Transcript incident angle

Conceptual Physics
Study Notes & Questions: Week 13—EM Waves (Chap. 19)
1)
An electromagnetic wave consists of interacting time-varying electric and
magnetic fields. (p399) As described by Maxwell’s equations, a change
electric field generates a magnetic field, and a changing magnetic field
generates an electric field. This mutually-generating pair of force fields
propagates through space at c, the speed of light, 3*108meter/sec (that is,
to the moon and back in 2.6 seconds).
2)
The intensities of these electric and magnetic fields vary sinusoidally, that
is, they vary in time and space like a sine curve: growing ‘positively’,
shrinking, reversing orientation, growing ‘negatively’, shrinking, reversing
orientation again, etc. (see Figure 19-1). Like all force fields, these electric
and magnetic fields are vector fields, that is, they have a direction to the
push or pull they exert. The direction of these field changes occur
perpendicular to the direction of their propagation.
3)
Polarization: Given an xyz coordinate system, if the EM wave is traveling in
the z direction, the electric field can vary along the x-axis and the magnetic
field will vary along the y-axis, OR the electric field can vary along the yaxis and the magnetic field will vary along the x-axis. These are the two
possible polarizations of the EM wave. There are special materials that will
allow one sort of polarization to transmit while blocking the other
polarization. This is a polarization filter and is important in laser technology
and sunglasses,
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When light reflects off a surface, one type of EM polarization reflects
better than the other. Polaroid sunglasses reduce glare by cutting
the dominant reflected polarization while allowing the other
polarization to pass through.
4)
The energy of an EM wave is quantized—that is, it’s energy comes packed
in a unit, called a photon, that is absorbed or emitted by an atom as a
single quantum of energy. A photon’s energy is related to its wavelength:
Ephoton = hf, where f is the photon’s frequency, and h is Planck’s constant (h
= 6.63*10-34 Joule-seconds). Even though a photon has no mass, it does
have momentum, which can impart a push against a reflective surface:
Momentumphoton = hf/c.
5)
EM waves come in various forms depending on their frequency: radio,
microwaves, infrared, visible, ultraviolet, X-ray and gamma rays.
(p403).These families of frequency will be absorbed, transmitted or
scattered by matter in different ways. (p402—414)
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Conceptual Physics
Study Notes & Questions: Week 13—Optics (Chap. 20)
1)
Radiation interacts with matter in three basic ways (p419)
a) Transmission—the EM wave passes through the material, however,
the photon’s electric field drags on electrons and protons, slowing
the EM wave’s speed. A material’s index of refraction indicates how
much the material slows light (p428)
b) Absorption—the EM photon is absorbed by the material
c) Scattering—the EM photon interacts strongly with the matter, their
wave functions mix momentarily and when they separate the photon
is moving in a different direction.
2)
Scattering is either diffuse—light scatters uniformly in all directions—or it is
reflective in varying degrees. A perfectly reflective surface is a mirror, a
partially reflective surface (such as a waxed car) is a specular reflector
(p421). Both natural and man-made materials tend to have a mixture of
diffuse and specular reflection. ‘Shiny’ material have more specular
reflection, while ‘drab’ or ‘flat’ surfaces are much more diffuse.
3)
A vector projecting straight out from a given surface is called the surface
normal vector (or simply, the normal). For a reflective surface, the incident
angle (the direction the light comes in, measured from the normal vector),
is equal in magnitude to the reflection angle (the direction the light comes
off, measured from the normal vector) (p421).
4)
Concave mirrors (which belly in) focus light. Light rays coming from a large
distance away, like from a star, get reflected and focused at a single spot
called the focal point. The distance from the mirror to this focal point is
called the focal distance (p422). Telescopes use concave mirrors to gather
large areas of faint light rays and focus their combined intensities so
distance stars and galaxies can be observed. Convex mirrors (which bow
outward) disperse light rays, spreading them outward—the opposite of
focusing.
5)
Refraction is the change in light’s speed as it passes from one material’s
index of refraction, to another’s. If the incident angle is not zero—that is,
the incoming ray is not parallel to the normal of the boundary surface—the
light ray’s direction bends at the boundary surface (p427). Figure 20-9
(p429) shows how a light ray’s refraction angle changes from its incident
angle as it passes from a material with a low index of refraction, n1, into a
material with a higher index of refraction, n2: if n1<n2, then angleincident >
anglerefraction. On the other hand, if n1>n2, then angleincident < anglerefraction. 2
6)
Refraction can be understood more easily if we discuss the wavefront
of the incident light ray. Wavefront lines lie perpendicular to the
direction of a light ray, aligned along the crest points of the EM wave’s
electric field:
Ray
Wavefronts
7)
When wavefronts enter a medium with a higher index of refraction,
they slow. If they enter this medium at an angle, one part of the
wavefront slows first, causing the overall direction of the ray to
change (see Figure 20-8 on p429).
8)
The boundary between two mediums’ indices of refraction does not
have to be sharp, it can be a gradual change, such as the fuzzy
boundary between hot and cold air. These soft boundaries cause light
rays to curve instead of bend sharply(p431). Rays curve away from
the faster medium, i.e. the material with the lower index of refraction.
9)
Something special happens when a light ray from a high index
material passes into a low index material. At a critical angle, the ray’s
bend is so severe that it never leaves the first material but travels
along the boundary surface (p425, Figure 20-6). At even larger
incident angles the ray reflects off the surface, never leaving the first
medium—we have total internal reflection.
10) Total internal reflection makes fiber optics work—once a ray travels
along the inner core of a fiber, total internal reflection prevents it from
leaving the fiber core. If there is very low absorption by the fiber’s
material, a light ray can travel 100 kilometers. (p424).
11) Lenses are transparent materials, such as glass, that are carefully
constructed to control refraction (p432). Convex lenses bulge in the
center and have a focal point like concave mirrors—these are called
converging lenses. Concave lenses are thinner in the center and
cause light rays to spread out—these are diverging lenses. Complex
lenses combine these simpler lenses to produce sharp images inside
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a camera, telescope or microscope (p432).
12) A material’s index of refraction is wavelength dependent. That is, EM
waves of different frequencies will slow and bend differently as they
cross the material surface. Shorter wavelengths, such as blue light,
bend more than longer wavelengths (such as red light). This
wavelength dependence of refraction is called dispersion.
13) What we call white light is actually the mixture of light rays with many
different wavelengths. Special glass shapes, called prisms, use
dispersion to separate white light into its component colors—the
colors of the rainbow (p434).
14) What are the 3 primary additive colors (p437)? What are the 3
primary subtractive colors? Why are they given these “additive” and
“subtractive” names? Which are used in TVs? Which are used in book
illustrations?
15) Why is the sky blue (p437)? Why are sunsets red? Why are clouds
white? Are these caused by scattering or absorption?
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Conceptual Physics
Study Notes & Questions: Week 14—Quantum Mechanics (Chap. 22)
1)
Atoms are small. Really small. Really, really small. Extremely tiny.
2)
Strange things happen on very small size scales. Things sometime behave
like particles (usually when they interact with other things), sometimes they
behave like waves (usually when they are traveling). This is called waveparticle duality, and is the key feature of quantum mechanics. Though many
day-to-day quantities seem continuous—things like solids, liquids, electricity,
energy—at very small size scales we have found all of these things are
quantized—that is, they come packaged in units or quanta. Solids and liquids
are made of discrete atoms, electricity is made of electrons, and energy is
packed in photons. It’s the quanta that puts the quantum in quantum
mechanics (p472).
3)
Uncertainty Principle: At the quantum scale, any measurement alters the
object that is being measured (p474). One consequence of the this is that
you can not simultaneously measure a particle’s position and speed at the
same time: Dx Dp > h, Dx is the uncertainty in particle position, and Dp is the
uncertainty in the particle momentum, and h is Planck’s constant. There is a
similar relationship between measuring the energy of an event and its time
duration: DE Dt > h.
4)
The famous Schrödinger equation,
relates the wave nature of a particle
to the energy field around it. The solution to this equation is very complex
and except for the simple hydrogen atom, it can only be approximated by
digital computations. However, its approximate solution can be converted to
a probability density function—describing where a particle is likely to be at
any given moment (p478).
5)
An important feature of the quantum world is that the wave function for an
electron orbiting an atomic nucleus must be a standing wave—that is, the
orbital circumference must be an integer number of electron wavelengths (for
the electron in its potential energy field—created by protons in the nucleus
and its neighboring electrons). (p484) This fact determines what orbital
energy levels an electron can occupy in the atom.
6)
Another important aspect of quantum mechanics is the Pauli Exclusion
Principle. It means that no two electrons can occupy the same atomic orbital
(and spin state). This principle makes chemistry and life possible. More on
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this later…
So small you can’t see them.
Puence.