AQA A-Level Physics: Medical physics (7408)

This guide teaches section 3.10 Medical physics of the AQA AS and A-level Physics (7407/7408) specification, version 1.4 (AS and A-level exams June 2016 onwards), covering every sub-section from 3.10.1 to 3.10.6. The section is A-level only. Sections 3.9-3.13 are options: you study one, and it is assessed in Paper 3 Section B (35 of the paper’s 80 marks). Section A of Paper 3 assesses practical skills and data analysis.

Links: course hub, printable checklist, free diagnostics, revision notes, practice questions. Core background: fibres in Waves, decay in Nuclear physics, annihilation in Particles and radiation.

What this option covers

Spec	What you must be able to do
3.10.1	Eye as a refracting system; spectral response; rods, cones and resolution; lens equations; myopia, hypermetropia, astigmatism
3.10.2	Ear structure; intensity and dB; equal loudness curves; dBA; hearing loss
3.10.3	Obtaining an ECG; the normal waveform
3.10.4	Ultrasound and acoustic impedance; fibre optics and endoscopes; MR scanner
3.10.5	X-ray production, detection, attenuation; CT scanner
3.10.6	Tracers, Mo-Tc generator, PET; half-lives; gamma camera; therapy; comparing methods

The specification lists no required practicals in section 3.10.

3.10.1 Physics of the eye

Vision. The cornea does most of the refraction; the lens, reshaped by the ciliary muscles, adjusts the focus. A real, inverted image forms on the retina. In ray diagrams treat the eye as one converging lens with the retina at a fixed distance.

• Cones work in bright light. Three types peak near 420 nm, 530 nm and 560 nm, giving colour vision. The fovea is almost all cones.
• Rods are far more sensitive and work in dim light, with one peak near 498 nm, so no colour.

Resolution. Each foveal cone has its own connection to the optic nerve, so images on separate cones give separate signals. Many rods share a nerve fibre, so two images on the same group give one signal: resolution is poorer away from the fovea and in dim light.

Lenses. power = 1/f (dioptres, D, f in m); 1/u + 1/v = 1/f; m = v/u. Here we use “real is positive”: a virtual image has negative v, and a diverging lens has negative f.

• Myopia: far point closer than infinity. Correct with a diverging lens that images infinity at the far point.
• Hypermetropia: near point beyond 0.25 m. Correct with a converging lens that images an object at 0.25 m at the near point.
• Astigmatism: the eye’s power differs between planes. Correct with a cylindrical lens. A prescription gives a spherical power, a cylindrical power and an axis (an angle in degrees giving the cylinder’s orientation).

Worked example 1. Far point 2.5 m; near point (another eye) 0.80 m.

Myopia:        u = ∞, v = −2.5 m:   P = 1/(−2.5) = −0.40 D
Hypermetropia: u = 0.25, v = −0.80: P = 4.00 − 1.25 = +2.75 D

3.10.2 Physics of the ear

Structure. The pinna and canal carry sound to the eardrum. Three ossicles in the middle ear lever the vibration to the oval window, whose much smaller area raises the pressure to drive the fluid of the inner ear. In the cochlea, the basilar membrane vibrates and hair cells send nerve impulses; different frequencies respond most at different places.

Intensity is power per unit area normal to the wave (W m⁻²). Perceived loudness follows roughly the logarithm of intensity, so a log scale is used:

intensity level = 10 log(I/I₀) dB, with I₀ = 1.0 × 10⁻¹² W m⁻² (threshold of hearing).

Worked example 2.

I = 3.2 × 10⁻⁵ W m⁻²:  10 log(3.2 × 10⁷) = 75 dB
85 dB:  I = 10⁻¹² × 10^8.5 = 3.2 × 10⁻⁴ W m⁻²
Doubling I adds 10 log 2 = 3.0 dB

Equal loudness curves are made by having listeners match the loudness of tones at different frequencies to a 1 kHz reference. The lowest curve is the threshold of hearing; the curves dip where the ear is most sensitive and rise at low and high frequencies. The dBA scale weights each frequency to match the ear’s response, so it reflects perceived loudness; plain dB does not.

Defects. Excessive noise raises the threshold over a band of frequencies, giving a “notch” on the curve. Age raises it most at high frequencies and lowers the upper limit. Either way the curves move up at the affected frequencies.

3.10.3 The ECG

The heart’s electrical activity gives p.d.s of about a millivolt at the skin. Electrodes go on the limbs and chest, with the skin cleaned and a conducting gel for low-resistance contact. A high-gain amplifier with high input impedance feeds a display.

• P wave: atria depolarise and contract.
• QRS complex: ventricles depolarise and contract; largest, as the ventricles have most muscle.
• T wave: ventricles repolarise.

3.10.4 Non-ionising imaging

Ultrasound

Z = ρc; fraction reflected I_r/I_i = ((Z₂ − Z₁)/(Z₂ + Z₁))². Intensity is also attenuated with distance, more at higher frequency.

Worked example 3. Soft tissue ρ = 1060 kg m⁻³, c = 1540 m s⁻¹; bone Z = 7.80 × 10⁶; air Z = 430 (kg m⁻² s⁻¹).

Z(tissue) = 1060 × 1540 = 1.63 × 10⁶
Tissue → bone: (6.17/9.43)² = 0.43
Tissue → air:  0.999, so coupling gel is needed
Echo after 65 µs: depth = ct/2 = 1540 × 65 × 10⁻⁶/2 = 0.050 m

Piezoelectric transducer. A short alternating p.d. makes the crystal vibrate and emit a pulse; backing material damps it so the pulse is short. Returning echoes deform the crystal and produce a p.d. A-scan: echo amplitude against time along one line. B-scan: the probe is swept, echoes show as dots whose brightness is echo strength, giving a 2D image. Uses: fetal scans, organ and eye measurement.

Advantages: non-ionising, cheap, portable, real-time. Disadvantages: poorer resolution than CT or MR; cannot pass bone or gas.

Fibre optics and endoscopy

Light stays in the core by total internal reflection at the core-cladding boundary. A flexible endoscope has a non-coherent bundle to carry light in, and a coherent bundle (fibres in the same relative positions at both ends) to carry the image out, with an objective lens and an eyepiece or camera. Thinner fibres give finer resolution. Endoscopes allow internal viewing and keyhole surgery through small incisions.

MR scanner

A superconducting magnet’s field makes hydrogen nuclei (protons) align with spins parallel and precess about the field lines. Gradient coils vary the field to select the cross-section. Short RF pulses excite protons in small regions in turn, changing their spin state. As they de-excite they emit RF signals, which are detected and processed by a computer into an image. (Field production and relaxation times are not examined.)

3.10.5 X-ray imaging

Production. Electrons accelerated through p.d. V hit a tungsten target. Maximum photon energy = eV. The continuous spectrum comes from electrons decelerating; characteristic lines come from inner-shell vacancies in target atoms being filled. Most energy becomes heat, so a rotating anode spreads it.

Worked example 4. 80 kV: E = 1.60 × 10⁻¹⁹ × 8.0 × 10⁴ = 1.28 × 10⁻¹⁴ J; λ_min = hc/E = 1.55 × 10⁻¹¹ m (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹).

To control	Use
Intensity	Tube current and exposure time
Photon energy	Tube voltage
Patient dose	Aluminium filter removes low-energy photons
Sharpness	Small focal spot
Contrast	Suitable voltage; lead grid absorbs scatter

Detection. A flat panel detector: an X-ray scintillator turns X-rays into light, photodiode pixels turn light into charge, pixels are read by electronic scanning. Compared with film it gives instant, digital, enhanceable images at a lower dose. A barium meal (strong X-ray absorber) outlines the gut. An intensifying screen emits light onto the film, which is more sensitive to light, so less dose is needed. A fluoroscopic image intensifier turns X-rays into light, then electrons, accelerates them onto an output phosphor and gives a bright, live image.

Absorption. I = I₀e^(−μx); half-value thickness x½ = ln 2/μ; mass attenuation coefficient μm = μ/ρ. Bone absorbs much more than soft tissue (differential absorption).

Worked example 5. Soft tissue, x½ = 0.025 m, ρ = 1060 kg m⁻³:

μ = ln 2/0.025 = 27.7 m⁻¹
Through 0.10 m: e^(−2.77) = 0.0625, i.e. (1/2)⁴
μm = 27.7/1060 = 0.026 m² kg⁻¹

CT scanner. The X-ray tube rotates round the patient with a narrow, monochromatic beam; an array of detectors records transmitted intensity at each angle; a computer builds cross-sectional images. Higher resolution and 3D, but expensive and a higher dose.

3.10.6 Radionuclide imaging and therapy

Tracers are γ emitters labelled onto a compound that collects in a target organ. Judge them on radiation (γ escapes to be detected; α or β only adds dose), half-life (long enough for the scan, short enough to limit dose), γ energy (escapes the body but is stopped in the camera crystal) and ease of labelling.

Approximate values:

• Technetium-99m: pure γ emitter, γ about 140 keV, half-life about 6 hours; labels many compounds.
• Iodine-131: emits β⁻ and γ (main γ about 364 keV), half-life about 8 days; taken up by the thyroid.
• Indium-111: decays by electron capture, γ about 171 and 245 keV, half-life about 2.8 days; labels compounds such as white blood cells.

Mo-Tc generator. Mo-99, half-life about 66 hours, decays by β⁻ to Tc-99m on a column; the Tc-99m is washed out with saline when needed, so hospitals can make the short-lived tracer on site for several days.

PET. A positron-emitting tracer is injected. Each positron annihilates with an electron, giving two γ photons in opposite directions (about 0.51 MeV each). Detectors in a ring record pairs arriving together; the source lies on the line between them.

Half-lives. Physical T_P: half the nuclei decay. Biological T_B: half the substance is removed by the body. Effective T_E: activity in the body halves. 1/T_E = 1/T_B + 1/T_P.

Worked example 6. T_P = 12 h, T_B = 30 h: 1/T_E = 1/12 + 1/30 = 0.117 h⁻¹, T_E = 8.6 h.

Gamma camera. A lead collimator passes only photons travelling along its holes. A scintillator crystal flashes for each photon. Photomultiplier tubes: light releases electrons from a photocathode; dynodes at rising potentials each multiply them, giving a pulse at the anode. Comparing pulses from neighbouring tubes locates each flash, and a computer builds the image.

Therapy. External high-energy X-rays: limit damage to healthy cells with several beams from different directions (or a rotating source) meeting at the tumour, beam shaping, shielding and several separate sessions. Internal β-emitting implants sit in or beside the tumour; the short range of β keeps the dose local.

Comparisons (resolution, convenience, safety only):

Method	Resolution	Convenience	Safety
Ultrasound	Lowest	Cheap, portable, live	Non-ionising
CT	High, 3D	Expensive	High dose
MR	High, best soft tissue	Expensive, slow	Non-ionising; metal risk
Gamma camera/PET	Lower, shows function	Needs tracer	Dose from tracer

Common errors

• Positive v for a virtual image, so a myopia lens comes out converging.
• Missing the 2 in depth = ct/2.
• Using log for ln with half-value thickness.
• Adding half-lives instead of reciprocals.

Next: revision notes, practice questions, exam preparation.

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.