Chapter 25 Reflection and Refraction of Light 2 Fig. 25-CO, p. 839.
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Transcript of Chapter 25 Reflection and Refraction of Light 2 Fig. 25-CO, p. 839.
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Chapter 25
Reflection and Refraction
of Light
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2Fig. 25-CO, p. 839
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25.1 The Nature of Light Before the beginning of the nineteenth
century, light was considered to be a stream of particles
The particles were emitted by the object being viewed, Newton was the chief architect of the particle
theory of light He believed the particles left the object and
stimulated the sense of sight upon entering the eyes
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Nature of Light – Alternative View Christian Huygens argued the light
might be some sort of a wave motion Thomas Young (1801) provided the first
clear demonstration of the wave nature of light He showed that light rays interfere with
each other Such behavior could not be explained by
particles
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More Confirmation of Wave Nature During the nineteenth century, other
developments led to the general acceptance of the wave theory of light
Maxwell asserted that light was a form of high-frequency electromagnetic wave
Hertz confirmed Maxwell’s predictions
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Particle Nature Some experiments could not be
explained by the wave nature of light The photoelectric effect was a major
phenomenon not explained by waves When light strikes a metal surface,
electrons are sometimes ejected from the surface
The kinetic energy of the ejected electron is independent of the frequency of the light
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Dual Nature of Light In view of these developments, light
must be regarded as having a dual nature
In some cases, light acts like a wave, and in others, it acts like a particle
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The Ray Approximation in Geometric Optics
Geometric optics involves the study of the propagation of light
The ray approximation is used to represent beams of light
A ray is a straight line drawn along the direction of propagation of a single wave It shows the path of the wave as it travels through
space It is a simplification model
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Ray Approximation The rays are straight lines
perpendicular to the wave fronts
With the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays
Fig 25.1
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Ray Approximation at a Barrier
A wave meets a barrier with <<d
d is the diameter of the opening The individual waves
emerging from the opening continue to move in a straight line
This is the assumption of the ray approximation
Good for the study of mirrors, lenses, prisms, and associated optical instruments
Fig 25.2(a)
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Ray Approximation at a Barrier, cont
The wave meets a barrier whose size of the opening is on the order of the wavelength, ~d
The waves spread out from the opening in all directions The waves undergo
diffraction
Fig 25.2(b)
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Ray Approximation at a Barrier, final
The wave meets a barrier whose size of the opening is much smaller than the wavelength >> d
The diffraction is so great that the opening can be approximated as a point source
Fig 25.2(c)
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Active Figure25.2
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Reflection of Light A ray of light, the incident ray, travels in
a medium When it encounters a boundary with a
second medium, part of the incident ray is reflected back into the first medium This means it is directed backward into the
first medium
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Specular Reflection
Specular reflection is reflection from a smooth surface
The reflected rays are parallel to each other
All reflection in your text is assumed to be specular
Fig 25.4(a)
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Diffuse Reflection
Diffuse reflection is reflection from a rough surface
The reflected rays travel in a variety of directions
A surface behaves as a smooth surface as long as the surface variations are much smaller than the wavelength of the light
Fig 25.4(b)
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Law of Reflection The normal is a line
perpendicular to the surface It is at the point where the
incident ray strikes the surface The incident ray makes an
angle of θ1 with the normal The reflected ray makes an
angle of θ1' with the normal
Fig 25.5
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Active Figure25.5
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Law of Reflection, cont The angle of reflection is equal to the
angle of incidence θ1'= θ1
This relationship is called the Law of Reflection
The incident ray, the reflected ray and the normal are all in the same plane
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20Fig. 25-6a, p. 844
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21Fig. 25-6b, p. 844
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Multiple Reflections The incident ray strikes the
first mirror The reflected ray is directed
toward the second mirror There is a second reflection
from the second mirror Apply the Law of Reflection
and some geometry to determine information about the rays
Fig 25.7
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Some Additional Points The path of a light ray is reversible
This property is useful for geometric constructions
Applications of the Law of Reflection include digital projection of movies, TV shows and computer presentations Using a digital micromirror device
Contains more than a million tiny mirrors that can be individually tilted and each corresponds to a pixel in the image
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25.4 Refraction of Light When a ray of light traveling through a
transparent medium encounters a boundary leading into another transparent medium, part of the energy is reflected and part enters the second medium
The ray that enters the second medium is bent at the boundary This bending of the ray is called refraction
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Refraction, 2 The incident ray, the reflected ray, the
refracted ray, and the normal all lie on the same plane
The angle of refraction depends upon the material and the angle of incidence
v1 is the speed of the light in the first medium and v2 is its speed in the second medium
constantv
v
sin
sin
1
2
2
1
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Refraction of Light, 3 The path of the light
through the refracting surface is reversible For example, a ray travels
from A to B If the ray originated at B,
it would follow the line AB to reach point A
Fig 25.8
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Following the Reflected and Refracted Rays
Ray is the incident ray Ray is the reflected ray Ray is refracted into the
lucite Ray is internally reflected
in the lucite Ray is refracted as it
enters the air from the lucite
Fig 25.8
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Active Figure25.8
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25.4 Refraction Details, 1 Light may refract into a
material where its speed is lower
The angle of refraction is less than the angle of incidence The ray bends toward the
normal
Fig 25.9
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Refraction Details, 2 Light may refract into a
material where its speed is higher
The angle of refraction is greater than the angle of incidence The ray bends away from
the normal
Fig 25.9
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Light in a Medium The light enters from the left The light may encounter an
atom, as in A The atom may absorb the light,
oscillate, and reradiate the light This can repeat at atom B The absorption and radiation
cause the average speed of the light moving through the material to decrease
Fig 25.10
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The Index of Refraction The speed of light is a maximum in a
vacuum The index of refraction, n, of a medium
can be defined as
speed of light in a vacuumn
average speed of light in a medium
cn
v
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Index of Refraction, cont For a vacuum, n = 1
We assume n = 1 for air, also For other media, n > 1 n is a dimensionless number greater
than unity n is not necessarily an integer
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Some Indices of Refraction
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Frequency Between Media As light travels from one
medium to another, its frequency does not change
Both the wave speed and the wavelength do change
The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same
Fig 25.11
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Index of Refraction Extended The frequency stays the same as the wave
travels from one medium to the other v = ƒ λ
ƒ1 = ƒ2 but v1 v2 so 1 2
The ratio of the indices of refraction of the two media can be expressed as various ratios
1 1 1 2
2 2 12
cv n n
cv nn
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More About Index of Refraction The previous relationship can be
simplified to compare wavelengths and indices: 1 n1 = 2 n2
In air, n1 1 and the index of refraction of the material can be defined in terms of the wavelengths
n
in vacuumn
in material
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Snell’s Law of Refraction
n1 sin θ1 = n2 sin θ2 θ1 is the angle of incidence
θ2 is the angle of refraction
The experimental discovery of this relationship is usually credited to Willebrord Snell and therefore known as Snell’s Law
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25.5 Dispersion For a given material, the index of
refraction varies with the wavelength of the light passing through the material
This dependence of n on λ is called dispersion
Snell’s Law indicates light of different wavelengths is bent at different angles when incident on a refracting material
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Variation of Index of Refraction with Wavelength
The index of refraction for a material generally decreases with increasing wavelength
Violet light bends more than red light when passing into a refracting material
Fig 25.13
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Angle of Deviation The ray emerges
refracted from its original direction of travel by an angle , called the angle of deviation
depends on and the index of refraction of the material
Fig 25.14
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Refraction in a Prism Since all the colors
have different angles of deviation, white light will spread out into a spectrum
Violet deviates the most
Red deviates the least The remaining colors
are in between
Fig 25.15
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The Rainbow A ray of light strikes a drop of water in
the atmosphere It undergoes both reflection and
refraction First refraction at the front of the drop
Violet light will deviate the most Red light will deviate the least
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The Rainbow, 2 At the back surface the light
is reflected It is refracted again as it
returns to the front surface and moves into the air
The rays leave the drop at various angles
The angle between the white light and the most intense violet ray is 40°
The angle between the white light and the most intense red ray is 42°
Fig 25.16
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25.6 Observing the Rainbow
If a raindrop high in the sky is observed, the red ray is seen
A drop lower in the sky would direct violet light to the observer
The other colors of the spectra lie in between the red and the violet
Fig 25.17
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Double Rainbow The secondary rainbow is
fainter than the primary and its colors are reversed
The secondary rainbow arises from light that makes two reflections from the interior surface before exiting the raindrop
Higher-order rainbows are possible, but their intensity is low
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Christiaan Huygens 1629 – 1695 Best known for his
contributions to the fields of optics and dynamics
He considered light to be a kind of vibratory motion, spreading out and producing the sensation of sight when impinging on the eye
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Huygen’s Principle Huygen assumed that light consists of
waves rather than a stream of particles Huygen’s Principle is a geometric
construction for determining the position of a new wave at some point based on the knowledge of the wave front that preceded it
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Huygen’s Principle, cont All points on a given wave front are
taken as point sources for the production of spherical secondary waves, called wavelets, which propagate outward through a medium with speeds characteristic of waves in that medium
After some time has passed, the new position of the wave front is the surface tangent to the wavelets
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Huygen’s Construction for a Plane Wave
At t = 0, the wave front is indicated by the plane AA’
The points are representative sources for the wavelets
After the wavelets have moved a distance cΔt, a new plane BB’ can be drawn tangent to the wavefronts
BB’ is parallel to AA’
Fig 25.18
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Huygen’s Construction for a Spherical Wave
The inner arc represents part of the spherical wave
The points are representative points where wavelets are propagated
The new wavefront is tangent at each point to the wavelet
Fig 25.18
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Huygen’s Principle, Example Waves are generated in a
ripple tank Plane waves produced to the
left of the slits emerge to the right of the slits as two-dimensional circular waves propagating outward
At a later time, the tangent of the circular waves remains a straight line
Fig 25.19
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Huygen’s Principle and the Law of Reflection The Law of Reflection
can be derived from Huygen’s Principle
AB is a wave front of incident light
The wave at A sends out a wavelet centered on A toward D
The wave at B sends out a wavelet centered on B toward C
AD = BC = c tFig 25.20
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Huygen’s Principle and the Law of Reflection, cont Triangle ABC is
congruent to triangle ADC
cos = BC / AC cos ’ = AD / AC Therefore, cos = cos
’ and ’ This gives θ1 = θ1’ This is the Law of
Reflection Fig 25.20
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Huygen’s Principle and the Law of Refraction Ray 1 strikes the
surface and at a time interval t later, ray 2 strikes the surface
During this time interval, the wave at A sends out a wavelet, centered at A, toward D
Fig 25.21
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Huygen’s Principle and the Law of Refraction, cont The wave at B sends out a wavelet,
centered at B, toward C The two wavelets travel in different
media, therefore their radii are different From triangles ABC and ADC, we find
1 21 2sin sin
v t v tBC ADand
AC AC AC AC
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Huygen’s Principle and the Law of Refraction, final The preceding equation can be simplified to
This is Snell’s Law of Refraction
1 1
2 2
1 1 2
2 2 1
1 1 2 2
sin
sin
sin
sin
sin sin
v
v
c n nBut
c n n
and so n n
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25.7 Total Internal Reflection A phenomenon called total internal
reflection can occur when light is directed from a medium having a given index of refraction toward one having a lower index of refraction
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Possible Beam Directions Possible directions
of the beam are indicated by rays numbered 1 through 5
The refracted rays are bent away from the normal since n1 > n2
Fig 25.22
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Critical Angle There is a particular
angle of incidence that will result in an angle of refraction of 90° This angle of
incidence is called the critical angle, C
21 2
1
sin C
nfor n n
n
Fig 25.22
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Active Figure25.22
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Critical Angle, cont For angles of incidence greater than the
critical angle, the beam is entirely reflected at the boundary This ray obeys the Law of Reflection at the
boundary Total internal reflection occurs only
when light is directed from a medium of a given index of refraction toward a medium of lower index of refraction
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25.8 Optical Fibers An application of
internal reflection Plastic or glass rods are
used to “pipe” light from one place to another
Applications include medical use of fiber optic
cables for diagnosis and correction of medical problems
TelecommunicationsFig 25.25
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Optical Fibers, cont A flexible light pipe
is called an optical fiber
A bundle of parallel fibers (shown) can be used to construct an optical transmission line
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Construction of an Optical Fiber The transparent
core is surrounded by cladding
The cladding has a lower n than the core
This allows the light in the core to experience total internal reflection
The combination is surrounded by the jacket Fig 25.26
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Multimode, Stepped Index Fiber Stepped index
comes from the discontinuity in n between the core and the cladding
Multimode means that light entering the fiber at many angles is transmitted
Fig 25.27
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Multimode, Graded Index Fiber This fiber has a core
whose index of refraction is smaller at larger radii from the center
The resultant curving reduces transit time and reduces spreading out of the pulse
Fig 25.29
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Optical Fibers, final Optical fibers can transmit about 95% of
the input energy over one kilometer Minimization of problems includes using
as long a wavelength as possible Much optical fiber communication uses
wavelengths of about 1 300 nm.
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94Fig. 25-30, p. 857