AQA A-Level Physics: Medical physics (7408) – Revision Notes

These notes condense section 3.10 Medical physics (3.10.1 to 3.10.6) of the AQA AS and A-level Physics (7407/7408) specification, version 1.4 (AS and A-level exams June 2016 onwards). The section is A-level only and is one of the five options in sections 3.9-3.13: you study one, assessed in Paper 3 Section B. For full explanations and worked examples, use the study guide.

Links: course hub, printable checklist, free diagnostics, practice questions. Exponential decay is revised in Nuclear physics and fibres in Waves.

Equations

Quantity	Equation	Notes
Lens power	P = 1/f	dioptres (D), f in metres
Thin lens	1/u + 1/v = 1/f	real is positive; virtual v negative; diverging f negative
Magnification	m = v/u
Intensity level	10 log(I/I₀)	dB; I₀ = 1.0 × 10⁻¹² W m⁻²
Acoustic impedance	Z = ρc	kg m⁻² s⁻¹
Reflected fraction	I_r/I_i = ((Z₂ − Z₁)/(Z₂ + Z₁))²
Echo depth	d = ct/2	t is the round trip
Max X-ray photon energy	E = eV	λ_min = hc/(eV)
Attenuation	I = I₀e^(−μx)	μ in m⁻¹
Half-value thickness	x½ = ln 2/μ
Mass attenuation coefficient	μm = μ/ρ	m² kg⁻¹
Effective half-life	1/T_E = 1/T_B + 1/T_P	T_E is shorter than both

3.10.1 Eye

• Refraction: mostly at the cornea; the lens fine-tunes. Image on the retina is real and inverted.
• Cones: bright light, colour, three types (peaks near 420, 530, 560 nm), packed in the fovea, one nerve connection each, so high resolution.
• Rods: dim light, one type (peak near 498 nm), no colour, many share one nerve fibre, so low resolution but high sensitivity.
• Resolution rule: two images are seen as separate if they stimulate separate cones with an unstimulated cone between.

Method: correcting lens power

Myopia:        u = ∞,       v = −(far point)   → P negative (diverging)
Hypermetropia: u = 0.25 m,  v = −(near point)  → P positive (converging)
P = 1/u + 1/v

• Astigmatism: different power in different planes; corrected with a cylindrical lens. Prescription = sphere power, cylinder power, axis angle in degrees.

3.10.2 Ear

• Outer: pinna, canal, eardrum.
• Middle: ossicles act as a lever; oval window area much smaller than eardrum, so pressure rises.
• Inner: cochlea fluid; basilar membrane; hair cells make nerve impulses; position along the membrane depends on frequency.
• Intensity: power per unit area normal to the wave.
• Log scale: loudness follows the log of intensity. Each ×10 in I is +10 dB; ×2 is +3 dB.
• Equal loudness curve: joins sounds that seem equally loud; built by matching tones to a 1 kHz reference; lowest curve is the threshold; most sensitive in the middle of the range.
• dBA: weighted for the ear’s frequency response; dB is not.
• Noise damage: threshold rises over a band (a notch). Age: threshold rises most at high frequency; upper limit falls.

3.10.3 ECG

• Electrodes on limbs and chest; skin cleaned; conducting gel for good contact; high-gain, high input impedance amplifier; signal of order 1 mV.
• P: atrial depolarisation. QRS: ventricular depolarisation (largest). T: ventricular repolarisation.

3.10.4 Non-ionising imaging

Ultrasound

• Large difference in Z, strong reflection. Air-skin almost total reflection, so use gel.
• Piezoelectric crystal: p.d. pulse, vibration, ultrasound pulse; echoes deform the crystal, producing a p.d. Backing material damps the crystal for short pulses.
• A-scan: amplitude against time, one direction, gives depths. B-scan: swept probe, brightness = echo strength, 2D image.
• Pros: non-ionising, cheap, portable, real-time. Cons: lower resolution; bone and gas block it.

Endoscope

• TIR at core-cladding boundary.
• Non-coherent bundle: light in. Coherent bundle: image out (fibre positions match at both ends).
• Objective lens forms image on bundle end; eyepiece or camera views it.

MR scanner (sequence)

1. Superconducting magnet: protons align with spins parallel and precess about the field.
2. Gradient coils select the cross-section.
3. Short RF pulses excite protons in successive small regions.
4. Protons de-excite and emit RF signals.
5. Signals detected and processed by computer into an image.

3.10.5 X-rays

• Continuous spectrum: electrons decelerate in the target. Characteristic lines: inner-shell vacancies filled. Cut-off at E = eV.
• Rotating anode: spreads the heat.
• Current → intensity. Voltage → photon energy. Al filter → removes soft X-rays, lowers dose. Small focal spot → sharpness. Lead grid → less scatter, better contrast.
• Flat panel detector: scintillator (X-rays to light) → photodiode pixels → electronic scanning. Instant, digital, lower dose than film.
• Barium meal: X-ray opaque material outlines the gut.
• Intensifying screen: light from phosphor exposes film; less dose. Image intensifier: X-rays → light → electrons → accelerated onto output phosphor; bright live image.
• Attenuation: bone absorbs much more than soft tissue (differential absorption).
• CT: rotating tube, narrow monochromatic beam, detector array, computer image. High resolution, 3D; costly; high dose.

3.10.6 Radionuclides

• Good tracer: γ only, half-life suited to the scan, γ energy that escapes the body yet is stopped in the camera crystal, can be labelled to an organ-seeking compound.
• Tc-99m: pure γ (about 140 keV), half-life about 6 h, widely labelled. I-131: β⁻ and γ (main γ about 364 keV), half-life about 8 days, thyroid. In-111: electron capture, γ about 171 and 245 keV, half-life about 2.8 days, labels e.g. white blood cells. (Approximate values.)
• Mo-Tc generator: longer-lived Mo-99 (half-life about 66 h) decays to Tc-99m; Tc-99m is eluted with saline on site.
• PET: positron emitter; annihilation gives two γ photons back to back; coincidence detection locates the line of the source.
• Gamma camera: collimator → scintillator crystal → photomultiplier tubes → position logic → computer.
• Photomultiplier: photocathode (photoelectric effect) → dynodes at rising potentials multiply electrons → anode pulse.
• High-energy X-ray therapy: several beams crossing at the tumour or rotation, beam shaping, shielding, dose split into sessions.
• β implants: inside or beside the tumour; short β range keeps dose local.

Imaging comparisons (3.10.6.6): answer on resolution, convenience and safety only.

• Ultrasound: lowest resolution; cheap, portable, live; non-ionising.
• CT: high resolution, 3D; expensive; high ionising dose.
• MR: high resolution, best for soft tissue; expensive and slow; non-ionising, but not with some metal implants.
• Gamma camera and PET: lower resolution but show organ function; need a tracer; ionising dose.

Must-know distinctions

• Coherent vs non-coherent bundle: image vs illumination.
• dB vs dBA: intensity level vs level weighted for the ear.
• A-scan vs B-scan: one-line depth graph vs 2D brightness image.
• T_P vs T_B vs T_E: decay vs removal by body vs both.
• μ vs μm: per metre of material vs divided by density.
• Continuous vs characteristic: deceleration vs inner-shell transitions.
• Myopia vs hypermetropia: far point too close (diverging) vs near point too far (converging).

Quick self-test

1. A lens has f = −0.40 m. Find its power.
2. A myopic eye has a far point of 0.50 m. Find the correcting power.
3. Find the intensity of a 60 dB sound.
4. Find the intensity level of 1.0 × 10⁻⁴ W m⁻².
5. By how much does the intensity level rise if the intensity rises by a factor of 100?
6. Fat: ρ = 950 kg m⁻³, c = 1450 m s⁻¹. Find Z.
7. Find the fraction reflected at a fat (Z = 1.38 × 10⁶) to muscle (Z = 1.70 × 10⁶) boundary.
8. What fraction of an X-ray beam passes through three half-value thicknesses?
9. μ = 0.50 cm⁻¹. Find the half-value thickness.
10. T_P = 6.0 h and T_B = 24 h. Find T_E.
11. Which part of the ECG shows ventricular repolarisation?
12. Find the maximum photon energy, in J, from a 120 kV tube.

Answers

1. P = 1/(−0.40) = −2.5 D
2. P = 1/(−0.50) = −2.0 D
3. I = 10⁻¹² × 10⁶ = 1.0 × 10⁻⁶ W m⁻²
4. 10 log(10⁸) = 80 dB
5. 10 log 100 = +20 dB
6. 950 × 1450 = 1.38 × 10⁶ kg m⁻² s⁻¹
7. (0.32/3.08)² = 0.011
8. (1/2)³ = 0.125
9. ln 2/0.50 = 1.39 cm
10. 1/T_E = 1/24 + 1/6.0 = 5/24, so T_E = 4.8 h
11. The T wave
12. 1.60 × 10⁻¹⁹ × 1.20 × 10⁵ = 1.92 × 10⁻¹⁴ J

Where marks are usually lost

• Using a positive v for a virtual image, so the sign of the lens power is wrong.
• Working with the near point for a myopia question, or the far point for hypermetropia.
• Leaving power in m⁻¹ without saying D, or using f in cm.
• Squaring only the top of the reflection ratio, or forgetting to square at all.
• Missing the 2 in d = ct/2.
• Using log in place of ln for half-value thickness, and mixing cm and m in μx.
• Describing an image intensifier when the question asks about an intensifying screen.
• Saying the coherent bundle carries light in.
• Writing T_E = T_B + T_P.
• In comparisons, giving cost alone when resolution and safety are also asked for.

Official syllabus

AQA AS and A-level Physics (7407/7408) specification, version 1.4, July 2026 (AS and A-level exams June 2016 onwards), section 3.10 Medical physics.