EM Waves, Physical Optics and Geometric Optics
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EM Waves
• Electromagnetic Waves
– An electromagnetic wave has a frequency f and a wavelength λ that
are related to the speed of the wave by:
v f
– Light is the most common example of an electromagnetic wave.
• electromagnetic waves include the microwaves you use to heat up
leftovers for dinner, and the radio waves that are broadcast from radio
stations.
– An electromagnetic wave can be created by accelerating charges; moving
charges back and forth will produce oscillating electric and magnetic fields,
and these travel at the speed of light. It would really be more accurate to
call the speed "the speed of an electromagnetic wave", because light is just
one example of an electromagnetic wave.
• speed of light in vacuum: c = 3.00 x 108 m/s
• Since all electromagnetic waves travel at the speed of light the wave
equation becomes:
C=f λ
– C is the ultimate speed limit in the universe.
• Nothing can travel faster than light in a vacuum.
C
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EM Waves
• Structure of Electromagnetic Waves
– An electromagnetic wave (such as a radio wave) propagates
outwards from the source (an antenna, perhaps) at the speed of
light.
• What this means in practice is that the source has created oscillating
electric and magnetic fields, perpendicular to each other, that travel
away from the source.
• The E and B fields of the EM wave
– Are perpendicular to each other
– are perpendicular to the direction the wave travels
– Therefore electromagnetic waves are transverse waves.
» The energy of the wave is stored in the electric and magnetic fields.
E and B vary
sinusoidally
with x
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EM Waves
•
Electromagnetic Waves
– Properties of electromagnetic waves
• Something interesting about light, and electromagnetic waves in general, is that
no medium is required for the wave to travel through. Other waves, such as sound
waves, can not travel through a vacuum. An electromagnetic wave is perfectly
happy to do that.
• An electromagnetic wave, although it carries no mass, does carry energy.
– The energy carried by an electromagnetic wave is proportional to the
frequency of the wave. Remember that wavelength and frequency of the
wave are connected via the speed of light
c f
– Electromagnetic waves are split into different categories based on their
frequency (or, equivalently, on their wavelength).
• Visible light, for example, ranges from violet to red. Violet light has a wavelength
of 400 nm, and a frequency of 7.5 x 1014 Hz. Red light has a wavelength of 700
nm, and a frequency of 4.3 x 1014 Hz. Any electromagnetic wave with a frequency
(or wavelength) between those extremes can be seen by humans.
– Visible light makes up a very small part of the full electromagnetic
spectrum. Electromagnetic waves that are of higher energy than visible
light (higher frequency, shorter wavelength) include ultraviolet light, Xrays, and gamma rays. Lower energy waves (lower frequency, longer
wavelength) include infrared light, microwaves, and radio and television
waves.
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EM Waves
ROY G BIV
once said
“So many
waves, so
little time”
•
•
•
Note the
overlap
between
types of
waves
Visible light
is a small
portion of
the spectrum
Types are
distinguished
by frequency
or wavelength
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EM Waves
•
Types of Electromagnetic Waves
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Radio Waves
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Microwaves
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Infrared waves
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Visible light
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Ultraviolet light
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X-rays
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Gamma rays
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Wavelengths of more than 104 m to about 0.1 m
Used in radio and television communication systems
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Wavelengths from about 0.3 m to 10-4 m
Well suited for radar systems
Microwave ovens are an application
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Wavelengths of about 10-3 m to 7 x 10-7 m
Incorrectly called “heat waves”
Produced by hot objects and molecules
Readily absorbed by most materials
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Part of the spectrum detected by the human eye
The human eye is most sensitive at about 5.5 x 10-7 m (yellow-green)
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Covers about 4 x 10-7 m to 6 x 10-10 m
Sun is an important source of uv light
Most uv light from the sun is absorbed in the stratosphere by ozone
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Wavelengths of about 10-8 m to 10-12 m
Most common source is acceleration of high-energy electrons striking a metal target
Used as a diagnostic tool in medicine
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Wavelengths of about 10-10 m to 10-14 m
Emitted by radioactive nuclei
Highly penetrating and cause serious damage when absorbed by living tissue
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EM Waves
•
Gamma Rays
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EM Waves
•
Studying the Universe with Electromagnetic Waves
– These are images of the Crab Nebula
• They are (clockwise from upper left) taken with
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x-rays
visible light
radio waves
infrared waves
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• EM Wave Polarization
–
polarized light is a form of polarized EM wave.
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•
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light in which there's a preferred direction for the electric and magnetic field vectors in the
wave.
unpolarized light
–
there is no preferred direction: the waves come in with electric and magnetic field vectors in random
directions.
» Most light sources emit unpolarized light
How can light be polarized?
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•
–
Optics
Reflection-Light reflecting off a surface will tend to be polarized, with the direction of
polarization (the way the electric field vectors point) being parallel to the plane of the
interface.
selectively absorbing light with electric field vectors pointing in a particular direction.
–
Certain materials, known as dichroic materials, do this, absorbing light polarized one way
Liquid crystal displays, such as those in digital watches and calculators, also exploit
the properties of polarized light.
Sunglasses can be polarized (with lenses that only allow vertically polarized light to
pass through)
Liquid crystalline material is
sandwiched between two glass
plates that have seven electrodes,
which can be individually charged,
attached to them. Light passing
through Polarizer 1 is polarized in
the vertical direction and, when no
current is applied to the
electrodes, the liquid crystalline
phase induces a 90 degree twist of
the light and it can pass through
Polarizer 2, which is polarized
horizontally. This light can then
form one of the seven segments on
the display.
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•
The Nature of Light
–
Optics
Before the beginning of the nineteenth century, light was considered to be a stream
of particles
•
The particles were either emitted by the object being viewed or emanated from the eyes of the viewer
• Newton was the chief architect of the particle theory of light
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–
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Christian Huygens argued that light might be some sort of a wave motion
Thomas Young (1801) provided the first clear demonstration of the wave nature of
light
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Maxwell asserted that light was a form of high-frequency electromagnetic wave
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Hertz confirmed Maxwell’s predictions
Some experiments could not be explained by the wave nature of light
•
The photoelectric effect was a major phenomenon not explained by waves
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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
Einstein (in 1905) proposed an explanation of the photoelectric effect that used the
idea of quantization
•
•
He showed that light rays interfere with each other
Such behavior could not be explained by particles
During the nineteenth century, other developments led to the general acceptance of
the wave theory of light
•
–
He believed the particles left the object and stimulated the sense of sight upon entering the eyes
The quantization model assumes that the energy of a light wave is present in particles called
photons
In view of these developments, light must be regarded as having a dual
nature
– Light exhibits the characteristics of a wave in some situations and the
characteristics of a particle in other situations, wave-particle duality
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• Light Rays
Optics
– Geometric optics involves the study of the
propagation of light (w/o regard to its wave nature)
– The ray approximation is used to represent beams
of light
• It uses the assumption that light travels in a straightline path in a uniform medium and changes its direction
– when it meets the surface of a different medium
– or if the optical properties of the medium are nonuniform
• A ray of light is a line drawn perpendicular to the wave
front and points in the direction of velocity of the wave
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Optics
• 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
• Specular reflection is reflection from a smooth surface
– The reflected rays are parallel to each other
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The Law of Reflection
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Optics
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
The angle of reflection is equal to the angle of incidence
This relationship is called the Law of Reflection
θr= θi
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The incident ray, the reflected ray and the normal are all in the same plane
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•
Optics
Formation of Images by a Plane Mirror
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The object distance is the distance from the object to the mirror or lens
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The image distance is the distance from the image to the mirror or lens
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Images
•
Denoted by do
•
Denoted by di
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always located by extending diverging rays back to a point at which they intersect
Images are located either at a point from which the rays of light actually diverge or at a point from which they
appear to diverge
A real image is formed when light rays pass through and diverge from the image point
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•
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Real images can be displayed on screens
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Virtual images cannot be displayed on screens
A virtual image is formed when light rays do not pass through the image point but only appear to diverge from that
point
Plane (Flat) Mirrors
–
Simplest possible mirror
•
Light rays leave the source and are reflected from the mirror
•
The image is virtual (always)
• /do/=/di/
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•
Spherical Mirrors
Optics
–
A spherical mirror has the shape of a section of a sphere
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A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of
the curve
A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the
curve
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•
The mirror focuses incoming parallel rays to a point
The mirror has a radius of curvature of R
Its center of curvature is the point C
The distance between the image point (focal point) F and the middle of the mirror is the
focal length f
1
R
2
1
focal length of a convex mirror: f   R
2
focal length of a concave mirror: f 
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Optics
•
Spherical Mirror Images and The Mirror Equation
–
In order to accurately describe an image formed by a concave or convex mirror we can use the
mirror equation and magnification equation below
Mirror Equation:
1 1 1
 
d o di f
f  the focal length of the mirror
d o  the distance between the object and the mirror
di  the distance between the image and the mirror
Magnification Equation:
h
d
m i  i
h0
do
hi  height of the image
ho  height of the object
sign conventions for spherical mirrors
f is + for a concave mirror, - for a convex mirror
d o is + for object in front of mirror, - for object behind mirror
di is + for image in front of mirror, - for image behind mirror
m is + for image that is upright, - for image that is inverted
–
Example 3
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• Ray Diagrams
–
A ray diagram can be used to determine the position and size of an image
They are graphical constructions which reveal the nature of the image
They can also be used to check the parameters calculated from the mirror and magnification
equations
To draw a ray diagram, you need to know:
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Three rays are drawn
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The intersection of any two of the rays at a point locates the image
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Ray 1 is drawn from the top of the object parallel to the principal axis and is reflected through
the focal point, F
Ray 2 is drawn from the top of the object through the focal point and is reflected parallel to
the principal axis
Ray 3 is drawn through the center of curvature, C, and is reflected back on itself
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The position of the object
The locations of the focal point and the center of curvature
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They all start from the same position on the object
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The third ray serves as a check of the construction
Ray Diagram for a concave mirror
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Optics
The
The
The
The
center of curvature is between the object and the concave mirror surface
image is real
image is inverted
image is smaller than the object (reduced)
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The NASA Hubble Space Telescope orbiting Earth.
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Saturn as Seen by Hubble
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Hubble Space Telescope image
shows Sirius A, the brightest star
in our nighttime sky, along with its
faint, tiny stellar companion,
Sirius B.
The two stars revolve around each
other every 50 years. Sirius A,
only 8.6 light-years from Earth, is
the fifth closest star system
known.
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Direct image of
exoplanets around
the star HR8799
using a vortex
coronograph on a
1.5m portion of the
Hale telescope
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A Newtonian-focus reflecting telescope.
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Workers study Hubble's main, eight-foot (2.4 m) mirror. Hubble, like all telescopes,
plays a kind of pinball game with light to force it to go where scientists need it to go. When
light enters Hubble, it reflects off the main mirror and strikes a second, smaller mirror. The
light bounces back again, this time through a two-foot (0.6 m) hole in the center of the main
mirror, beyond which Hubble's science instruments wait to capture it. In this photo, the hole
is covered up.
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•
Refraction of Light
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–
Optics
Index of Refraction
Light travels slower in a transparent material than it does in a vacuum
•
•
Photons are absorbed, reemitted and scattered by matter, therefore slowing the light down
This process causes the light ray to deviate or refract from its incident direction
•
This refraction is constant for various materials and is defined as the index of refraction and
is always less than 1
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This is called refraction

c
v
•
As light travels from one medium to another, its frequency does not change
•
•
The frequency stays the same as the wave travels from one medium to the other
v = ƒλ
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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
–
ƒ1 = ƒ2 but v1 < v2 so λ1 < λ2
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•
Refraction of Light
Optics
– Snell’s Law
– When light travels from one material to another, the angle of refraction
and angle of incidence are related by:
• n1 sin θ1 = n2 sin θ2
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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 is therefore known as Snell’s law of refraction
– Example 1
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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
Prisms
Since all the colors have different angles of deviation
white light will spread out into a spectrum
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Violet deviates the most
Red deviates the least
The remaining colors are in between
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Refraction of Light
Optics
– Total Internal Reflection
–
When light crosses an interface into a medium with a higher index of refraction, the light bends
towards the normal. Conversely, light traveling across an interface from higher n to lower n will bend
away from the normal. This has an interesting implication: at some angle, known as the critical angle,
light traveling from a medium with higher n to a medium with lower n will be refracted at 90°; in
other words, refracted along the interface. If the light hits the interface at any angle larger than
this critical angle, it will not pass through to the second medium at all. Instead, all of it will be
reflected back into the first medium, a process known as total internal reflection.
•
The critical angle can be found from Snell's law, putting in an angle of 90° for the angle of the refracted ray. This
gives:
1   c and  2  90
 sin 90 2
sin  c  2

1
1
•
–
(1  2 )
For any angle of incidence larger than the critical angle, Snell's law will not be able to be solved for the angle of
refraction, because it will show that the refracted angle has a sine larger than 1, which is not possible. In that
case all the light is totally reflected off the interface, obeying the law of reflection.
Optical fibers are based entirely on the principle of total internal reflection. An optical fiber is a
flexible strand of glass. A fiber optic cable is usually made up of many of these strands, each
carrying a signal made up of pulses of laser light. The light travels along the optical fiber, reflecting
off the walls of the fiber. With a straight or smoothly bending fiber, the light will hit the wall at an
angle higher than the critical angle and will all be reflected back into the fiber. Even though the light
undergoes a large number of reflections when traveling along a fiber, no light is lost to refraction
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Fiber Optic Cable
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•
Refraction of Light
Optics
– Applications of Refraction
– Lenses
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•
Lenses are commonly used to form images by refraction
Lenses are used in optical instruments
•
Light passing through a lens experiences refraction at two surfaces
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Cameras, Telescopes, Microscopes
The image formed by one refracting surface serves as the object for the second surface
Converging
lens
Diverging lens
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Optics
•
Lens Images and The Thin Lens Equation
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In order to accurately describe an image formed by a converging or diverging lens we can use
the lens equation and magnification equation below
Thin Lens Equation:
1 1 1
 
d o di f
f  the focal length of the lens
d o  the distance between the object and the lens
di  the distance between the image and the lens
Magnification Equation:
h
d
m i  i
h0
do
hi  height of the image
ho  height of the object
sign conventions for lenses
f is + for a converging lens, - for a diverging lens
d o is + for object to the left of the lens, - for object to the right of the lens
di is + for image formed to the right of lens, - for image to the left
m is + for image that is upright, - for image that is inverted
–
Example 8
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