#### Transcript redshift

```Key Areas covered
• The Doppler effect is observed in sound and light
• The Doppler effect causes shifts in wavelengths
of sound and light
• The light from objects moving away from us is
shifted to longer (more red) wavelengths
• The redshift of a galaxy is the change in
wavelength divided by the emitted wavelength
• For slowly moving galaxies, redshift is the ratio of
velocity of the galaxy to the velocity of light
What we will do today
• Describe how the Doppler effect
affects light
• State what is meant by redshift
• Carry out calculations on the above
Redshift
Spectroscopy of Stars Wonders of the Universe:
Stardust - BBC Two - YouTube
Background information
• Astronomer Edwin Hubble noticed that
light from distance galaxies was shifting
towards the red end of the spectrum (ie
its wavelength was increasing)
• Physics: The Doppler effect and red
shift of galaxies - Animations - Higher
Sciences
Background information
• White light (light from galaxies and
stars) is broken up into all the colours
of the rainbow
• Red Orange Yellow Green Blue Indigo Violet
• Longer λ
shorter λ
• All the colours have different
wavelengths
What is redshift?
•
Redshift (also known as Doppler shift) is how much the frequency of
light from a far away object has moved toward the red end of the
spectrum.
•
It is a measure of how much the ‘apparent’ wavelength of light has been
increased.
•
It has the symbol Z and can be calculated using the following equation:
•
Z = λo – λr
λr
•
•
λo = the wavelength observed
λr = the wavelength at rest
it can also expressed as: Z = λo
λr
-1
NOT given
used to
calculate λr
What is a blueshift?
• When we use the equation for redshift,
we can sometimes end up with a –ve
value.
• This means the object is moving closer
to you and is said to be blueshifted.
• It is a measure of how much the
‘apparent’ wavelength of light has been
decreased.
Redshift and velocity
• We can also work out the redshift if we
know the velocity that the body is
moving at (for slow moving galaxies):
• Z=
v
c
Wavelengths
• With a redshift, moving away, the
wavelength increases.
• With a blueshift, moving towards, the
wavelength decreases.
Example 1
•
Light from a distant galaxy is found to contain the spectral lines of
hydrogen. The light causing one of these lines has (an observed)
measured wavelength of 466 nm. When the same line is observed (at
rest) from a hydrogen source on Earth it has a wavelength of 434 nm.
(a) Calculate the Doppler shift, z, for this galaxy.
(b) Calculate the speed at which the galaxy is moving relative to the
Earth.
(c) In which direction, towards or away from the Earth, is the galaxy
moving?
(a)
Z
Z = 0.074
= λo – λ r
λr
= 466 - 434
434
Example 1
(b)
Z=
0.074 =
v
c
v .
3 x 108
v = 2.22 x 107 ms-1
(c)
Z is positive therefore galaxy is moving
away
Example 2
•
(a)
(b)
A distant star is travelling directly away from the Earth at a speed of 2·4 ×
107 ms1.
Calculate the value of z for this star.
A hydrogen line in the spectrum of light from this star is measured to be 443
nm. Calculate the wavelength of this line when it observed from a hydrogen
source on the Earth.
(a)
Z = v / c = 2.4 x 107 / 3 x 108 = 0.08
(b)
Z = λo - 1
λr
0.08 = (443x10-9) – 1
λr
0.08 + 1 = (443x10-9)
λr
λr
= (443x10-9)
0.08 + 1
λr
= 410 x 10-9 m / 410 nm
Questions
• You can now do qu’s: 19-20 on The
Expanding Universe in your class jotter
•
•
•
•
•
•
•
19. A = longer; B = red; C = shorter; D = blue; E = away
20. (a) 1·01 × 10−1
(b) 5·07 × 10−2
(c) 525 nm
(d) 682 nm
(e) 434 nm
(f) 365 nm
Revised Higher 2013
A
Revised Higher 2014 Qu: 25(b)
Revised Higher 2014 Qu: 25(b)
Specimen Paper Qu: 6(a)
Solution
WATCH OUT!!!!
• You have to be careful with the wording
of some questions when deciding which
wavelength is the observed and which is
at rest.
Revised Higher 2012
• What is this
for?
• It is actually
• The 450nm is
emitted from the
galaxy (therefore
λr = 450nm)
• By the time it
reaches the Earth
will have shifted.
Revised Higher 2012
•
Z = v / c = 1.2x107 /
3x108 = 0.04
• Z = λo - 1
λr
• 0.04 =
λo - 1
450x10-9
1 + 0.04 = λo
450x10-9
λo = 1.04 x 450x10-9
λo = 468nm
```