Waves and Particle Nature of Light Flashcards
Describe the difference between longitudinal and transverse waves?
Longitudinal waves oscillate in parallel to its direction of propagation.
Whilst transverse waves oscillate in parallel to its direction of propagation.
Describe the difference between mechanical and electromagnetic waves?
Mechanical waves require a medium to travel through whilst electromagnetic waves are constantly varying electric and magnetic fields.
Show that the units on both sides of the wave equation are consistent?
wave speed (ms⁻¹) = frequency (Hz) x wave length (m)
v = fλ v = (¹/period)λ
ms⁻¹ = (¹/s)m
= ms⁻¹
What is rarefaction?
When particles are spread out in a longitudinal wave.
What is compression?
When particles are close together in a longitudinal. wave?
Why is there a variation in pressure as a longitudinal wave passes a point?
Because to travel the wave need to go through rarefaction and compression.
Is there is a pressure variation from transverse waves?
No.
Define amplitude.
The maximum displacement from the mean position (in meters).
Define period.
The time taken for one complete oscillation (in seconds)
Define frequency.
The number of waves per second (Hz).
Define oscillation.
The repetitive motion about an equilibrium point, with the object at rest at the maximum displacement.
Define displacement.
The position of a particular point on a wave, at a particular instant, measured from the mean (equilibrium).
Define wavelength.
The distance between a point on a wave and the same point on the next cycle of the wave.
What is at the end of a positive amplitude?
A peak/crest.
What is at the end of a negative amplitude?
A trough.
Other than the wave equation, How else can wave speed be calculated?
Distance a single crest (or another point on the waveform) travels / time taken.
Define phase.
The phase of an oscillation refers to the position within a cycle that a given point occupies, relative to the onset of the cycle.
Define a radian.
The angle subtended by an arc which is equal in length to the radius.
1 rad ≈
57.296⁰
π rad =
180⁰
A full circle = ___⁰ = __ rad
= 360⁰ = 2π rad
antiphase =
180⁰ or π rad out of phase.
What is the phase difference between two crests?
In perfect phase.
What is the phase difference between a crest and the next trough?
In antiphase (180⁰ or π rad out of phase).
What is the phase difference between a trough and the crest three waves in front?
In antiphase (900⁰ or 5π rad out of phase).
A direction is given in _ axis.
1.
A plane is given in _ axis.
2.
What are unpolarised waves?
Waves that oscillates in all planes which include the direction of propagation.
What are polarised waves?
Waves that oscillate in only one plane, which includes the direction of propagation
A vertically oscillating wave passing through a verticle filter will…
…pass through the filter unchanged.
A horizontally oscillating wave passing through a verticle filter will…
…not pass through the filter.
What are methods of polarising light? (with examples)
- A polaroid filter (light through a phone screen or sunglasses).
- Reflection off a surface (light bouncing off snow or water).
- Refraction through a substance (light passing through plastic).
- Scattering through a substance (light through the atmosphere).
When light is polarised why is ther a reduction in intensity?
Because only certain waves pass through.
Therefore less light gets to our eyes.
Resulting in a weaker intensity.
How do we observe polarisation?
- Unpolarised light is produced.
- The light passes through a polarizing filter, which limits the oscillations to a single plane.
- A polarizing filter is rotated until it allows no light through to the eyepiece.
- The angle of the rotating polarising filter is recorded.
A student looks at the sunlight reflected off a puddle of water. She puts a polarising filter in front of her eye. As she rotates the filter the puddle appears darker and then lighter.
Explain this observation.
- Reflected light is polarised.
- Polarised light oscillates in one plane.
- Polaroid filter only allows oscillations in one plane to pass through.
- When the planes are parallel the puddle appears light OR when perpendicular to the puddle it appears dark
What are the uses of polarisation?
- Identification and analysis of optically active chemicals.
- Liquid crystal displays.
- Sunglasses and snow goggles.
- TV and radio signals.
- 3D film glasses.
_________ in between the filters rotate the plane of the polarised light when there is a current across them ∴ _______.
Liquid crystals
light can pass through.
TV and radio signals are _______, so the detector needs to be aligned with the ____ of the ______ wave to receive the maximum signal strength.
polarised
plane of the polarised
What is radiation flux density?
Intensity.
What is intensity?
How much energy reaches an area per second.
How is intensity calculated?
Intensity of radiation = power/ area
I = P / A
What makes waves coherent?
- The same frequency.
- The same waveform (shape of the wave).
- A constant phase relationship.
What is path difference?
- The difference in the length of the paths that two waves take.
What are wavefronts?
All the points on a wave where phase = 90⁰.
What is the principle of superposition?
Where two or more waves meet, the total displacement at a point is the vector sum of the displacements that the individual waves would cause at that point.
What will happen if two waves in phase superpose?
Maximum constructive superposition.
What will happen if two waves in antiphase superpose?
Maximum destructive superposition.
What is superposition?
Two or more waves meeting.
What is monochromatic light?
One magnitude of wavelength.
What happens when waves pass through gaps?
They diffract.
larger wavelength = ____ diffreaction.
larger wavelength = larger diffreaction.
After a wave has travelled through a slit of past an object, what direction does it go in?
Any.
If two diffracted waves meet at the central maximum, what is the path difference?
0
If two diffracted waves meet at the 1st maximum, what is the path difference?
λ
If two diffracted waves meet at the 2nd maximum, what is the path difference?
2λ
What will light waves that superpose in phase look like?
Bright (due to constructive interference)
What will light waves that superpose in antiphase look like?
Dark (due to destructive interference)
What is a progressive wave?
A means for transferring energy via oscillations?
Coherent waves are ____ in phase.
Always.
What is a diffraction grating?
A solid with lots of slits cut into it, with a constant spacing, d.
What is the diffraction grating equation?
What does each letter mean?
nλ = d sinθ
n: the order of the ray you are considering.
λ: wavelength.
d: distance between slits.
θ: the angle between the normal ray and the ray you are considering.
How do you work out the distance between slits on a diffraction grating, using N?
N is the number of slits per meter.
∴ you divide 1 by the number of slits (d = 1/N).
When using a diffraction grating, what will be seen if the spacing between the slits increases?
Points of constructive interference will be wider.
When using a diffraction grating, what will be seen if the lines per mm increase?
More points of constructive interference.
When using a diffraction grating, what will be seen if the wavelength increases?
Points of constructive interference will be wider.
When using a diffraction grating, what will be seen if the distance to the screen increases?
Points of constructive interference will be wider.
When using a diffraction grating, what will be seen if a grid is used instead of a series of lines?
Points of constructive interference in two directions (a square)
What did Huygens suggest?
That points on a wavefront were themselves the source of small waves and that they combined to produce further wavefronts.
They would also, be spherical and travel at the same speed and wavelength as the original wave.
What can Hygen’s Construction be used to explain?
Diffraction.
Refraction.
What will happen if the gap is bigger than the wavelength during diffraction?
The central part of the wavefront that will continue ‘un-diffracted’ will be larger, but the edges will curve.
What will happen if white light is diffracted?
At the zero order there will be white.
At the first order, there will be a spectra
At the second order, there will be a wider spectra.
At the third order, there will be an even wider spectra
and so on…
Why does shining white light through a diffraction grating produces a spectrum in each bright spot except the central one?
This is because white light is made up of all wavelengths of light.
They all converge at the zero-order so there is white light there.
Because longer wavelengths diffract more, each wavelength will diffract by different angles, so there is a spectrum.
How do we determine the spacing and arrangement of atoms in crystals?
Why does this work?
X-Ray crystallography
because X-rays are diffracted through the spaces between molecules which can then bee seen on photographic film.
What is the resolution of a detector (eye, telescope)?
The smallest separation two objects can have to still be distinguished separately.
As the aperture decreases, the _____ increases
Diffraction caused by the aperture.
Smaller aperture = ____ resolution
lower.
What is a node on a standing wave?
Points of zero displacement.
What is an antinode on a standing wave?
Points of maximum displacement.
What properties must waves have to create a standing wave?
- the same frequency.
- the same speed.
- the same amplitude.
- a constant phase relationship.
- travelling in opposite directions.
How do standing waves differ from travelling waves?
Standing waves store energy, whereas travelling waves transfer energy from one point to another.
The amplitude of standing waves varies from zero at the nodes to a maximum at the antinodes, but the amplitude of all the oscillations along a progressive wave is constant.
The oscillations are all in phase between nodes, but the phase varies continuously along with a travelling wave.
What is a standing wave?
Waves of same frequency/wavelength travel in both directions along wire and are reflected (not bounced).
Superposition occurs producing nodes (destructive interference due to antiphase) and antinodes (constructive interference, in phase).
What happens when a wave is reflected from a fixed point?
there is a phase change of π rad (180⁰).
If the wavelength of the reflected wave can fit the relationship ______, then a standing wave will be set up.
nλ = 2L
n: an integer (also the mode, nth harmonic)
λ: wavelength
L: length of wire(m)
How many nodes do the following modes have?
1) fundamental
2) 1st overtone
3) 2nd overtone
4) 3rd overtone
5) 4th overtone
1) 2
2) 3
3) 4
4) 5
5) 6
number of nodes = 1 + n
(n is the nth harmonic)
How many antinodes do the following modes have?
1) fundamental
2) 1st overtone
3) 2nd overtone
4) 3rd overtone
5) 4th overtone
1) 1
2) 2
3) 3
4) 4
5) 5
number of nodes = n
(n is the nth harmonic)
Why does a violin and viola playing the same note sound different?
Because the number of harmonics which superpose are different, creating different complex waveforms.
What is the equation for the speed of waves on strings?
v = √(T/μ)
v: wave speed
T: tension of the string
μ: mass per unit length of the spring
Show the units are consistent in the equation for the speed of waves on strings.
v = √(T / μ)
= √(T / (m/x))
= √((F/A) / (m/x))
= √((ma/A) / (m/x))
ms⁻¹ = √((kgms⁻²m⁻²) / (kgm⁻¹))
= √(kgm⁻¹s⁻² / kgm⁻¹)
= √(m²s⁻²)
= (m²s⁻²)¹/²
= m¹s⁻¹
= ms⁻¹
What is a normal?
The normal is an imaginary line drawn perpendicular to the point where the ray hits a boundary between media.
When does a wave refract towards the normal?
When it moves into a more dense medium.
What does the refractive index tell us?
It tells us how much the speed of light will change (and therefore how much light will change direction) when it arrives at a boundary between two mediums.
How do you work our the refractive index from medium 1 to medium 2?
speed in medium 1 / speed in medium 2.
₁n₂ = v₁ / v₂
Why might n=c/v be wrong?
It assumes that the medium in which the incident light travels through is light when in a vacuum.
What is Snell’s Law?
n₁sinθ₁ = n₂sinθ₂
Where the refractive index is ₁n₂ = v₁ / v₂
And where θ is the angle from the normal.
What is refraction?
The change in wave speed when the wave moves from one medium to another. There is a corresponding change in wave direction, governed by Snell’s law.
What changes when travelling into a more dense medium?
The speed of the wave DECREASES
The refractive index INCREASES
The wavelength DECREASES
The angle of refraction DECREASES
The frequency remains CONSTANT
What is the refractive index of air?
1
What is the critical angle?
The critical angle, C, is the value of θᵢ when θᵣ becomes 90⁰
Use Snell’s law to derive an equation for the critical angle?
n₁sinθ₁ = n₂sinθ₂
[θ₂ = 90⁰] n₁sinθ₁ = n₂sin(90)
[sin(90) = 1] n₁sinθ₁ = n₂
sinθ₁ = n₂/n₁
[= sinC = 1/n₁ , assuming it moves into air]
What happens if θ₁ < C (the critical angle)?
Most light refracted.
Some light reflected.
What happen if θ₁ = C (the critical angle)?
Light refracted to 90⁰.
Total internal reflection begins.
What happen if θ₁ > C (the critical angle)?
Total internal reflection takes place.
What conditions must be met for total internal reflection (TIR)?
- the ray is attempting to emerge from the more dense medium.
- the angle between the ray and the normal to the interface is greater than the critical angle.
What do reflective surfaces cause?
Waves to leave the surface at the same angle to the normal but in a different direction.
Give some example of when pulse-echos are used?
- Bats.
- Dolphins.
- Sonar.
- Radar.
- Ultrasound.
- A-scans (amplitude scans).
How does the pulse-echo technique work?
- Pulses of a wave are shot from an object.
- The time taken for it to reflect back at the object is timed.
- A distance is then worked out by using the wave formula (or speed-distance-time formula) and halved to give the actual distance.
Why is distance halved during the pulse-echo technique?
Because the measurement of time emasures both the distance there and back.
What conditions must be met for the pulse-echo technique?
- Short wavelength (less diffraction of the wave, so a more precise measure of where the object/boundary is).
- Pulses (mean that the pulse doesn’t interfere with the echo).
What is the Focal length of a wave through a lens?
The distance between the optical centre (O) and the focal point of light waves that were parallel to the principal axis when incident on a lens.
Converging lenses have a ____ focal point, which means…
Converging lenses have a real focal point, which means…
…that the focal point actually exists, and the image formed at the focal point could be projected onto a screen.
Diverging lenses have a ____focal point, which means…
Diverging lenses have a virtual focal point, which means…
…the rays don’t actually intersect at this point, but they appear to, when you look at the refracted rays.
When is the focal length positive?
When the image is real.
When is the focal length negative?
When the image is virtual.
How is the power of a lens calculated?
Power of lens = 1/ focal length
P = 1 / f
…when f is in metres.
What are the units for the power of a lens?
Dioptres, D
More curved lenses have ______ focal lengths and are therefore more ______.
More curved lenses have shorter focal lengths and are therefore more powerful.
What happends if two or more lenses are used?
You sum the powers of the lenses.
P = P₁ + P₂ + P₃ + ….
(Diverging lenses are negative)
How do we descirbe the result of frefraction through a lens?
Change in size: Magnified/Dominished
Orenentation: Upright/Inverted
Image: Real/Virtual
What happends to a wave hitting a convex lens parallel to the principle axis?
Tends to the prinsiple axis.
Through focal point.
What happends to a wave hitting a convex lens after passing the focal point?
Tends to the principle axis.
Parallel to the principle axis.
What happends to a wave hitting a convex lens passing through its optical centre?
Continues through the lens unchanged.
What happends to a wave hitting a concave lens parallel to the principle axis?
Tends away from the prinsiple axis.
In line with the focal point.
What happends to a wave hitting a concave lens passing through its optical centre?
Continues through the lens unchanged.
What is the differnece between a real and virtual image?
Real:
- Can be projected onto a screen
- Is on the other sode of the lens from the object
Virtual:
- Cannot be projected onto a screen
- Is on the same side of the lens as the object.
What is the lens formula?
1/u + 1/v = 1/f
u (m): distance from teh lens to the object.
v (m): distance from lens to the image.
f (m): distance from lens to the focal point.
When are variables in the lens formula positive?
f is positive when the focal point is real.
v is positive when the image is real.
u is always real.
When are variables in the lens formula negative?
f is positive when the focal point is virtual.
v is positive when the image is virtual.
u is never real.
What is the equation to work ou the magnification of a lens?
m= image hight / object height = v / u
What did de Broglie hypothesise?
That electrons should also behave as waves.
How did Thomson and Davisson prove the de Broglie hypothesis?
By firing beams of electrons at a metal film asd a crystal lattice respectively.
What did Thomson and Davisson find when proving the de Broglie hypothesis?
The electron beams produced diffraction patterns. The constructive and destructive patterns can only be explained if the electrons were behaving as waves.
What did Thomson and Davisson findings evidence for?
This provided evidence for wave-particle duality.
What did de broglie link?
wavelength of light to the momentum of a particle:
λ = h/p wavelength = plank's constant / particle momentum
(momentum = mass x velocity)
What is wave-particle duality?
Particles can behave as waves which have a wavelength which is linked to their mass and velocity.
What is an electronvolt?
The amount of energy gained by an electron when it moves through a potential difference of 1 volt.
What is the unit of an electronvolt?
eV
What is the relation between Joules and Electronvolt?
1J ÷ 1.6 x 10⁻¹⁹ = 1eV
1eV x 1.6 x 10⁻¹⁹ = 1J
Why are elctronvolts used?
They are good to deal with small quanta of energy.
In the 19th, Century what did Huygens, Hooke, and Young develop?
An explanation for properties of light based on wave behaviour.
In 1897, what did Thomson do?
Showed electrons are particles with quantised charge.
In the late 1800s ,what did Maxwell do?
Suggested light and related waves are propagating electric and magnetic fields.
In 1900, what did Plank do?
RElated energy to frequency of light via E = hf (including a suggestion that light can be quantised).
In 1905, what did Einstein do?
Proposed the photoelectric effect: Light must be quantized (later confirmed by Millikan).
In 1924, what did de Broglie do?
Suggested all matter with momentum has a wavelike nature.
From E = hf and another formula (from the formula sheet) link the energy of a photon to the wavelength of the wave.
E = hf, v = fλ v = c [because c is the speed of light]
∴
E= hc / λ
What does the fact that the wavelength of an electron depends on its momentum, and that momentum can be changed by the voltage across it tell us about microscopy?
- Electrons under higher voltages have a short λ, similar to the scale of an atom.
- This allows detailed microscopy - far more than light.
