# Light acts like a Wave

Urban and Civil

Nov 16, 2013 (4 years and 8 months ago)

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Light acts like a Wave

Light can be though of as a propagating
electromagnetic wave. The wave travels at
the maximum allowed speed (c=3x10
8

m/s)
through a vacuum. The electric and magnetic
fields are felt to oscillate at right angles to
each other as the wave passes.

Properties of a Wave

The distance between crests or troughs is the wavelength
l
. If the wave

travels at speed c, the crests will
pass with a frequency f. The
relation between these is

l
x f = c.

People wondered what
“medium” the light waves are
travelling in. Today we just say
it is the vacuum (which isn’t
totally empty in modern physics.
We also now know that the
speed in this medium is the
same no matter how fast the
emitter is travelling (very odd: a
result of Einstein’s relativity).

Light also acts like a particle : the “Photon”

When detectors (or atoms) “see” light, it arrives in discreet packages,
which we call “photons”. You can think of each photon as having a
wavelength. The energy of a photon depends on its wavelength or
frequency: E
~

f
~

c /
l
.

As a whole, the photons have the statistical behavior of waves of that
wavelength. They experience “interference” like waves.

All wavelengths (or energies) of light are the same basic stuff.
Together they constitute the “electromagnetic spectrum”. Visible
light is a tiny portion of this. Although our eyes cannot detect the
rest of the spectrum, we now have detectors that can. We give
different names to the different “colors”. We use different units for
the different wavelengths

whatever is convenient.

The Spectrum of E
-

Astronomical objects are capable of producing different parts of the
spectrum depending on how energetic the processes that are going
on, or how hot the object is.

The Atmospheric “Windows”

Any opaque body produces E
-
M radiation characteristic of its temperature. It follows
the “Planck curve” shape, which has a peak. The wavelength of the peak follows
“Wein’s law”:
l
max
(nm)=3x10
6

/ T(K) (so hotter sources are bluer).

The total energy emitted (or total area under the curve) by hotter sources of the
same
size

goes up like T
4

, and they are brighter at
all

wavelengths.

because it’s what you get from a little hole in a
dark cavity, or a black
-
looking absorber (which is
also an excellent emitter). A better name is
“thermal” radiation, because it is related to T.

Astro Quiz

Two stars are the same distance and size, but one looks
brighter. It must also be hotter.

Two stars are the same distance and temperature, but one
looks brighter. It must also be larger.

Two stars are the same size and temperature, but one looks
brighter. It must also be bluer.

Which statement below is FALSE?

Reminder: The wavelength of the peak follows “Wein’s law”:
l
max
(nm)=3x10
6

/ T(K) (so hotter sources are bluer).

The total energy emitted (or total area under the curve) by hotter sources of
the
same size

goes up like T
4

, and they are brighter at
all

wavelengths.

There are also a variety of
“non
-
thermal” processes
(often involving magnetic
fields) which produce
wavelengths (and can
produce VERY high
way up through gamma
rays. They are often
associated with violent
phenomena (explosions,
black holes, etc.).

Energy Levels in Atoms

We can think of an atom as consisting of a positive nucleus (protons and neutrons)
surrounded by negative electrons. The electrons can be thought of as “orbiting” the
nucleus, but are only allowed in certain orbits (or energy levels).

A photon with exactly the right energy can excite the electron from one level to
another. The electron will drop back to the “ground state”, and emit photons with
specific energies as it does so.

“Chemistry” is caused by the fact that no 2 identical electrons can be in the same
orbital at the same time.

Energy transitions and photons

The energy of photon that can interact with a level jump just depends
on the energy difference between the levels. Levels can be skipped.

Unique Atomic Signatures

Each atom has a specific set of energy levels, and thus a
unique set of photon wavelengths with which it can interact.

The Doppler Shift

how it works

c
v
rest
rest
new
l
l
l
l

When a source is moving, an observer gets the waves either stretched
out or crunched together, depending on their relative motion with the
source. In the case of light, longer wavelengths look redder and shorter
wavelengths look bluer. This is given by the Doppler formula:

v is negative for an
approaching source:

if the distance is shrinking,
the wavelength is too

To get an appreciable
change, you have to be
moving with an
appreciable fraction of
the speed of the wave

The Doppler Shift

how we use it

Atomic energy transitions leave features in the spectrum whose rest
wavelengths are known from laboratory work. We can measure
observed shifts in these wavelengths from astronomical objects,
and see how fast they are moving (you only get the line
-
of
-
sight
motion: towards or away from you).

More subtle analysis can
also yield other motions,
like rotation or turbulent
motions. These are all
direct uses of the
Doppler shift. It doesn’t
matter how far away the
source is, either.