Download Reflection and refraction

Physics 272
April 17
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
[email protected]
Phys272 - Spring 14 - von Doetinchem - 328
Standing electromagnetic waves
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Electromagnetic waves can be reflected on surfaces
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Dielectrics or conductors can serve as reflectors
Superposition principle of electric and magnetic fields
also applies to electromagnetic waves
Superposition of
incident and
reflected wave
forms a standing
wave
Phys272 - Spring 14 - von Doetinchem - 329
Standing waves in a cavity
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Insert a second conducting plane: cavity
→ example: microwave oven
On both planes the electric field has to vanish
A standing wave is created
when the electromagnetic
wave wavelength is an
integer multiple of /2
Measuring the node positions
→ measurement of
wavelength
Reflections generally also
happen on surfaces of two
materials:
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Part of the wave is transmitted and a part is reflected
Phys272 - Spring 14 - von Doetinchem - 330
Review
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Maxwell's equations predict the existence of
electromagnetic waves that propagate at the speed of
light
Electromagnetic waves are transverse:
–
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In matter the wave speed is reduced
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Electric and magnetic fields are perpendicular to
propagation direction
Electromagnetic wave cannot travel faster than the speed
of light.
The poynting vector describes the energy flow rate.
The averaged value is called the intensity
Nodal planes occur for standing electromagnetic
waves
Phys272 - Spring 14 - von Doetinchem - 331
The nature and propagation of light
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Understanding the properties of light:
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Blue color of the sky
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Red color of a sunset
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Rainbows
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Cameras
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Glasses
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Human eye
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lasers
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and so much more
Wave properties of light began to be discovered 1665
Maxwell predicted electromagnetic waves and
predicted speed of propagation
Phys272 - Spring 14 - von Doetinchem - 332
The nature and propagation of light
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The wave picture is only describing one side of light
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Several aspects reveal particle properties
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Particles and wave properties combined → photon
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Photons are described in quantum electrodynamics
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Propagation can be well understood in wave picture
Phys272 - Spring 14 - von Doetinchem - 333
Waves, wave fronts, and rays
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A wave front is the leading edge of a wave
All points on a wave front are at the same part of the cycle of
their variation
Electromagnetic waves emitted by a point-like source:
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spherical surface concentric with
source is a wave front
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Far away from the source
(i.e., the radius is large)
→ spherical wave front can be
treated as plane wave
Light rays use the particle properties
of light and denote the direction of
travel of the wave front
Light rays are straight lines in a homogeneous material
→ we will study what happens when light travels from one
medium into another
Phys272 - Spring 14 - von Doetinchem - 334
Reflection and refraction
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When a light ray strikes a plane
→ light is partly reflected
→ light is partly transmitted
We will mostly concentrate on smooth surfaces
→ rough surface causes wide angular
distributions
Keep in mind most objects we see do not emit
light
→ they reflect light in a diffuse manner
No reflection
→ no wonderful mirror selfies
→ what a sad world that would be
Phys272 - Spring 14 - von Doetinchem - 335
The laws of reflection and refraction
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Optical materials have an important property
→ index of refraction
(related to the electric and magnetic properties of
the material)
Light travels slower in a material than in vacuum
Index of refraction is 1 for vacuum and larger than 1
for any other material
Phys272 - Spring 14 - von Doetinchem - 336
The laws of reflection and refraction
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Incident, reflected, and
refracted rays and the
normal to the surface
all lie in the same
plane
Incident angle
= reflected angle
Snell's law:
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air
glass
Incident light ray




Source: http://en.wikipedia.org/wiki/Refractive_index
Ratio of sines of the angles and is equal to the
inverse ratio of the two indexes of refraction
Phys272 - Spring 14 - von Doetinchem - 337
The laws of reflection and refraction
air
glass
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If a ray passes into
a material with higher
index of refraction
→ refraction angle
is smaller in
material
Incident light ray




Source: http://en.wikipedia.org/wiki/Refractive_index
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At normal incident on the surface: zero refraction angle
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The path of a refracted ray is reversible
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Intensities of reflected and refracted rays depend on angle of
incidence, index of refraction, polarization
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Index of refraction of air: ~1.0003 (increases with density)
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Glasses have index of refraction of 1.5-2.0
Phys272 - Spring 14 - von Doetinchem - 338
Flattened sun at sunset
Deviation from circular shape
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Rays path through atmosphere
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Atmosphere gets denser at lower altitudes
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rays from the lower limb of the sun and from the
upper limb path through different densities of the
atmosphere → different refraction
Phys272 - Spring 14 - von Doetinchem - 339
Index of refraction and the wave aspects of light
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When light passes from one medium to the other:
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Frequency stays constant:
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number of wave cycles per time is conserved
A surface cannot destroy or create waves
The wavelength changes:
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Wavelength becomes shorter after refraction into medium with
higher index of refraction
Wave gets squeezed at lower velocities and stretched at higher
velocities
Phys272 - Spring 14 - von Doetinchem - 340
Reflection and refraction
Phys272 - Spring 14 - von Doetinchem - 341
Total internal reflection
Source: http://en.wikipedia.org/wiki/Optical_fiber
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AMS-02
AntiCoincidence Counter
All the light can be reflected from a surface
→ no transmission
Important effect to transport light without losses from one
place to the other → light guides
Used in cars for sending signals to sensors → does not feel
electric interference → more reliable signal
Phys272 - Spring 14 - von Doetinchem - 345
AMS-02 AntiCoincidence Counter
Plastic optical fiber light guides
are part of a detector for cosmic
ray measurement
AMS-02 during ground testing
Connecting plastic optical
fiber light guides
AMS-02 on the International Space Station
Phys272 - Spring 14 - von Doetinchem - 346
Total internal reflection
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Total reflection occurs even when the second material is
transparent
If a ray passes from a higher refractive index medium to a
lower refractive index medium
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At a certain critical incident angle the refracted angle in the second
medium becomes 90deg
→ no transmission possible
Phys272 - Spring 14 - von Doetinchem - 347
Total internal reflection
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Start with Snell's law:
What happens when the refraction angle in the
second medium is 90deg:
this is the critical angle between:
transmission/refraction possible and total
reflection
Phys272 - Spring 14 - von Doetinchem - 348
Applications of total internal reflection
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In contrast to polished metallic surfaces total
reflection can really totally reflect light without
losses
(inhomogeneities in material make this
statement a bit weaker)
Diamonds have a large refractive index
(2.417 → critical angle: 24.4deg):
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light enters a cut diamond
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internal total reflection on the back surface
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light leaves the light in the front → wonderful sparkle!
Phys272 - Spring 14 - von Doetinchem - 349
Dispersion
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White light is a superposition of
electromagnetic waves with a wide
variety of wavelength
Speed of light is the same for all
wavelength in vacuum
copyright: Harvest/Capitol
Speed of light in matter is different for different
wavelength
→ index of refraction depends on wavelength
(dispersion)
In most materials the index of refraction decreases
with longer wavelengths
Phys272 - Spring 14 - von Doetinchem - 351
Dispersion
Source: http://de.wikipedia.org/wiki/Prisma_%28Optik%29
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Violet light is the slowest in this case, red light the fastest
inside the prism
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Different wavelengths (colors) have different refractive angles
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Prism reveals the spectrum of colors
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Diamonds also have a large dispersion → wide spectrum of
colors adds to the sparkling effect
Phys272 - Spring 14 - von Doetinchem - 352
Rainbows
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Dispersion, refraction, and
reflection are important
White light is reflected on
the back of a water droplet
Waves of different
wavelength feel different
index of refraction
Phys272 - Spring 14 - von Doetinchem - 353
Rainbows
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Exit angle of water
droplet is different
for different
wavelength
Observation at a
quite narrow angle:
the refracted,
reflected spectrum
from the water droplets meet in observer's eye
Rainbow is visible from different locations: for example
the red color is now coming from a different region of
the sky
Double rainbow comes from two internal reflections in
water droplet (→ reversed colors)
Phys272 - Spring 14 - von Doetinchem - 354
Rainbow
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What do we know about the
reflection angles in the water
droplet?
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Water droplet is spherical:
How large is the angle between incident and exit ray
→ add up all refraction angles:
Phys272 - Spring 14 - von Doetinchem - 355
Rainbow
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How does the the deflection
angle depend on the index of
refraction?
Phys272 - Spring 14 - von Doetinchem - 356
Rainbow
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This is the deflection
angle for a particular
wavelength using the
index of refraction
for this particular
wavelength
Deflection angle
Variation of deflection
angle is small
Incident angle
the deflection angle
varies with the incident angle of the light on the water droplet
To form a bright region on the sky in a particular color: incident
light is reflected at the same (similar) deflection angle:
Larger index of refraction → lower deflection angle
→ light comes from a lower position on the sky
Phys272 - Spring 14 - von Doetinchem - 357