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 SciencesPhysics: 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 R ed O range Y ellow G reen B lue I ndigo V iolet 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 = λ o – λ r it can also expressed as: Z = λ o - 1 NOT given λ r λ r used to calculate λ r λ o = the wavelength observed λ r = the wavelength at rest

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 = λ o – λ r λ r = Z = 0.074

Example 1 (b) Z = v c = v. 3 x 10 8 v = 2.22 x 10 7 ms -1 (c)Z is positive therefore galaxy is moving away

Example 2 A distant star is travelling directly away from the Earth at a speed of 2·4 × 10 7 ms  1. (a)Calculate the value of z for this star. (b)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 10 7 / 3 x 10 8 = 0.08 (b)Z = λ o - 1 λ r 0.08 = (443x10 -9 ) – 1 λr λr = (443x10 -9 ) λ r λ r = (443x10 -9 ) λ r = 410 x m / 410 nm

Questions You can now do qu’s: on The Expanding Universe in your class jotter

Answers 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)

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.

What is this question asking for? It is actually asking for λ o The 450nm is emitted from the galaxy (therefore λ r = 450nm) By the time it reaches the Earth will have shifted. Revised Higher 2012

Z = v / c = 1.2x10 7 / 3x10 8 = 0.04 Z = λ o - 1 λ r 0.04 = λ o x = λ o 450x10 -9 λ o = 1.04 x 450x10 -9 λ o = 468nm Revised Higher 2012