sparkle because they are cut so that total
internal reflection occurs on their back surfaces. See
Figure 33.17 below.
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Dispersion
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Dispersion: The index of
refraction depends on the
wavelength of the light. See
Figure 33.18 (right).
Figure 33.19 (below) shows
dispersion by a prism.
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