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What is charge? What is the unit of electric charge? Which symbol represents it?

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

Coulomb (C)
(C) = Ampere-Second (As)

Charge is represented by the symbol Q.


What is the charge of a proton? What is the charge of an electron?

The charge of a proton is represented by e.
The charge of an electron is represented by -e.

e = 1.6 x 10^(-19)C
(A small fraction of a Coulomb)


Which materials does charge flow through?

Electric charge flows through materials which are conductors. They do not flow through insulators.


What is the law of conservation of charge?

Providing that charges cannot enter or leave a system, the net charge in a system will remain constant.


What is electric current? What is the unit of electric current? Which symbol represents it?

Electric current through a conductor is the rate of flow of charge. The charge passing per unit time through a cross-section of the conductor.

Ampere (A)
(A) = (Cs^(-1))

Current is represented by the symbol I.


In a circuit, which way does charge flow?

In circuits, electrons will flow from the negative terminal of a cell to the positive terminal.

Before the discovery of protons and electrons, scientists made an agreement to say that charge was positive. This conventional current flows in the opposite direction to the flow of electrons. Diagrams with arrows denoting current still show the direction of positive charge.


What is the equation for current (In terms of charge and time)?

I = ΔQ / Δt


Why do metals conduct?

In metal conductors, the positive nucleus of each atom is surrounded by most of the atom's electrons, making a positive ion. The ions vibrate randomly about a fixed position in regular crystal lattice. There will then be some electrons which are free to flow in the conductor. The free electrons is what makes metals conduct.


What is drift velocity?

Drift velocity is the flow velocity that an electron attains in a magnetic field.


What is the equation for current (In terms of charge per electron, drift velocity, free electron concentration, and cross-sectional area)? How can this equation be derived?

I = nAve

I = Current
n = Free electron concentration (the number of free electrons per unit of volume of the conductor)
A = Cross-sectional area of the wire
v = Drift velocity
e = The charge of an electron

Derivation -
If the drift velocity is v, then the electrons will travel a length vΔt in the time Δt. The volume is the calculated by multiplying vΔt by the cross-sectional area A, leaving you with AvΔt. The number of free electrons in this volume is therefore nAvΔt, n representing the number of free electrons per unit of volume.
As the charge of an electron is -e, charge passing through a point in time Δt is ΔQ = -nAvΔte.
I = ΔQ / Δt, can be substituted in and you are left with I = nAve. (you drop the - sign).


How is current measured in a circuit?

An ammeter is an instrument used to measure current. It is placed in series, not in parallel.

The ammeter can be placed anywhere in a circuit (as long as it is in series) and it will read the same result, as the current is the same throughout.


What is potential difference?

The potential difference, V, between two points on both sides of a component is the work done (by charge), that is the loss of electrical potential energy, per unit of charge passing between the two points.


What is the unit of potential difference and how is it measured?

The symbol for potential difference is V (sometimes p.d.).

It is measured in volts (V)
(V) = (JC^(-1))

To measure the p.d. between two points (usually across a component) a voltmeter is placed in parallel with the circuit, connected to the two points where you want to measure the p.d.

If a voltmeter reads 5V, then for every coulomb passing between the two points, 5J of energy is done, resulting in 5J of energy changing from electrical potential energy to another form.


What is the equation for potential difference?

V = W / Q
(JC^(-1)) = (J) / (C)
(V) = (JC^(-1))


What is the equation for work done by charge?

Work done = Electric potential energy lost per unit of charge * Charge passing

Work = VIΔt (not provided in exam)


What is power? What is the symbol for power? What is the unit of power?

Power is the rate of doing work, or the rate of transfer of energy.

Power is represented by P.

It is measured in Watts.


What is the equation for power in terms of current and voltage? How is it derived?

P = IV
(Js^(-1)) = (Cs^(-1))(JC^(-1))
(W) = (Js^(-1))
(Provided in exam)

Power = Work done / Time taken

P = VIΔt / Δt
P = VI


What is Ohm's Law? What is resistance?

V = IR (Provided in exam)
(R = V/I)
(VA^(-1)) = (V)/(A)
(VA^(-1)) = (Ω)

The current through a conductor is proportional to the pd across it when at a constant temperature.


What is a I-V graph and what do they show?

An I-V graph is a graph with current (I) through a conductor plotted on the y-axis and the pd (V) across it on the x-axis. The gradient of this line is the resistance (Ω) of the material.


What are the characteristics of an I-V graph for a filament lamp? For a metal wire at a constant temperature?

A filament lamp is an example of an non-ohmic conductor. The graph starts with a steep incline but then begins to level out.

The metal wire at a constant temperature is ohmic and the graph increases proportionally.


What equations can be derived from P =IV and R = V/I

P = IV
P = I^(2)R
P= V^(2)/R

(These derived equations are not provided in the exam).


What is conductance? What is conductance in terms of resistance?

Conductance, G = I/V

(AV^(-1)) = (A)/(V^(-1)
(AV^(-1)) = Siemens (S)

G = 1/R

Not in specification.


How does resistance arise in a metal?

A metal will have finite resistance - due, essentially to collisions between free electrons and vibrating ions. Electrical resistance increases with temperature.


What is resistivity?

The resistance, R, of a wire of length, l and cross-sectional area, A, is given by...

R = ρl/A

in which ρ is a constant for the material of the wire at a given temperature, called its resistivity.

(Ω) = (Ωm)(m)/(m^2)

The lower the resistivity, ρ, the better a material conducts electricity. At room temperature (20°C), most relativities measure between 1x10^(-8)Ωm to 10x10^(-8)Ωm.


What is conductivity?

The conductivity, σ, of a material at a particular temperature is the reciprocal of its resistivity.

σ = 1/ρ

G = σA/l

Not in specification.


How does the resistance of a material depend on temperature?

A metal wire's resistance increases with temperature. It is mainly due to the change in resistivity, ρ, of the material as thermal expansion makes very small changes to l and A. When temperature is plotted against resistivity there is a positive correlation. Different materials will have different gradients.

Free electron explanation:
The higher the temperature, the greater vibration amplitude of the ions, creating more collisions. This decreases the drift velocity. As the drift velocity decreases, current decreases and therefore resistance increases.


What is a superconductor?

A superconductor is a material that, below a certain temperature (the superconducting transition/critical temperature), loses all of its resistance.


How do superconductors work?

Once the conductors reach a certain sub-zero temperature (critical temperature), the amplitude of the vibrations of the lattice ions decreases to a negligible amount, meaning that resistance becomes exactly zero. To reach this critical temperature, conventional conductors are cooled with liquid helium whereas some cuprate superconductors can be cooled using liquid nitrogen. Nitrogen gas is more abundant then helium in the atmosphere so superconductors which can reach their transition temperature using liquid nitrogen are more sustainable.
Also at these low temperatures, Cooper pairs are formed within the material. These occur when electrons pair together within the conductor, and become less scattered, allowing them to move more freely, with no collisions.


What temperatures do different materials superconduct?

Many metals have a transition temperature within a few degrees of absolute zero (-273°C). The critical temperature of magnesium diboride (MgB2), a conventional superconductor, is -234°C. This is the highest known critical temperature amongst conventional superconductors.

Certain ceramic materials have a transition temperature slightly above -196°C, the boiling point of liquid nitrogen.

Some mercury-based cuprate superconductors have been discovered to have critical temperatures in excess of -143°C.


What are some uses of superconductors?

Superconducting magnets are extremely powerful. They are used in Magnetic Resonance Imaging (MRI) scanners in order to force protons in the body to align with the magnetic field. The process is usually to identify disease in the body. So the magnets are very useful in saving lives and identifying health risks. They are also very important in other aspects of science including particle accelerators.
Future applications may include generators, motors, transformers, magnetic levitation devices and magnetic refrigeration. In the future they may become commonplace in most circuits and household items to increase efficiency of products.


What temperature is named 'absolute zero'?

Absolute zero = -273.15°C = 0°K


How can the I-V characteristics of the filament of a lamp and a metal wire at constant temperature be investigated?

1. A variable voltage supply, an ammeter (series), the conductor/filament lamp, and voltmeter (parallel) are placed in a circuit.
2. The voltage supply is increased gradually, and readings are taken from the ammeter and voltmeter. (10+ readings for the filament bulb, less for the metal wire.)
3. The results of each are plotted on an I-V graph, with current, I, on the y-axis, and voltage, V, on the x-axis.
4. If the trend of the graph is not clear, more readings can be taken to have an accurate graph.
5. I-V characteristics will then be clear.


How can the resistivity of the metal of a wire be determined?

1. In order to calculate the resistivity of the wire, the resistance, length and cross-sectional area must be found.
2. Resistance can be calculated by using a ohmmeter. (Alternatively, it can be calculated from using a battery, ammeter and voltmeter.)
3. Length can be found using a meter rule.
4. Cross-sectional area can be calculated by measuring the diameter, d, using an electronic caliper or micrometer screw gauge. Taking multiple measurements to find an average increases accuracy. (πd^(2))/4 will calculate the area.
5. Multiple readings for R at varying lengths, l,can be plotted on a graph. The resistivity can be calculated by multiplying the gradient by the cross-sectional area of the wire.


How can the dependence of the resistance of a metal wire on temperature be investigated?

-Glass beaker (with water)
-Bunsen burner
-Coil of thin, insulated, waterproof copper wire.

1. Set up the apparatus so that the beaker of water is placed on the tripod, above the Bunsen burner. With the ohmmeter attached to either end of the coil. The coil and thermometer are both held in place in the water by the clamp.
2. Turn on the Bunsen burner and increase the temperature gradually, measuring the resistance on the ohmmeter every time the temperature rises 10°C.
3. Resistance can then be plotted against temperature. The gradient should be positive and the line straight.


What happens to current through a series circuit?

Current remains the same throughout a series circuit.


What happens to current when components are added in parallel to a circuit?

The current in both branches of the parallel section add to the current in the series section.


What is Kirchhoff's first law?

The sum of currents coming into a point in a circuit equals the sum of the currents going out from it.


What is the pd across different components in parallel?

When components are in parallel, the pd is the same across all of them: there is only one pd.


What happens to pds of components in series? Why does this happen?

When components are in series within a circuit, their pds are added together. This total will equal the pd across the battery. This is a consequence of the conservation of energy.


What is the equation for resistances in series? Why?

R = R1 + R2 + R3 ...

pds in series add up...
V = V1 + V2 ...

Current is the same throughout... so can be written as.
IR = IR1 + IR2 + IR3 ...

Dividing through by I gives...
R = R1 + R2 + R3 ...


What is the equation for resistances in parallel? Why?

1/R = 1/R1 + 1/R2 + 1/R3 ...

Currents add to give total current...
I = I1 +I2...

Only one pd in each branch so...
V/R = V/R1 + V/R2 + V/R3 ...

Dividing through by V gives...
1/R = 1/R1 + 1/R2 + 1/R3 ...


What is a potential divider?

A potential divider is the name given to resistances in series which divide the pd across the combination.


1. V1 = IR1, V2 = IR2... V(total) = I*R(total)
2. V1/V2 = R1/R2
3. V1/V(total) = R1/R(total), V2/V(total) = R2/R(total)

The ratio of pds is equal to the ratio of the resistance across which the pds would be measured.


How can using a potential divider give a desired output pd?

Input pd, V(in), across two resistors in series - an output pd, V(out), across either of the resistors can be obtained. By varying resistors, V(out) can equal any output desired, providing that V(out) ≤ V(in)

If R2 is chosen as the resistor to obtain output from...

V(out)/V(in) = R2/(R1+R2), V(out) = V(in)*R2/(R1+R2)


How do variable potential dividers work? What are their uses?

Variable potential dividers make the ratio of resistor 1 (R1) to resistor 2 (R2) variable. Usually done using a rheostat. So the is a fixed resistance on the rheostat, and a sliding contact can be connected to the coil at any point along it.

Uses of variable potential dividers are seen in many electronics.


How can potential dividers incorporate resistive sensors?

Thermistors -
A resistor which changes resistance with a change in temperature. Changes will result in a change in output pd.
In the case of a negative temperature coefficient (ntc) thermistor, as the temperature increases, the resistance of the thermistor will decrease (the other resistor will barely change). As the resistance decreases, output pd will increase.

Light-dependant resistors (LDRs) -
Some materials have high resistivities in the dark and conduct better as light levels increase.
As it gets brighter, the higher the output pd. (Very similar to the thermistor.

Outdoor lights
Other digital systems


What is a cell?

A cell consists of a positive and negative electrode, separated by a conducting liquid, with positive and negative terminal at either end of the case. Multiple cells make up a battery.


What is the emf of a cell?

Emf stands for Electromotive Force. (Not a logical name as it is measured in volts.)

The emf, E, of a cell is the energy that changes category from chemical to electrical potential per unit of charge passing through the cell. It is equal to the potential difference across the terminals of the cell when no current is flowing.

Unit: JC^(-1) = V


What is internal resistance?

An electrical cell is made from materials (metal or chemicals, for example). All materials have some resistance. Therefore, a cell must have resistance. This resistance is called the internal resistance, r, of the cell measured in ohms (Ω). (Internal resistance can not be directly measured only calculated).

When current flows through the cell a voltage develops across the internal resistance. This voltage is not available to the circuit so it is called the lost volts, (VL). VL can also be written as Ir.

The voltage across the ends of the cell is called the terminal potential difference, (Vt.p.d).

Vt.p.d can also be written as IR

Because voltage is a measure of energy, and energy is always conserved, the e.m.f. of a cell is equal to the sum of its terminal potential difference, (Vt.p.d), and the lost volts, (VL).

This gives rise to the equation E = Vt.p.d.+ VL

This equation can be written in different forms, e.g. E = I (R + r), Vt.p.d. = E - Ir


What does 'Vt.p.d. = E - Ir' mean?

Energy transferred per unit charge to the external circuit = Energy transferred per unit charge from chemical to electrical potential inside the cell - Energy per unit charge dissipated inside the cell.

(Equation provided in exam)


What can be said about the emfs of multiple cells in series?

Emf of battery = Sum of emfs of cells in series.

(This is providing that the positive terminal of one battery is connected to the negative terminal of the next battery in series. The emf of a cell connected the opposite way is considered negative.)


What can be said about the internal resistances of multiple cells in series?

Internal resistance of battery = Sum of internal resistances of cells in series.

(The total internal resistance in the battery is not dependant on the direction of the batteries the total emf is.)


What can be said about the emfs of multiple identical cells in parallel?

Emf of battery = Emf of one cell

(No increase in Emf when connecting cells in parallel)


What can be said about the internal resistances of multiple identical cells in parallel?

If n identical cells are connected in parallel...

Internal resistance of battery = 1/n * Internal resistance of one cell.


How can current and potential difference in a circuit containing one cell or cells in series be calculated?

Measuring -
Ammeters are used in series with a circuit to measure current.Voltmeters are used in parallel with a circuit to measure voltage.

Calculating -
To calculate current and voltage the equation 'V = E - Ir' and equations for pd, current and resistance.

V = IR, V = E - Ir --> IR = E - Ir --> I = E / (R+r)

I = V/R, V = E - Ir --> V = E - Vr/R --> V = ER / (R+r)


How can you determine the internal resistance of a power supply?

There are multiple experiments which can be undertaken in order to determine the internal resistance of a power supply.

1. (Measuring I and V)
-Use a voltmeter in parallel with the power source and an ammeter in series.
-A rheostat can be used to vary the external resistance in the circuit.
-Multiple readings of V and I are taken and plotted on a V-I graph. This will result in a downwards sloping line. The gradient of this line is multiplied by -1 to find r.

2.(Measuring I and R)
-Equations V = E - Ir and V = IR --> 1/I = 1/E * R + r/E
-A graph of 1/I plotted against R gives a y-intercept of r/E... from which r can be calculated.

3.(Measuring V and R)
-Equation V = ER / (R+r) can be flipped to give... 1/V = (R+r) / ER. --> 1/V = r/E * 1/R + 1/E
-A graph of 1/V plotted against 1/R gives a gradient of r/E... from which r can be calculated.


What is a progressive wave?

A progressive wave is disturbance, or sequence of disturbances, travelling through a medium, taking energy with it, but not taking the particles of the medium with it.


What is the difference between transverse and longitudinal waves?

In transverse waves, the particles of the medium are displaced perpendicular (transverse) to the direction of wave travel.

In longitudinal waves. the particles of the medium are displaced parallel to the direction of wave travel.


What is polarisation?

Polarisation is wave property.
In a transverse wave, the oscillations are at right angles to the direction of travel. The plane of this oscillation defines the polarisation of the wave (one direction).

Polarisation is not possible in longitudinal waves.


What is the difference between the terms in phase, out of phase and antiphase?

Oscillations of the same frequency are in phase if they are at the same point in their cycles at the same time.

Antiphase means the exact opposite.

Out of phase means anything in-between.


What is the cycle of a wave?

A cycle is the smallest portion of an oscillation, starting at any point, which repeats exactly.


What do the terms displacement, amplitude, wavelength, frequency, period and velocity of a wave mean?

Displacement- Displacement is a measurement of distance of the movement of a particle from its equilibrium position.
Amplitude (A)- The amplitude of an oscillation is the maximum value of displacement.
Wavelength (λ)- Wavelength is the distance between two consecutive particles that are oscillating in phase.
Frequency (f)- The frequency of an oscillation is the number of cycles per unit time. Measured in Hertz (Hz)
Period (T)- The period (periodic time), is the time for one cycle of oscillation.
Velocity (v)- The velocity of the wave is the speed of the wave in the direction it is travelling.


What is the equation for the period, T, in terms of frequency?

T = 1 / f
(s) = 1 / (s^(-1)

(Provided in exam)


What is the equation for wave speed in terms of frequency and wavelength?

v = fλ
(ms^(-1)) = (s^(-1))(m)

(Written as c = fλ in exam (c = velocity in a vacuum/air))


What are the properties of a displacement-distance from source graph for transverse waves? What are the properties of displacement-time graph for transverse waves?

Over time, transverse waves tend to dampen, so their peaks and troughs will slowly move closer towards the equilibrium position.


What is a wavefront?

A wavefront is a surface at all points on which the oscillations are in phase. Many waves travel in 2 or 3 dimensions.

The direction of travel of a wavefront at any point is at right angles to the wavefront through that point.


How can you measure the intensity variations for polarisation?

Equipment -
- Light intensity meter
- Two polarising filters
- A light beam

1. Set up the light source.
2. Fix one polarising filter in position, and place another one behind it.
3. Then place the light intensity meter behind those. So the light should pass through both filters and into the meter.
4. Rotating the second filter will vary the intensity of the light reaching the meter.Two maxima and two minima are observed per rotation. These are equally spaced (90° between each maximum and adjacent minimum).


What is diffraction?

Diffraction is the spreading of waves round slits or obstacles in their way.


What is the link between wavelength and the width of the slit the wave is passing through?

When slit width is less than or equal to the wavelength, the diffracted wavefronts at some distance from the slit are almost semi-circular (large diffraction). Whereas when the slit width is greater than the wavelength, there is a central beam of diffracted waves that spreads through only a small angle either side (little diffraction).


What is wave interference?

Interference occurs when waves from multiple sources superimpose/overlap in the same position.


What is the principle of superposition?

The resultant displacement at each point is the vector sum of the displacements that each wave passing through the point would produce by itself.


What is the difference between constructive and destructive interference?

When two waves superimpose in phase with each other, they interfere constructively.

When two waves superimpose in antiphase with each other, they destructively interfere.


What is path difference and how does it impact two-source interference?

The path difference of two waves is the difference between the distances the two waves have travelled to reach the same point. If the waves are oscillating in phase, then constructive interference will occur at path differences of 0λ, 1λ, 2λ, 3λ etc... destructive interference occurs at 0.5λ, 1.5λ, 2.5λ, 3.5λ etc...


What is Young's fringes/two slit experiment?

When light is shone through two slits, the light diffracts. As the two slits act as two sources, interference occurs. When the light then appears on a wall some distance away, there are points of concentrated light (AKA fringes) with gaps of no light in between.


Which equation summarises Young's two slit experiment?

λ = ay/D

(Provided in exam)

λ = Wavelength of the light passing through the slits.
a = The distance between the slits.
y = The distance between two fringes.
D = The distance between the slits and the wall.


What was the significance of Young's two slit experiment?

-Young deduced from his experiments that light was wave-like.
-Young was able to determine the wavelengths of different colours of light.


What is coherent light?

In Young's two slit experiment, fringes never occur when two sources are used (one for each slit) an it is very difficult for fringes to occur using other ordinary light sources such as an LED. The experiment works best with a laser as it emits coherent light.

A beam of coherent light is almost monochromatic, that is a continuous of oscillations of a single frequency. It also has wavefronts across its width as if it cam from a point source.

Two or more sources are coherent if there is a constant phase relationship between their oscillations.


What is diffraction grating?

Instead of using Young's two slits, the diffraction grating experiment uses multiple slits (usually in the hundreds/thousands). The slits are all straight, parallel and equally-spaced. To be used with visible light, the distance between adjacent slits is usually 2x10^(-6) to 3x10^(-6)m. The set up is very similar to Young's two slit experiment.

For a diffraction grating with a very small distance between slits, the fringes are much further apart than in Young’s experiment, and the large number of slits makes the fringes much sharper.


Which equation represents the diffraction grating experiment? How is it derived?

d*sinθ = nλ
(Provided in exam)

d = Distance between each slit.
d*sinθ = The path difference between light from adjacent slits.
θ = Angle of the maxima.
n = Order maximum.
λ = Wavelength.

sin θ = opposite/hypotenuse = nλ/d
sin θ = nλ/d
d*sin θ = nλ


What is a stationary wave?

A stationary (standing) wave is formed when two identical waves travelling in opposite directions meet and superimpose on each other. This usually happens when one wave is the reflection of the other.

There is no net flow of energy.


What is a node? What is the internodal distance?

In a stationary wave, a node is a point of minimum and an antinode is a point of maximum amplitude.

The internodal distance is the distance between the nodes of a stationary wave. It is equal to λ/2.


What are some key differences between progressive and stationary waves?

In a standing wave, all points between a pair of nodes oscillate in phase. In a progressive wave there is a gradual change of phase along the wave.

In a progressive wave, all points oscillate with the same amplitude. In a stationary wave the amplitude varies from 0 at nodes to a maximum and antinodes.

A stationary wave can be regarded as a superposition of two progressive waves of equal amplitude and frequency, travelling in opposite directions.


How can the wavelength of light be determined by Young's two slit experiment?

-Microscope slide, with two slits (typically 02.-0.3mm wide and 0.4-0.5mm apart)
-Meter rule

1. Set up the laser perpendicular to the two slits (with distance, a, between the slits) and switch it on.
2. Set up the screen, D meters away from the slits (distance measured with the meter rule).
3. Measure the distance between two fringes, y, with the meter rule.
4. The wavelength of the light from the laser can be then calculated from λ = ay/D.


How can the wavelength of light be determined by a diffraction grating experiment?

-Microscope slide, with many slits.
-Meter rule

1. Set up the laser perpendicular to the diffraction grating and switch it on. To calculate the distance between the slits in terms of meters, d, 1 is dived by the number of slits per meter.
2. Set up the screen, D meters away from the slits (distance measured with the meter rule).
3. To find θ, the distance between the fringes, x, must be measured using the meter ruler. θ = tan-1 (x/D)
4. For whichever order, n, the experiment has been carried out for the equation d*sinθ = nλ can be used.
5. This can be rearranged for λ to give, λ = d*sinθ/n


How can the speed of sound in air be determined using stationary waves?

-Variety of tuning forks.
-Open-ended glass tube
-Scale (Meter rule)
-Flexible rubber tube
-Water reservoir

1. Set up the equipment.
2. Adjust the water reservoir so until sound of maximum intensity is heard.
3. The distance between the top of the glass tube and the surface of the water, l, must be as small as possible as long as a node forms at the surface of the water and an antinode just above the end of the glass tube, c.This distance c is unknown and is called the end correction.
4. The distance between a node and its adjacent antinode is λ/4... so λ/4 = l+c
5. Measure the resonance level, l, accurately for a variety of tuning forks of known frequencies.
6. Plot a graph of l against 1/f will have a gradient of v/4 and an intercept of -c on the y-axis. From this the speed of sound can be calculated.


What is refraction? Why does this happen? How is refraction measured?

Refraction is the change of direction of travel of light when its speed of travel changes.

Refraction occurs when light passes from one material to another. Why does the light change direction? Waves come in wavefronts which are perpendicular to the direction of wave travel. So if the light waves are travelling in a vacuum and then pass into another material at an angle, part of the wavefront will hit the material first. The end of the wavefront which firsts passes into the material will begin moving slower as the other end continues at the same pace. This causes the direction of travel to change.

The ability of a material to refract light is called its refractive index (n).

n = wave speed in a vacuum / wave speed in the material
n = c / v
n does not have units.


What is Snell's law?

Imagine a ray of light passing from one medium to another. The ray going into the second material is called the incident ray and is moving at velocity v1. The angle between the incident ray and the normal is the angle of incidence (θ1). The ray in the second medium is called the refracted ray and moves at the velocity v2. The angle between the refracted ray and the normal is called the angle of refraction (θ2).

By using trigonometry we can get to the following ratio:

sin θ1 / v1 = sin θ2 / v2 (A form of snells law)

Using this ratio and n = c / v we can get to this:

n1 sin θ1 / c = n2 sin θ2 / c (Multiply out by c)

n1sinθ1 = n2sinθ2... This is Snell's law.


What is optical density?

Optical density is a qualitative term used to describe the refractive property of a material. Diamond has a high optical density and air has a low optical density.


What is reflection?

Reflection occurs when not all of a light ray passes into a second medium (with a lower refractive index) but instead partly or totally reflects off of it. The angle between the reflected ray and the normal is equal to the angle of incidence.


What is Total Internal Reflection (TIR)?

TIR occurs when a ray of light travels from a medium with a higher refractive index to a medium with a lower refractive index. As the angle of incidence increases it eventually reaches a critical angle so that the angle of refraction is equal to 90°. This means that any angle greater than the critical angle (


Which equation allows you to calculate a critical angle? How is it derived?

n1 sin θc = n2


n1 sin θ1 = n2 sin θ2, θ1 = θc, θ2 = 90°

n1 sin θc = n2 sin 90
n1 sin θc = n2 * 1
n1 sin θc = n2

θc = sin^(-1) (n2/n1)


What are optical fibres? How do they work?

They are used for data transmission, in medicine etc. Typically they consist of a single glass thread, the central part of which (the core) carries the light signal and the cladding on the outside prevents the signal from leaving the core. The core has a high refractive index and the cladding has a low refractive index. This then has a plastic cover on the outside typically 0.25 mm thick. A optical-fibre cable usually has hundreds of these fibres.

Optical fibres work because of total internal reflection.


How can the concept of total internal reflection be applied to multimode optical fibres?

All light rays which hit the cladding at greater angle than the critical angle will cause total internal reflection. This reflection then reflects off of the opposite side of the core at the same angle, continuing the reflection down the optical fibre. This is repeated to the other end of the fibre (unless the ray is impacted by impurities in the glass). The fibres do not have to be straight as they are so thin. Any small /gradual change in direction will hardly change the angle of incidence so there shouldn't be an issue.


What problems can occur from using multimode fibres?

Multimode fibres work perfectly over a short distance but not so well over a long distance. There are two reasons for this...

1. Multimode dispersion is the data degradation due to the number of different paths light ray can take. This consequently limits the distance that these cables become reliable.

2. Overlap is another problem. Most modern data systems operate at 10^9 bits per second. However if transmission rates are higher than 10^5 bits per second, the time between pulses will be less than 10μs, so the arrival of different pulses can overlap and become unreadable.


What are monomode fibres (single-mode fibres)?

With core diameters of less than 10μm, light waves can no longer take multiple paths, as in multimode fibres. This means that waves are limited to travelling parallel to the axis of the fibre. These fibres are monomode fibres.


Why can monomode fibres travel further then multimode fibres?

There is no dispersion and no overlapping of waves, so the light can travel further in the monomode fibres. However, scattering can still occur due to impurities in the glass fibre, ultimately causing some signal loss.


How can you determine the refractive index of a material?