Chapter 33
The Nature and
Propagation of Light
PowerPoint® Lectures for
University Physics, Thirteenth Edition
– Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 33
• To understand light rays and wavefronts
• To analyze reflection and refraction of light
• To understand total internal reflection
• To analyze the polarization of light
• To use Huygens’s principle to analyze reflection
and refraction
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Introduction
• Why does a rainbow of colors
appear when these tools are
placed between polarizing
filters?
• Our study of light will help us
understand why the sky is
blue and why we sometimes
see a mirage in the desert.
• Huygens’s principle will
connect the ray and wave
models of light.
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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. See Figure
33.4 at the right.
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Reflection and refraction
• In Figure 33.5 the light is both reflected and refracted by the window.
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Specular and diffuse reflection
• 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
• The frequency does not change on
passing through a surface, but
velocity does, and so wavelength.
• f = f0 => v/l = v0/l0=> v/cl = v0/cl0
• 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 l = l0/n.
• Figure 33.7 (right) illustrates the
laws of reflection and refraction.
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Reflection and refraction in three cases
• Figure 33.8 below shows three important cases:
ü If nb > na, the refracted ray is bent toward the normal.
ü If nb < na, the refracted ray is bent away from the normal.
ü A ray oriented along the normal never bends.
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Why does the ruler appear to be bent?
• 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
Air 1.00029
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An example of reflection and refraction
• Read Problem-Solving Strategy 33.1.
• Example 33.1, find the angles of reflection (qr) and refraction
(qb). Use Figure 33.11 below.
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The eye and two mirrors
• Example 33.3 reflection from two mirrors. Use Figure 33.12
below.
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Total internal reflection
• Light striking at the critical angle emerges tangent to the surface.
(See Figure 33.13 below.) na sin qa = nb sin qb = nb for total internal reflection
• If qa > qcrit, the light is undergoes total internal reflection.
qcrit = sin -1 ( nb / na )
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Some applications of total internal reflection
• A binocular using Porro prisms (below)
and a “light pipe” (right) make use of
total internal reflection in their design.
Can the above
work if the outside
of the rod is air?
How do optical
fibers work?
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A diamond and a periscope
• Diamonds sparkle because they are cut so that total internal
reflection occurs on their back surfaces. See Figure 33.17 below.
• Example 33.4, leaky, crown-glass periscope.
• Why will periscope no longer work if
one of the prisms is in water?
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Dispersion
• 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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Rainbows—I
• The formation of a rainbow is due to the combined effects of
dispersion, refraction, and reflection. (See Figure 33.20 below
and on the next slide.)
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Rainbows—II
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Polarization
• An electromagnetic wave is linearly polarized if
the electric field has only one component.
E( x, t ) = ˆjEmax cos(kx - wt )
B( x, t ) = kˆ B cos(kx - wt )
max
• Figure 33.23 at the right shows a Polaroid
polarizing filter.
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Malus’s law
• Figure 33.25 below shows a polarizer and an analyzer.
• A polarizer reduces the intensity of unpolarized light (I0) by a factor of 2, so
the intensity of transmitted light is I0/2.
• A second polarizer (the analyzer) at angle f relative to the first further reduces
the intensity according to:
Malus’s law: I = Imaxcos2f.
• Example 33.5.
polarizer and
analyzer with
f = 30°.
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Polarization by reflection
• When light is reflected at the polarizing angle qp (Brewster’s angle), the
reflected light is linearly polarized. See Figure 33.27 below.
• The polarizing angle qp is when the reflected and refracted rays are 90° from
each other, i.e. when qp + qb = 90 °.
na sin q p = nb sin qb
na sin q p = nb sin(90 - q p ) = nb cos q p
nb
tan q p = (Brewster's Law)
na
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Reflection from a swimming pool
• Follow Example 33.6 using Figure 33.29 below.
fully polarized
partially polarized
partially polarized
fully polarized
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Circular polarization
• Circular polarization results from the superposition of two
perpendicularly polarized electromagnetic waves having equal
amplitude but a quarter-cycle phase difference. The result is that
the electric field vector has constant amplitude but rotates about
the direction of propagation. (Figure 33.30 below.)
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Scattering of light
• Scattering occurs when light has been absorbed by
molecules and reradiated.
• Figure 33.32 below shows the effect of scattering for
two observers.
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Why are clouds white?
• Clouds are white because they scatter all wavelengths
efficiently. See Figure 33.33 below.
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Huygens’s principle
• Huygens’s principle: Every
point of a wave front can be
considered to be a source of
secondary wavelets that
spread out in all directions
with a speed equal to the
speed of propagation of the
wave. See Figure 33.34 at
the right.
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Reflection and Huygens’s principle
• Figure 33.35 at the right
shows how Huygens’s
principle can be used to
derive the law of
reflection.
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Refraction and Huygens’s principle
• Huygens’s principle can be used to derive the law of refraction.
• Follow the text analysis using Figure 33.36 below.
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A mirage
• Huygens’s principle can also explain the formation of a
mirage. See Figure 33.37 below.
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