Theories of Relativity
Newton's theory works extremely well, but there are some
things it cannot explain.
Einstein developed the theory of gravitation, but in doing so,
had to abandon the idea of absolute space and time.
Interesting Results
-the length of an object depends on the velocity of the observer
-twin paradox
Special Theory of Relativity
-The theory which deals with observers/objects moving at
constant velocity.
General Theory of Relativity
-The theory which deals with accelerating observers/objects.
Gravity causes space to be curved and time to slow down.
The curvature of space and slowing of time gives rise to
accelerated motions.
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Light and Matter
Our knowledge of stars and galaxies comes from analysis of radiation
they emit. Through analyzing light, it is possible to determine:
-composition (atoms, molecules, ions)
-physical conditions (temperature, pressure, density)
… and only because matter obeys the same physical laws regardless
of its location in the universe.
Light
Light travels very quickly. Through the work of Galileo, Roemer and
Fizeau, it has been determined to be;
c = 3 x 108m/s, or 3 x 105km/s
Theories about Light
Newton - Corpuscular Theory
-White light is a mixture of colours
Huygens - Wave Theory
-Light is made up of a wave structure
-Established beyond doubt in 1801.
James Clerk Maxwell - Electromagnetism
-1860 was when Maxwell developed EM theory
Albert Einstein - Quantum Theory
Beams of light consist of small packets of energy called photons
Energy is measure in Joules, and is calculated using Planck's constant
(h), which is 6.626 x 10-34 Joule seconds (Js).
Since energy of a single photon is small, it is customary to express
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energy not in Joules, but in electron Volts, where 1 eV = 1.6 x 10
E = hf and because c = fλ then E = hc/λ
2
J.
Components of Light Waves
An electromagnetic wave has two components associated with the
magnetic and electric fields. These are at right angles to each other
and propagate at the speed of light.
Amplitude - the maxmum displacement a wave reaches is called the
amplitude.
Wavelength (λ) - the distance between two points at the same location
on two adjacent waves. Measured in millimetres (mm), micrometres
(μm) or nanometres (nm).
Frequency (f) - the number of waves that pass a fixed point each
second, measured in Hertz (Hz, or waves per second)
Wavelength and Frequency are related by the speed of propagation (in
the case of light, the speed of light)
c = fλ
Eg. if a light has a wavelength of 10 μm
3 × 10
f = =
= 3 × 10 Hz
λ 10 × 10
8
c
18
−6
Discovery of Different Types of Waves
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Wavelength (μm)
102
10-2
10-5
5 x 10-7
10-8
10-10
Name
Radio
Microwave
Infrared
Visible Light
Ultra Violet
X-ray
Discovered by
Hertz (1888)
Herschel (1800)
Röntgen (1895)
Temperature
All objects emit radiation. The intensity of the emitted radiation at a
given wavelength depends on the temperature of the object and is
given by Planck’s equation.
Scientists use the Kelvin temperature scale
Temperature
Absolute Zero
Water Freezes
Boils
Kelvin
0K
273 K
373 K
Celsius
-273º C
0º C
100º C
Planck's equation used for determining intensity is very complex;
-c is the speed of light, 3 x 108 m/s
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-k is Boltzmann's constant, 1.38 x 10
-T is temperature in Kelvin
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-h is Planck's constant, 6.63 x 10
JK
Js
- λ is wavelength in metres
I (λ , T ) =
2πc
2
1
λ ⎛ ⎛ hc ⎞ ⎞
⎜ exp⎜
⎟ − 1⎟
⎝ λkT ⎠ ⎠
⎝
5
4
While this is complex, it yields two simple laws: the Stefan-Boltzmann
Law and Wien's Law
Stefan-Boltzmann Law
An object emits energy at a rate which depends on the fourth power of
its temperature. It is measured in Watts per square metre (Wm-2), and
is called the energy flux.
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F = σT4 , where σ = 5.67 x 10 Wm-2K-4
L = Surface Area x F = σT4 x 4πR2 = 4σπR2T4
For example If an object has a surface area of 2 m2 , what is the power
radiated (luminosity) when the object has a temperature of 100 K?
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F = σT4= (5.67 x 10 Wm-2 K-4 ) x (100 K) 4 = 5.67 W/m2
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Luminosity = 2 m2 x 5.67 Wm = 11.34 W
What if the object had a temperature of 200 K? By what factor would
the luminosity increase?
All objects emit radiation, but they also absorb radiation and often
reflect radiation. A perfect absorber reflects no energy and is called a
Blackbody
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Wien's Law
The wavelength of maximum emission is given (where λ is measured
in metres, T in Kelvin) by λMAX T = 0.0029 m K
Object
Temperature
Wavelength
Maximum Emission
(K)
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Supernova
10
2.9 x 10-9
Sun
6000
4.8 x 10-7
Man
300
10-5
Big Bang
3
10-3
Name
Xray
Visible
Infrared
Submillimeter
The Sun
The sun has a radius (approximate) of 6.96 x 108 metres, and an
approximate temperature of 5800 Kelvin. Its total luminosity can be
determined as follows:
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Lsun = 4π(6.96 x 108)2 x 5.67 10-8 x (5800) = 3.9 10
W
A human being has an approximate surface area of 3 m2, and an
approximate temperature of 300 K. So a human being's total luminosity
can be determined as follows;
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Lman = 3 x 5.67 10 x (300)4 = 1400 W
Questions to Consider
What wavelength of electromagnetic radiation is emitted with maximum
intensity by a human?
Why does exposure to UV (Ultraviolet) radiation often lead to skin
cancer but exposure to visible light does not?
A Blackbody is a perfect absorber of radiation. Why then do some
nomads wear dark clothing in the desert?
How could you build a stealth aircraft?
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