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A-Level Physics Paper 2, The refractive index of material is a measure of…
A-Level Physics Paper 2
MUS
For a longitudinal wave, rarefactions indicate drops in pressure, compressions indicate increases in pressure.
The two main types of graphs that can be used for representing waves are displacement-distance graphs (these show how the amplitude of a wave varies with distance and can be used to measure wavelength) and displacement-time graphs (used to measure time period).
Key Definitions:
- Phase: Position of a certain point on a wave cycle, this is measured in radians.
- Phase difference: How much a particle "lags" behind another wave.
- Path difference: Difference in distance travelled by two waves from the same source.
- Coherence: Coherent light sources have the same frequency and the same constant phase difference.
- Superposition: Displacement of two waves combine as they pass each other, the resulting displacement is the vector sum of each wave's displacement.
- Wavefront: A surface used to represent points on a wave that have the same phase.
Constructive interference occurs when interfering coherent waves are in phase (this is indicated by a phase difference of 2npi rads). Destructive interference occurs when the coherent waves are anti-phase (this is indicated by a phase difference of (2n+1)pi rads).
A stationary wave is formed when two progressive waves travelling in opposite directions along the wave plane experience interference / superposition. No energy is transferred by a stationary wave. When the wave meet in phase, antinodes are formed (points of maximum displacement). When the waves meet in antiphase, nodes are formed (points of no displacement).
A reflected sound wave will have a phase difference of 180 degrees compared to the incident wave. The reason that these waves do not completely cancel out is because the reflected wave has a lower amplitude.
We can calculate the speed of a wave on a string with the equations v = sqrt(T / u) where u (mu) is the mass per unit length of the string and T is the tension.
CPAC 7
The fundamental frequency is the lowest frequency standing wave that can be formed. It is characterised by the frequency of the standing wave with length equal to half the wavelength.
When we observing the fundamental, we have lambda = 2L.
This practical sees us vary the tension in the string and calculate the fundamental frequency for this tension. This can then be used to calculate the mass per unit length.
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The photon model of EM waves states that waves travel in discrete packets of energy (called photons). The energy of a photon is proportional to their frequency. The wave model describes light as a transverse wave.
Electrons can only exist in discrete energy levels. If an electron absorbs a photon that is equal to the energy difference between the next energy level then it will experiences excitation. The electrons will quickly drop to the original energy level however, releasing a photon in the process.
A line spectrum is unique to a particular molecule. The light emitted due to excitation is diffracted and a line spectrum is formed. Each line corresponds to a particular wavelength of light.
EAT
The critical angle is the incident angle at which the refracted angle is 90 degrees. This will only occur when the wave is entering a less optically dense medium. As a result of this, total internal reflection can occur (when we exceed the critical angle).
The refractive index of a solid block can be measured with this procedure:
- Place the block in the centre of a piece of paper. Draw around it. Pick it up and use a protractor to draw the normal (dotted line) on the paper (should extend either side of the block's boundary).
- Draw incident angles from the normal (10 degree intervals). Place the block back and use a ray box (thin slit) to create incident light on the block.
- Make a mark where the light leaves the block. Connect the point of entry with the point of exit to determine the path of the wave through the block. Use this to measure the angle of refraction.
- Use Snell's Law to graph a linear relationship.
Refraction occurs when a wave enters a medium with a different optical density, this causes the velocity of the wave to change and therefore its direction. In cases where the wave is entering a more dense medium, the wave bends towards the normal.
Upthrust is experienced by an object because of the differences in pressures exerted on the object at different depths in a fluid. Archimedes principle states that the upthrust experiences by an object is equal to the weight of the fluid it displaced.
We can calculate the upthrust on an object with W = rho x V x g where rho is the density of the fluid, V is the volume of fluid displaced and g is the gravitational field strength.
Viscous drag is the resistive force experiences by an object moving through a fluid. We can use stokes law to calculate this viscous drag if the object is small, spherical, moves at a small speed
Laminar flow is when particles follow smooth paths with little mixing between adjacent layers of fluid. Turbulent flow is where particles in the fluid mix between layers, this forms separate current.
The viscous drag force experiences by a small sphere travelling in a fluid is given by: F = 6(pi)(eta)rv
- The limit of proportionality is the point after which Hooke's Law is not obeyed.
- The elastic limit is just after the limit of proportionality and is the point at which the material will plastically deform.
- The yield point is the point at which a material will continue to stretch without an increase in load.
Elastic deformation occurs when an object returns to its original shape once the applied force is removed (all the work done is stored as elastic strain energy). Plastic deformation is where a material's shape is deformed permanently (energy is dissipated as heat).
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SPC
The frequency of light needed to liberate electrons from the surface of a photoelectric material is known as the threshold frequency.
The work function is the minimum amount of energy needed for electrons to be emitted from the surface of a metal. The photoelectric effect tells is that E = (phi) + E[k]
The photoelectric effect could not be explained by the wave model of light because:
- The wave theory of light would predict that any frequency of light would be able to cause photoelectrons to be emitted (provided the intensity is high enough).
- The photoelectric effect is immediate. The wave model would suggest this to be a gradual process.
- Increasing the intensity of light does not increase the kinetic energy of photoelectrons, it just causes more photoelectrons to be emitted per second.
- Photoelectrons are released with a large range of kinetic energies.
DIG
Diffraction is the spreading out of waves when they pass through a gap similar in size to their wavelength.
Huygens construction states that each point on a wavefront acts as a source of secondary, smaller wavelets. The tangent line to these wavelets is the new wavefront.
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Electron diffraction tubes show concentric circles. The fact that electrons can be diffracted at all provides evidence for wave particle duality.
CPAC 8
Vary slit separation, measure theta.
SUR
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- Ductile: Undergoes a large amount of plastic deformation before fracturing.
- Brittle: Material undergoes little plastic deformation before breaking at a low strain (steep gradient).
- Plastic: Undergoes a large strain for a small stress.
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In a converging lens, the principle focus is the point at which the light rays parallel to the principal axis focus. In a diverging lens, this is the point from which light rays appear to come from.
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The power is negative for a diverging lens and positive for a converging lens. Power is a measure of a lenses ability to bend light.
For ray diagrams: Draw one ray from the top of the lens parallel to the principle axis and draw one ray directly through the centre of the lens. If the image is real then it will form where the two lines meet. Else, it will form where the two lines appear to come from.
v is the image distance, u is the object distance.
When we have a thin lens, we can say that light is refracted but does not experience dispersion or aberrations. The power of a combination of thin lenses can be found by the sum or the individual powers.
A real image is one which can be projected onto a screen as light reaches the image location. A virtual image is one that can not be projected onto a screen.
- Short pulse ultrasound waves used.
- Some sound is reflected when it reaches a boundary. The greater the difference in densities, the greater the reflection.
- The intensity of the reflected waves helps us deduce the structure and the time taken helps us deduce the position.
If the duration between pulses is too long then they will overlap which will decrease the resolution of the image seen.
As the wavelength of a the waves used increases, the less fine details can be resolved and so the amount of information obtained will decrease.
BLD
Simple harmonic motion is described by oscillating motion where the (restoring) force acting on the object is proportional to its displacement but opposite in direction.
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Resonance: when the amplitude of oscillation of a system increases dramatically due to gaining an increased amount of energy from the driving force.
Resonance occurs when the driving frequency provided to the system is equal to the natural frequency.
Damping is where a force acts opposite to the driving force:
- Light damping: Amplitude gradually decreases.
- Critical damping: Reduces the amplitude of oscillation to 0 in shortest time possible.
- Heavy damping: Amplitude reduces slower than critical damping but with no extra oscillations.
A ductile material can undergo a large amount of plastic deformation before fracturing. Ductile materials can be used to reduce the amplitude of oscillation.
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STA
In order to derive the equation for pressure-average kinetic energy equation, we have to make the following assumptions:
- No intermolecular forces act on the particles.
- The duration of collisions is negligible.
- Particles move with random motion and experience elastic collisions.
In order to derive the pressure - average KE equation:
- Consider the change in momentum for a particle colliding elastically with the wall.
- Consider the time between collisions as twice the length of the cubic container divided by the speed.
- Consider the force exerted as the change in momentum over time and then use F = p / t to get F = 2mu / (2l / u) = mu^2 / l.
- Find the pressure by dividing this by the area to get mu^2 / l^3 = mu^2 / V
- So PV = mu^2
- We have a total pressure related to the average speed of a collection of N particles. The sum of these speeds will include all 3 directions (x, y, z) and so we have <c^2> = 3<u^2> so
- PV = (1/3)Nm<c^2>
The assumptions we give to ideal gasses are:
- Perfectly elastic collisions.
- No intermolecular forces.
- No potential energy.
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The greater the angle of parallax, the closer the star is.
- Astronomical Units (AU): Average distance between the Earth and the Sun.
- Parsec (pc): Distance at which the angle of parallax is 1 arcsecond (60 arcseconds in an arcminute, 60 arcminutes in a degree).
- Lightyear (ly): Distance travelled by light in one year (in a vacuum).
Standard candles are objects of a known luminosity. We can use these to determine astronomical distances. If distances are VERY large then Hubble's Law can be used.
A H-R diagram shows the relationship between a star's temperature and its luminosity. On the x axis is temperature which begins at 40,000K and decreases as we move right along the axis.
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- Protostar:
- Clouds of gas and dust clump together under gravity. Gravity spins these clumps inwards to form a dense centre.
- Main Sequence:
- Radiation pressure and gravitational forces are equal so the star is in equilibrium.
- Hydrogen nuclei are fused into helium here.
- The greater the mass of a star, the shorter its main sequence period.
- Red giant (< 3 solar masses):
- Hydrogen fuel runs out and the outer layers expand and cool.
- Heavier elements are fused.
- A red supergiant is formed instead if > 3 solar masses.
- White dwarf (< 1.4 solar masses):
- A red giant's fuel runs out and so the star collapses and cools (eventually to a black dwarf).
- Supernova (> 1.4 solar masses):
- When all fuel runs out, the core collapses and becomes rigid. The outer layers then collapse and rebound off the core, flinging elements heavier than iron into space.
- Neutron Star (Between 1.4 and 3 solar masses):
- Gravity forces protons and electrons together to form neutrons.
- Black Hole (> 3 solar masses):
- Gravitational pull is so large that not even light can escape.
Hubble's Law states that a galaxy's recessional velocity is directly proportional to its distance from Earth. The reciprocal of Hubble's constant will give you the age of the universe (time taken for a galaxy to get to its present position given its velocity).
By considering the centripetal force on planets in different orbits in a galaxy, we find that stars should have a larger mass than they appear to. This mass deficit is explained by dark matter.
The refractive index of material is a measure of how much it slows down incoming light. It is the ratio of c / v where v is the speed in the material. We can also use Snell's law to compute a refractive index.
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