There are three units in the higher physics course.
Download your own copy of the Higher Physics Relationship Sheet (pdf)
If you are using past papers to prepare for an assessment, the Revised Higher papers are a good match for CfE Higher. There is also significant overlap between CfE Higher and Traditional Higher; some of the content was moved to National 5 (e.g. vectors, gas laws) but other topics were removed completely, so you should expect questions in Traditional Higher past papers that you won’t be able to answer.
This table contains links to SQA past papers for the Higher Physics exam. These papers and solutions are reproduced to support SQA qualifications on a non-commercial basis according to SQA conditions of use.
Unit 1 – Our Dynamic Universe
equations of motion
The equations of motion can be obtained by analysing a velocity-time graph.
I have some handwritten examples of how to apply the equations of motion to different scenarios. They are available as pdf files by clicking on the links below. There is a commentary in red pen alongside the solution as it progresses.
Thanks to Valdo at Yoker Uni in Glasgow for this video on projectile motion.
projectile off a cliff (similar to equation of motion examples above)
example of projectile motion – shoot the monkey (video)
projectile motion (video)
Here is a worked example of a projectile problem.
Newton’s 2nd Law
Here are two worked examples of tension that can be solved using Newton’s 2nd law (F=ma).
When a force acts at an angle, resolve the force into its x and y components, as shown in this video.
In a lift, you might notice that your apparent weight increases or decreases as the lift accelerates
Read my blog post on Newton III in action (equal and opposite forces)
momentum & impulse
simulation of collisions on an airtrack – set mass/velocity and predict what happens after the collision
explosion simulator – predict motion of the person and the cart after the jump
Of course, Valdo has a lesson on momentum in his own style
Elastic and Inelastic collision simulator
Valdo also has a video about impulse.
Before we look at Special Relativity, here is a video about the speed of light
This video follows Einstein’s thought process as he worked through his special theory of relativity.
another take on special relativity and the twins paradox
…and the Glesga Physics version
This video has helpful examples to explain length contraction. Sometimes it’s easier to imagine we’re a stationary observer watching a fast moving object go whizzing past. For other situations, it’s better to put yourself into the same frame of reference as the moving object, so that everything else appears to be moving quickly, while you sit still. The muon example in this video shows how this alternative perspective works to our advantage in Special Relativity.
Another way to think about this alternative perspective is that it’s hard to measure distances when you yourself are moving really quickly. Think about it, you’d get tangled up in the measuring tape like an Andrex puppy.
It would be far easier to imagine you’re the one sitting still and all the objects are moving relative to your position. That keeps everything nice and tidy – including your measuring tape. Got to love Einstein’s postulates of special relativity.
the expanding universe
Stars – colour, temperature & the Hertzsprung-Russell diagram
As the temperature of a star increases, the emitted light will appear to move from the red end of the spectrum, through to orange, yellow, white and even blue. The most intense (peak) wavelength emitted by a star shortens as the temperature increases. This relationship is called Wien’s Displacement Law. Additional explanations and activities are available here and here.
and Yoker Uni’s video about Doppler and stuff
While redshift can be used to tell us about the recession velocity of (non relativistic) galaxies, we also need to find a way to measure the distance to these galaxies. Astronomers have two main methods to measure these distances; parallax (more parallax here) and cepheid variable stars – there’s a Khan Academy video on cepheid variable stars.
Edwin Hubble had access to the Hooker telescope on Mount Wilson outside Los Angeles. This was the largest telescope in the world at that time. His first breakthrough was the discovery of a cepheid variable star in the Andromeda nebula. This enabled him to calculate the distance to Andromeda and he quickly realised this was not a nebula but a galaxy outside the Milky Way.
This video follows his work.
Hubble then turned his attention to other galaxies, looking for cepheid variable stars that would allow him to determine their distances from the Milky Way. He used redshift to calculate their recession velocity and plotted a graph against distance.
He found that the recession velocity v was directly proportional to distance d. We can express this relationship as
where is the Hubble constant. Astronomers agree that the current value of the constant is
Since this is a SQA course, we need to convert into SI units – giving
In this video, Professor Jim Al-Khalili looks at Hubble’s work on the expanding universe.
Although he was American, Edwin Hubble transformed himself into a tea drinking, pipe smoking, tweed wearing Englishman during his time as a Rhodes Scholar at Oxford. He probably wouldn’t approve of this video.
Of course, if the Universe is expanding, it means that we can imagine the Universe originated at a point in space and expanded out to its current size. This theory is called the Big Bang and is attributed to Georges Lemaître.
Have we found any evidence to support this theory?
1- cosmic microwave background radiation
The cosmic microwave background radiation (CMB) is radiation left over from the big bang. When the universe was very young, just as space became transparent to light, electromagnetic energy would have propagated through space at a much shorter wavelength. Nowadays, the temperature of space has fallen to approximately 2.7 K (that’s 2.7 K above absolute zero!) and, using Wien’s Displacement Law, we can confirm that the peak wavelength of the electromagnetic radiation is now so long that the background radiation lies in the microwave portion of the electromagnetic spectrum.
The CMB was first detected in 1964 by Richard Woodrow Wilson and Arno Allan Penzias, who worked at Bell Laboratories in the USA. They were building a radio wave detector when they found a source of noise that seemed to come from every direction. That the noise came from every direction ruled out a specific star or galaxy.
Wilson and Penzias shared the 1978 Nobel Prize for Physics for their discovery of the CMBR. In recent years, three different spacecraft have mapped the CMBR.
- COBE (1989-1993)
- WMAP (2001-2010)
- Planck (2009-2013)
Each mission has given a better map of the CMBR than its predecessor – see below.
2- the distribution of hydrogen and helium throughout the universe
Immediately after the Big Bang, the young universe was hot. Very hot. After 1 second, the universe had cooled enough for fundamental particles to come together and form protons and neutrons. During the next 3 minutes, the universe still really hot. Hot enough for the protons (hydrogen nuclei) to combine through nuclear fusion and form helium. Looking at the gas clouds around the universe, we find they are 75% hydrogen and 25% helium. It’s no coincidence that these two gases are in the same proportion wherever we look. The ratio of hydrogen:helium is the same because they were formed at the same time, during the first three minutes of the Big Bang.
For more information on the significant points in the evolution of the universe, click on the image below.
3- Olber’s Paradox
In solving Olber’s Paradox, we identify evidence that supports the Big Bang. This video considers Olbers’ Paradox. It’s 19 minutes long but the points are very well presented.
How will the universe end?
It’s complicated and cosmologists are not certain. One of the issues is only being able to see about 4% of the mass in the universe – the stars, planets, gas and dust. About 25% of the mass of the universe is Dark Matter. It’s “dark” because it doesn’t emit light that enables us to see it. Vera Rubin and Fritz Zwicky were the two astronomers who produced observations that led to the dark matter theory.
Vera Rubin measured star velocities in the Andromeda galaxy and plotted these against the star’s distance from the centre of the galaxy. Knowledge of rotational speeds within our Solar System would predict a graph similar to curve A. What she obtained was a relatively flat graph (B).
image from Quantum Diaries
The rotational speed of the stars in curve B are far too fast for the Andromeda galaxy to stay together. The only explanation for the galaxy staying together was the presence of an awful lot of additional mass that couldn’t be detected. This new mass was named dark matter.
Rubin talks about her discovery in this video.
Zwicky had been looking at clusters of galaxies, rather than individual stars within galaxies. He found something similar; the galaxies were swirling round at too great a speed and should fly apart. There had to be an awful lot of invisible mass in that part of space to produce a gravitational force strong enough to hold the cluster together.
There’s a further complication. The expansion of space appears to be caused by an unknown force called Dark Energy, that fights against the pull of gravity which should be reducing the rate of expansion.
Saul Perlmutter was awarded the Nobel Prize for Physics in 2011 for his work on Dark Energy. This video explains where we are in our understanding of where the universe will end up. It contains some similar footage from the end of the Vera Rubin video, so any déjà vu is real.
Unit 2 – Particles & Waves
Now we’re moving from big things like stars, galaxies and the Universe itself, to particles so small we need groups of them just to make a single atom. What’s the connection?
Why do we study particles? from mr mackenzie on Vimeo.
The Standard Model
An elementary (or fundamental) particle is a particle that is not built from other, smaller particles. Until the start of the 20th century, scientists had believed that atoms were elementary particles. However, the discovery of the electron (J.J. Thompson), proton (Rutherford), and neutron (Chadwick), together with Rutherford’s evidence for a heavy, positively charged nucleus at the centre of the atom suggested the atom was not an elementary particle after all.
Brian Cox explains in this video clip…
To go further, we have to introduce some particle physics vocabulary.
These new elementary particles are part of our Standard Model of how the building blocks of the universe interact with one another. The particles that form “matter” are called fermions, after Enrico Fermi (Fermi has an incredibly long list of things named after him). The fermions are divided into two groups; quarks and leptons, as shown in the diagram below.
The Standard Model of Particle Physics. image: The University of Tokyo
Quarks were predicted independently by theoretical physicists Murray Gell-Mann and George Zweig. The Nobel Prize in Physics was awarded to Gell-Mann in 1969 (interview here).
Quarks are held together in groups of two or three by the strong nuclear force, which acts via the exchange of gluons. Particles made from quarks are called hadrons. The subatomic particles we call protons and neutrons are actually made from quarks, so protons and neutrons are examples of hadrons. Protons are smashed together at CERN in a particle accelerator called the Large Hadron Collider.
- protons are made from two up quarks + one down quark
- neutrons contain two down quarks + one up quark
so protons and neutrons are baryons.
You may recall from Our Dynamic Universe that baryonic matter (matter made from baryons) i.e. protons & neutrons, only accounts for about 4% of the mass in the Universe.
Mesons have short lifetimes, even the most stable mesons exist for less than a millisecond. Mesons are a bit complicated because they contain one of the six quarks from the Standard Model bound to an antiquark by the strong nuclear force. An antiquark is the antiparticle of one of the six quarks. Antiquarks are an example of antimatter.
Antimatter was proposed in 1928 by British physicist Paul Dirac, who won the Nobel Prize in 1933 for his work. If a particle combines with its antiparticle, the two particles annihilate to produce pure energy. Consequently, a meson can’t be formed by a quark bound to its own antiquark.
Scientists are trying to discover out why our Universe is overwhelmingly matter-based. At CERN, the LHCb experiment is looking at quarks produced during proton-proton collisions to find out what happened to all the antimatter produced during at big bang.
The physicists at Sixty Symbols have a slightly different take on quarks
The 6 leptons exist individually, rather than joining together to form new particles. The electron (e), muon (μ), and tau (τ) have mass and a negative charge, while the electron neutrino (Ve), muon neutrino (Vμ), and tau neutrino (Vτ) have no charge. The weak nuclear force acts on all leptons and the three charged leptons are also acted upon by the electromagnetic force.
While we’ve met the electron several times, this is only the second time muons have been mentioned. In Our Dynamic Universe, we learned how the presence of muons at ground level is explained by the special theory of relativity. The muon was discovered in 1936 by American Physicist Carl Anderson. 1936 was a great year for Anderson, it’s also the year he won the Nobel Prize in Physics for his discovery of the positron, the antiparticle of the electron. Just 4 years after Dirac’s prediction, Anderson discovered the trail of a “positively charged electron” in 1932 and proved the existence of antimatter.
It was thought neutrinos are massless in the Standard Model. However, the Nobel prize in Physics 2015 was awarded to both Takaaki Kajita and Arthur B. McDonald for their experimental discovery of neutrino oscillations, which demonstrates that neutrinos must have mass. It is incredibly difficult to detect neutrinos because these particles rarely interact with anything. Since neutrinos have a mass, albeit a very small mass, they may be the source of dark matter – the “missing” mass of the universe.
An electric field can be used to accelerate charged particles. Conservation of energy tells us that the work done by the field is equal to the change in the particle’s kinetic energy. The speed of the particle can be determined if its charge and the accelerating voltage are known. These notes show how to perform the calculation.
These short video clips show how to draw electric field lines for point charges and parallel plates, with example calculations for the work done by electric fields and the final speed of charged particles in electric fields.
These Bitesize pages will help if you need to recap on the basics of magnets. A magnetic field is produced whenever current flows through a wire. The magnetic field is represented by a series of concentric circles around the wire, as shown below.
Magnetic field lines around a current carrying wire. image: physick wiki
The direction of the arrows on these magnetic field lines is found using a left hand rule:
Point your thumb in the direction of electron flow, then wrap your fingers around the wire. The direction in which your fingers curl is the same as the arrow direction.
A charged particle will experience a force as it moves through a magnetic field – apart from the special case where the particle enters parallel to the magnetic field lines. There are different ways to determine the direction of the force acting on the charged particle. The following method works for negatively charged particles.
Hold out your right hand and make a fist like Batman.…BIF!
Batman making a fist with his right hand. image: infinitehollywood.com
Still thinking about BIF…
- Straighten your thumb (B), first finger (I), and middle finger (F) so they are at 90 degrees to one another, like the x,y,z axes on a graph.
- Align your thumb so it points in the same direction as the arrows† on the magnetic field lines (B).
- Rotate your right hand until the first finger direction matches the path of the negative particle (I).
- Your middle finger will reveal the direction in which magnetic force (F) acts on the negative particle.
† if no field lines are shown, position your thumb so it points from N to S in the magnetic field
If you’ve done everything correctly, the fingers of your right hand will look like this.
Right hand rule for negatively charged particles in a magnetic field.
If you are working with positive particles, there are two options:
- use your left hand instead of the right, keeping the same BIF order for the fingers OR
- use the right hand rule described above but reverse the direction of the force at the end.
Try both methods and decide which is best for you. If you opt to use different hands, make sure you know which hand to use for each type of charge.
Why do we use B as the symbol for magnetic fields? I have no idea, but there are some suggestions here.
Here are two animations about the photoelectric effect.
In animation#1, the effect of frequency can be investigated. Find out which of the light sources shown produces the photoelectric effect. You should find that the effect only occurs when the high frequency light is used.
In animation#2, you can investigate how irradiance affects the photoelectric effect by changing the position of the uv lamp. Remember that irradiance is the power per unit area.
To explain the photoelectric effect, we have to think of the light behaving as particles rather than waves. We call these particles of light photons. Click here to see a short animation of photons freeing electrons from a surface.
Here is a video showing the photoelectric effect on an electroscope.
Here is a simulation of interference between sound waves. Click on the picture to take you to the site and choose the Two Source Interference option at the top of the screen. Move the man’s head very slowly and listen for changes in the volume (remember to switch the audio on!)
You can also investigate the effects of amplitude, wavelength, bright fringe spacing and slit-to-screen distance on interference patterns obtained using sound, water or light waves in this second simulation. Click on the image to go to the site.
Diffraction is a test for wave behaviour. When a ray of light passes through a grating, the rays travelling through each line of the grating are diffracted. These diffracted rays interfere and a series of bright fringes are observed. Constructive interference is occurring at each location where a fringe (or spot) is observed. The energy of the incident beam of light is shared out amongst the fringes. Find out about gratings here.
We can measure the relative positions of the fringes in a diffraction pattern to determine the wavelength of the light used. The diffraction grating equation is
- m is the diffracted order – some older resources may use n instead of m
- λ is the wavelength
- d is the line spacing.
Here are some notes with problems on diffraction gratings. Working through these will give you a good grounding in the interference and diffraction topic.
Light containing more than one wavelength is called polychromatic light. White light is an example of polychromatic light as it contains all the colours in the visible spectrum. We can split polychromatic light into its constituent colours using a prism. Notice how red light is refracted least when a prism is used.
We could also use a grating to split the polychromatic light into the individual colours it contains, such as the white light from this candle.
Each wavelength emitted by the polychromatic light source undergoes constructive interference at a slightly different angle. The result is a sequence of blurry spectra, rather than the clear spots we obtained from a monochromatic light source. The diagram below might help you to understand how these images are formed.
Notice that there are several differences between the prism and the grating;
- the prism produces only one spectrum but the grating gives many spectra;
- the zero order light (centre candle image) from the grating is not split up – it is the same as the original incident light;
- the long wavelengths (such as red light) that are refracted (bent) least by the prism are diffracted (bent) the most by the grating;
- the grating spectra either side of the centre (zero order) are mirror images – long wavelengths (e.g. red) are always diffracted to the outer side of the spectrum.
You were introduced to refraction during the National 5 course. At Higher level, we are interested in the relationship between the angles of incidence (θi) and refraction (θr).
Snell’s law tells us that
Usually material 1 is air, and so . This simplifies Snell’s law to
where n is the absolute refractive index of material 2. The refractive index is equal to the ratio of the ray’s speed v in materials 1 & 2 and also equal to the ratio of the wave’s wavelength λ in materials 1 & 2, so we can show that
Read more about Snell’s law here.
total internal reflection
Nice video explaining the origin of emission and absorption spectra.
The first laser was demonstrated in 1960 by Theodore Maiman and his research group at Hughes Aircraft Corporation in California. Here is a good background article on the first laser, its inventor and the role that Einstein played in developing the theory of stimulated emission.
The principle of laser operation is outlined in this description of Maiman’s laser, which used a rod of polished ruby inside a spiral flashtube.
My favourite James Bond film, Goldfinger, has a scene where Sean Connery (the best 007 imho) is strapped to a table under a huge red laser. It should have been a saw but the invention of the laser, just 4 years earlier, was a gift for the writers. This scene helped the film win the best effects Oscar in 1965 and, more importantly, gave us the ultimate Bond quote:
Bond: Do you expect me to talk?
Goldfinger: No, Mr. Bond, I expect you to die.
Everyone should watch the laser scene.
Bonus points if you can identify the bad physics in that clip…
You can try running a laser for yourself. Click on the picture below to load a simulator. You’ll need Java on your computer to run the simulation.
Try changing lamp (pump) irradiance and mirror reflectivity on the single atom version before moving on to the multiple atom tab.
Here are some pdf notes on lasers.
Unit 3 – Electricity
Here are Mr Noble’s notes on the Electricity unit.
BBC Bitesize page about EMF and internal resistance – good explanation.
Have you seen Valdo’s internal resistance video?
You can practise calculating the internal resistance and emf of a cell using this blog post.
I have written a blog post about Wheatstone Bridges
This short video is an introduction to capacitors and how they work.
This article describes the different types of capacitors available and looks at their application in smoothing a dc voltage obtained by rectifying an ac voltage.
These 2 videos are included with some others in a blog post I wrote about capacitors.
Valdo from Yoker Uni has put a capacitor video on youtube.