Mini-Lesson

Waves, Photons & Astronomy

This mini-lesson covers CCEA Unit AS 2: waves (transverse/longitudinal, polarisation, the EM spectrum), refraction and total internal reflection, lenses, superposition (stationary waves, Young's slits, diffraction gratings), quantum physics (photons, the photoelectric effect, energy levels, lasers, X-rays), wave–particle duality, and astronomy (Doppler shift, red shift and Hubble's law).

Answer the questions as you go — several are full A-level calculations. Press Start when you are ready.

2.1 Waves

Progressive waves and the EM spectrum

In a transverse wave the oscillations are perpendicular to the direction of energy transfer (all EM waves, waves on a string). In a longitudinal wave they are parallel to it (sound: compressions and rarefactions).

v = fλ and f = 1 / TAmplitude, period, frequency, wavelength and phase can all be read off a displacement graph.

Polarisation — restricting the oscillations to one plane — is only possible for transverse waves. The fact that light can be polarised is direct evidence that light is transverse.

EM spectrum (longest → shortest λ): radio (> 10⁻¹ m) · microwaves (~10⁻² m) · infrared (~10⁻⁵ m) · visible (400–700 nm) · ultraviolet (~10⁻⁸ m) · X-rays (~10⁻¹⁰ m) · gamma (~10⁻¹² m). Learn the two ends of the visible range: violet 400 nm, red 700 nm. All travel at c = 3.00 × 10⁸ m s⁻¹ in a vacuum.

Quick check

Which waves can be polarised?

?A student passes sound and light through a polarising filter and rotates it. Which observation is correct, and why?

2.2 Refraction · 2.3 Lenses

Refraction, total internal reflection, fibres and lenses

Light slows and bends when it enters a denser medium. Snell's law:

n₁ sin θ₁ = n₂ sin θ₂ · n = c / vGoing from a dense to a less dense medium, at the critical angle C the refracted ray grazes the boundary: sin C = 1 / n. Beyond C you get total internal reflection.

Step-index optical fibre: a high-index core surrounded by a lower-index cladding. Light hitting the core–cladding boundary above the critical angle is totally internally reflected and stays trapped. The cladding protects the surface and prevents light leaking (or crossing) between touching fibres. A flexible endoscope uses a coherent bundle of fibres to carry the image out and a non-coherent bundle to carry light in.

1/u + 1/v = 1/f · m = v / u · P = 1 / fPower P is in dioptres (D) when f is in metres. Converging lens: f positive. Diverging lens: f negative.

Sight correction: myopia (short sight) — the eye focuses in front of the retina, so a diverging (negative power) lens is used. Hypermetropia (long sight) — needs a converging (positive power) lens.

Calculate

Your turn — critical angle

1The core of an optical fibre has refractive index 1.50. Calculate the critical angle at a core–air boundary.

°

Hint: sin C = 1/n = 1/1.50 = 0.667, so C = sin⁻¹(0.667).

2.4 Superposition

Stationary waves, Young's slits and gratings

Principle of superposition: where two waves meet, the resultant displacement is the vector sum of the individual displacements. In phase → constructive; antiphase → destructive.

Stationary (standing) waves form when two waves of the same frequency and amplitude travel in opposite directions and superpose — e.g. a wave reflected back along a stretched string, or sound in a tube closed at one end. Nodes (zero amplitude) and antinodes (maximum amplitude) stay in fixed positions; adjacent nodes are λ/2 apart.

Conditions for observable interference: the sources must be coherent (same frequency, constant phase difference) and of similar amplitude. Constructive interference where the path difference is a whole number of wavelengths (nλ); destructive where it is an odd number of half-wavelengths.

λ = ay / d (Young's slits)a = slit separation, y = fringe spacing, d = slits-to-screen distance. Note the CCEA symbols carefully.

d sin θ = nλ (diffraction grating)d = grating spacing = 1 ÷ (lines per metre); n = order number (0, 1, 2 …).

Grating vs double slit: a grating has thousands of slits, so the maxima are far sharper and further apart — which is why gratings, not double slits, are used to measure wavelength accurately with a laser.

Calculate

Your turn — Young's slits

2In a Young's slits experiment the slit separation is 0.50 mm, the screen is 1.0 m from the slits, and the fringe spacing is 1.2 mm. Calculate the wavelength of the light in nanometres.

nm

Hint: λ = ay/d = (0.50 × 10⁻³ × 1.2 × 10⁻³) ÷ 1.0 = 6.0 × 10⁻⁷ m. Now convert to nm (1 m = 10⁹ nm).

Calculate

Your turn — diffraction grating

2bA laser of wavelength 633 nm is shone at a grating with 300 lines per mm. Calculate the angle of the first-order maximum.

°

Hint: d = 1 mm ÷ 300 = 3.33 × 10⁻⁶ m. sin θ = nλ/d = 633 × 10⁻⁹ ÷ 3.33 × 10⁻⁶ = 0.190, so θ = sin⁻¹(0.190).

Sort it

Which model explains it?

Tap a phenomenon, then the model needed to explain it.

🌊 Wave model

⚡ Photon model

🔁 Both models

2.5 Quantum physics

Photons, the photoelectric effect and energy levels

Light is emitted and absorbed in discrete packets — photons — each carrying energy

E = hf = hc / λh = 6.63 × 10⁻³⁴ J s. Handy shortcut: E (in eV) = 1240 ÷ λ (in nm). 1 eV = 1.60 × 10⁻¹⁹ J.

Photoelectric effect: shine light on a metal surface and electrons are emitted — but only if the frequency exceeds a threshold frequency f₀, no matter how intense the light. That cannot be explained by a wave model; it needs one-photon-one-electron:

½mv²_max = hf − hf₀hf₀ = φ, the work function — the minimum energy needed to release an electron from the surface.

Increasing the intensity (more photons per second) increases the number of electrons emitted per second, but not their maximum kinetic energy. Only raising the frequency does that.

Energy levels: electrons in atoms occupy discrete levels. A photon is emitted when an electron drops between levels, with

hf = ΔE = E₂ − E₁This gives line spectra. In a laser, a population inversion (more atoms in the upper metastable state than the lower one) allows stimulated emission to dominate, producing coherent light. X-rays are produced when fast electrons hit a target and make inner-shell transitions (characteristic lines) or decelerate (continuous background).

Calculate

Your turn — photoelectric effect

3A metal has a work function of 2.30 eV. Light of wavelength 400 nm falls on it. Calculate the maximum kinetic energy of the emitted electrons, in eV.

eV

Hint: Photon energy in eV = 1240 ÷ 400 = 3.10 eV. KE(max) = photon energy − work function = 3.10 − 2.30.

Quick check

Turn up the brightness?

?Light above the threshold frequency causes photoemission from a metal. The intensity of the light is doubled, at the same frequency. What happens?

2.6 Wave–particle duality

Duality and the de Broglie wavelength

Some phenomena need the wave model (diffraction, interference, polarisation); others need the photon model (the photoelectric effect, line spectra, X-ray production). Light is both — this is wave–particle duality.

Louis de Broglie proposed that matter also has a wave aspect:

λ = h / p = h / mvConfirmed by electron diffraction: fire electrons at a thin graphite film and they produce concentric diffraction rings — a wave effect from particles.

Why we do not see it: for a 70 kg person walking at 1 m s⁻¹, λ = 6.63 × 10⁻³⁴ ÷ 70 ≈ 10⁻³⁵ m — far too small to diffract off anything. Electrons are light enough for λ to be comparable with atomic spacing, which is exactly why the effect shows up for them.

Quick check

Speed up the electron

?The speed of an electron is doubled. What happens to its de Broglie wavelength?

2.7 Astronomy

Doppler shift, red shift and Hubble's law

When a source of waves moves relative to an observer, the received wavelength changes — the Doppler effect. A galaxy moving away shifts the spectral lines to longer wavelengths: a red shift.

z = Δλ / λ = v / c (for v ≪ c)z is the red shift parameter, Δλ the change in wavelength, λ the laboratory (emitted) wavelength.

Hubble's law: the recession speed of a distant galaxy is proportional to its distance:

v = H₀dWith H₀ ≈ 2.4 × 10⁻¹⁸ s⁻¹, the age of the universe is estimated as t ≈ 1 / H₀ (assuming a constant rate of expansion).

Cosmological vs Doppler red shift: a Doppler shift is caused by a source moving through space. A cosmological red shift is caused by the expansion of space itself stretching the wavelength while the light is in transit. For distant galaxies the shift is cosmological, even though we can still use z = v/c to get an effective recession speed.

Calculate

Your turn — age of the universe

4Using H₀ = 2.4 × 10⁻¹⁸ s⁻¹, estimate the age of the universe in billions of years. Take 1 year = 3.15 × 10⁷ s.

billion years

Hint: t ≈ 1/H₀ = 1 ÷ 2.4 × 10⁻¹⁸ = 4.17 × 10¹⁷ s. Divide by 3.15 × 10⁷ to get years, then by 10⁹.

Quick check

Reading a red shift

?A spectral line emitted at 500 nm in the laboratory is observed at 505 nm in the light from a distant galaxy. What is the galaxy's recession speed? (c = 3.0 × 10⁸ m s⁻¹)

Quick check

Which model?

?Which phenomenon can only be explained by treating light as a stream of photons?

Match it

Match each equation to its meaning

Tap an item on the left, then its partner on the right.

Equation

What it describes

Recap

Unit AS 2 — the big ideas

Waves: v = fλ, f = 1/T; only transverse waves polarise; EM spectrum radio → gamma

Refraction: n₁sin θ₁ = n₂sin θ₂; sin C = 1/n; step-index fibres and the endoscope

Lenses: 1/u + 1/v = 1/f; m = v/u; P = 1/f (dioptres); myopia → diverging, hypermetropia → converging

Superposition: nodes λ/2 apart; λ = ay/d; d sin θ = nλ

Quantum: E = hf; ½mv²(max) = hf − hf₀; hf = ΔE; population inversion → laser

Duality: λ = h/p; electron diffraction

Astronomy: z = Δλ/λ = v/c; v = H₀d; age ≈ 1/H₀

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