Title: InkPhysics / Waves
On every note of this deck, unless a note says otherwise:
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Front: DEFINITION
Define: Material dispersion.
Back: Pulse broadening caused by different wavelengths travelling at slightly different speeds in the glass.

Front: DEFINITION
Define: Real image.
Back: An image formed where rays actually meet, so it can be caught on a screen.

Front: RECALL
State the equation for the critical angle.
Back: sin θ_c = n_2/n_1, valid only when n_1 > n_2.

Front: DEFINITION
Define: Virtual image.
Back: An image formed where rays only appear to come from when projected backwards; it cannot be caught on a screen.

Front: RECALL
State the colour of the central fringe of the white-light double-slit pattern.
Back: White, because the path difference there is zero for every wavelength.

Front: RECALL
Explain diffraction at a slit using Huygens' construction.
Back: The barrier deletes every wavelet source it covers, so only the wavelets inside the gap survive. The wavelet at each edge has no neighbour beyond it to bury its outer flank, so the envelope wraps round that flank and into the region the barrier shades.

Front: RECALL
State how the powers of thin lenses in contact combine.
Back: The powers of thin lenses in contact add: P = P_1 + P_2.

Front: RECALL
State what the y-gain of an oscilloscope sets.
Back: The vertical scale of the trace, in volts per division, so divisions from the centre line to a peak × y-gain = the amplitude.

Front: RECALL
State the distance between adjacent nodes.
Back: Half a wavelength, λ/2.

Front: RECALL
State what happens to energy in a stationary wave.
Back: A stationary wave stores energy rather than transferring it along the wave.

Front: RECALL
State how the refractive index of a solid is measured from a graph.
Back: Trace the ray through a block for several angles of incidence, plot sin θ_1 against sin θ_2, and take the gradient of the straight line through the origin.

Front: RECALL
State the unit of frequency.
Back: The hertz, Hz: one complete oscillation per second.

Front: DEFINITION
Define: Longitudinal wave.
Back: A wave whose oscillations are parallel to the direction of energy transfer, as compressions and rarefactions.

Front: RECALL
State the main use of a diffraction grating.
Back: Splitting light into its line spectrum so wavelengths can be measured precisely and elements identified.

Front: RECALL
State the first-harmonic wavelength of a tube closed at one end.
Back: Four times the tube length, λ = 4L, because a quarter of a wavelength fits between the node at the closed end and the antinode at the open end.

Front: SPOT THE ERROR
Say what is wrong with this claim: Total internal reflection happens at any boundary, as long as you hit it steeply enough.
Back: A steep hit is not enough. Total internal reflection needs the light to travel towards a medium of lower refractive index, with the angle of incidence greater than the critical angle.

Front: RECALL
State the safe practice for using a classroom laser.
Back: Never look along the beam or point it at anyone, and keep it away from reflective surfaces.

Front: RECALL
State the quantity read from the repeat of a displacement-time graph.
Back: The period, because the graph follows a single particle through time.

Front: RECALL
State the colour order in the white-light single-slit side fringes.
Back: Each side fringe is a spectrum with violet on its inner edge and red on its outer edge, because longer wavelengths diffract more.

Front: RECALL
State the quantity unchanged when light enters a new medium.
Back: The frequency; the speed and wavelength both change in the same ratio.

Front: RECALL
State the appearance of double-slit fringes with monochromatic light.
Back: Bright fringes that are evenly spaced and equally bright.

Front: RECALL
State the sign convention for image distance.
Back: Real is positive: a negative image distance v means the image is virtual, on the same side as the object.

Front: DEFINITION
Define: Diffraction.
Back: The spreading of a wave as it passes through a gap or past an edge.

Front: SPOT THE ERROR
Say what is wrong with this claim: A stationary wave is a wave that has stopped moving.
Back: Nothing has stopped: two progressive waves are still travelling in opposite directions through each other. Their superposition holds a fixed pattern of nodes and antinodes: the pattern stands still, not the waves.

Front: DEFINITION
Define: Node.
Back: A point on a stationary wave where the displacement is always zero.

Front: DEFINITION
Define: Path difference.
Back: The difference in the distances from two sources to a point, often expressed in wavelengths.

Front: RECALL
State the speed of electromagnetic waves in a vacuum.
Back: All electromagnetic waves travel at 3.00 × 10^8 m s^−1 in a vacuum.

Front: RECALL
State where a compression lies on a displacement-distance graph of a longitudinal wave.
Back: Where the curve crosses the axis running from positive displacement to negative, taking positive as displacement along the direction of travel. A rarefaction is the crossing the other way. The crests and troughs are maximum displacement at ordinary pressure.

Front: SPOT THE ERROR
Say what is wrong with this claim: Shine two lights on the same spot and you simply get a brighter spot.
Back: Ordinary lamps have no constant phase difference, so no steady fringes form; only coherent sources hold a fixed phase relationship long enough for a stable pattern.

Front: EQUATION · NOT ON THE DATA SHEET
Grating spacing from N lines per metre:
d = ?\(d = \, ?\)d = ?
Back: d = 1N\(d = \frac{1}{N}\)d = 1/N

Front: RECALL
State the best orientation of a receiving aerial.
Back: With its rods parallel to the plane of polarisation of the incoming signal.

Front: RECALL
State the quantity read from the repeat of a displacement-distance graph.
Back: The wavelength, because the graph is a snapshot of every particle at one instant.

Front: DEFINITION
Define: Huygens' construction.
Back: The rule that every point on a wavefront acts as a source of secondary circular wavelets, and that the wavefront a short time later is the envelope of those wavelets, the surface that touches all of them.

Front: DEFINITION
Define: Polarised wave.
Back: A transverse wave whose oscillations are confined to a single plane containing the direction of travel.

Front: EQUATION · NOT ON THE DATA SHEET
Constructive interference condition:
constructive: path difference = ?\(\text{constructive: path difference} = \, ?\)constructive: path difference = ?
Back: constructive: path difference = nλ\(\text{constructive: path difference} = n\lambda\)constructive: path difference = nλ

Front: DEFINITION
Define: Stationary wave.
Back: The superposition of two progressive waves of the same frequency and equal amplitude travelling in opposite directions.

Front: DEFINITION
Define: Focal length of a lens.
Back: The distance from the centre of the lens to the principal focus.

Front: RECALL
State the highest order a grating can produce.
Back: The whole-number part of d/λ, because sin θ can never exceed 1.

Front: RECALL
State what happens to a ray through the centre of a thin lens.
Back: Passes straight on, undeviated.

Front: RECALL
State how the wavelength is found in the resonance-tube experiment.
Back: From the two resonance lengths, λ = 2(L_2 − L_1), so that the offset of the antinode beyond the open end cancels.

Front: RECALL
State the phase difference across a node.
Back: Points on opposite sides of a node oscillate in antiphase, π rad apart.

Front: DEFINITION
Define: Principal focus.
Back: The point where rays arriving parallel to the principal axis are brought together by a converging lens (or appear to come from, for a diverging lens).

Front: RECALL
State the wavelength range of visible light.
Back: About 400 nm at the violet end to 700 nm at the red end.

Front: RECALL
State what the time-base of an oscilloscope sets.
Back: The horizontal scale of the trace, in seconds per division, so divisions across one cycle × time-base = the period.

Front: DEFINITION
Define: Critical angle.
Back: The angle of incidence in the denser medium for which the angle of refraction is 90°.

Front: SPOT THE ERROR
Say what is wrong with this claim: The wave carries the water along with it.
Back: The wave does not carry the water along: each particle only oscillates about a fixed equilibrium position while the pattern travels. A progressive wave transfers energy, not matter.

Front: DEFINITION
Define: Transverse wave.
Back: A wave whose oscillations are perpendicular to the direction of energy transfer.

Front: DEFINITION
Define: Refractive index.
Back: The ratio of the speed of light in a vacuum to its speed in the material: n = c/v.

Front: DEFINITION
Define: Period of a wave.
Back: The time taken for one complete oscillation: T = 1/f.

Front: DEFINITION
Define: Antinode.
Back: A point on a stationary wave where the amplitude of oscillation is maximum.

Front: RECALL
State the condition for total internal reflection.
Back: Light in the denser medium must meet the boundary at an angle of incidence greater than the critical angle.

Front: RECALL
State the width of the central maximum in the single-slit pattern.
Back: The central maximum is twice the width of the other maxima, and far brighter.

Front: DEFINITION
Define: Superposition.
Back: When two waves meet, the resultant displacement is the vector sum of the individual displacements.

Front: RECALL
State the unit of magnification.
Back: None: magnification is a ratio of lengths, v/u or image height over object height.

Front: RECALL
State the phase of points between one pair of adjacent nodes.
Back: They all oscillate in phase, each with its own amplitude.

Front: SPOT THE ERROR
Say what is wrong with this claim: Adding thousands more slits should smear the pattern into a blur.
Back: More slits sharpen the maxima, not smear them: away from the exact angle the many contributions fall out of step and cancel, leaving light only where d sin θ = nλ.

Front: DEFINITION
Define: Frequency.
Back: The number of complete oscillations per second; equivalently, the number of complete waves passing a point per second.

Front: RECALL
State what a progressive wave transfers.
Back: Energy, without transferring the medium itself.

Front: DEFINITION
Define: Wavelength.
Back: The distance between two adjacent points on a wave oscillating in phase, such as crest to crest.

Front: RECALL
State the sign convention for lens power.
Back: A converging lens has positive power; a diverging lens has negative power.

Front: DEFINITION
Define: Amplitude.
Back: The maximum displacement of a particle from its equilibrium position.

Front: SPOT THE ERROR
Say what is wrong with this claim: Waves only diffract when the gap is smaller than the wavelength.
Back: Diffraction happens at every gap, whatever its size, not only below the wavelength. The spreading is greatest when the gap width is comparable to the wavelength.

Front: DEFINITION
Define: Diffraction grating.
Back: A plate ruled with a very large number of equally spaced slits, typically hundreds per millimetre.

Front: DEFINITION
Define: The order n of a grating maximum.
Back: The whole number in d sin θ = nλ; n = 0 is the straight-through maximum along the normal.

Front: EQUATION · NOT ON THE DATA SHEET
Harmonic wavelengths on a string of length L:
λ_n = ?\(\lambda_n = \, ?\)λ_n = ?
Back: λ_n = 2Ln\(\lambda_n = \frac{2L}{n}\)λ_n = 2L/n

Front: RECALL
State the effect of narrowing the slit on the single-slit pattern.
Back: The pattern spreads out, with a wider central maximum, but becomes dimmer.

Front: EQUATION · NOT ON THE DATA SHEET
Phase difference from path difference d:
phase difference = ?\(\text{phase difference} = \, ?\)phase difference = ?
Back: phase difference = 2πdλ\(\text{phase difference} = \frac{2\pi d}{\lambda}\)phase difference = 2πd/λ

Front: RECALL
State what μ means in the first-harmonic equation.
Back: The mass per unit length of the string, in kg m^−1.

Front: RECALL
State the speed of a transverse wave on a stretched string.
Back: v = √(T/μ), with T the tension in newtons and μ the mass per unit length in kg m^−1. It is the speed of the travelling waves along the string, not the speed of any point of the string.

Front: EQUATION · NOT ON THE DATA SHEET
Destructive interference condition:
destructive: path difference = ?\(\text{destructive: path difference} = \, ?\)destructive: path difference = ?
Back: destructive: path difference = (n + 12)λ\(\text{destructive: path difference} = (n + \tfrac{1}{2})\lambda\)destructive: path difference = (n + 1/2)λ

Front: DEFINITION
Define: Modal dispersion.
Back: Pulse broadening caused by rays taking paths of different lengths along the fibre.

Front: RECALL
State which harmonics a tube closed at one end can sound.
Back: Only the odd harmonics, f_1, 3f_1, 5f_1, because the tube must hold an odd number of quarter wavelengths to have a node at one end and an antinode at the other.

Front: DEFINITION
Define: Step-index optical fibre.
Back: A thin glass core carrying light by total internal reflection, wrapped in cladding of slightly lower refractive index.

Front: RECALL
State the evidence that light is a transverse wave.
Back: Light can be polarised, which is possible only for transverse waves.

Front: DEFINITION
Define: Coherent sources.
Back: Sources with the same frequency and a constant phase difference.

Front: DEFINITION
Define: Phase difference.
Back: The fraction of a cycle by which one oscillation leads or lags another, in radians or degrees.

Front: RECALL
State what a closed end and an open end of a pipe must be.
Back: A closed end is always a displacement node; an open end is always a displacement antinode.

Front: SPOT THE ERROR
Say what is wrong with this claim: Cover half a lens and you lose half the image.
Back: Every point of the object sends rays through every part of the lens, so the uncovered half still forms the complete image. Covering half a lens costs brightness, never half the picture.

Front: SPOT THE ERROR
Say what is wrong with this claim: Any wave can be polarised if you build the right filter.
Back: Only transverse waves can be polarised: polarisation confines the oscillations to a single plane. A longitudinal wave oscillates parallel to the direction of travel, so there is no plane of oscillation to select.

Front: DEFINITION
Define: Power of a lens.
Back: One over the focal length in metres: P = 1/f, measured in dioptres.

Front: RECALL
State the condition for greatest diffraction.
Back: Diffraction is greatest when the gap width is comparable to the wavelength.