Medical Physics
Physics of the eye and ear, biological measurement, non-ionising and ionising imaging, and radionuclide techniques.
Spec Points Covered
- Describe the properties of converging and diverging lenses and draw ray diagrams to locate images.
- Apply the thin lens equation $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$ and calculate magnificationThe ratio of image height to object height, or equivalently the ratio of image distance to object distance. $m = v/u$..
- Use $P = 1/f$ to calculate lens powerThe reciprocal of the focal length in metres. Measured in dioptres (D). Converging lenses have positive power; diverging lenses have negative power. in dioptres and find the combined power of lenses in contact.
- Describe the structure of the eye and explain the roles of the cornea, lens, ciliary muscles, retina, and fovea.
- Compare rodsPhotoreceptor cells sensitive to low light. They cannot distinguish colour. About 120 million per eye. and conesPhotoreceptor cells that detect colour (red, green, blue). They require high light intensity. About 6 million per eye. in terms of sensitivity and spatial resolution.
- Explain myopia, hyperopia, and astigmatism, and describe how each is corrected.
- Describe the structure of the ear and explain the roles of the outer, middle, and inner ear.
- Apply $\text{IL} = 10 \log_{10}(I/I_0)$ and interpret equal loudness curvesGraphs showing the intensity level needed at each frequency for sounds to be perceived as equally loud., the phon scale, and the dBA scale.
- Interpret audiogramsGraphs of hearing level against frequency used to diagnose hearing loss. and distinguish between age-related and noise-induced hearing loss.
- Describe the main features of an ECGA recording of the electrical activity of the heart. The P wave, QRS complex, and T wave represent depolarisation and repolarisation of heart chambers. trace and explain the significance of each wave.
- Explain piezoelectric transducers, acoustic impedance$Z = \rho c$. The product of density and speed of sound in a medium. $Z = \rho c$, the intensity reflection coefficient, and the role of coupling gel.
- Compare A-scan and B-scan ultrasound and state advantages and disadvantages.
- Describe fibre optics (TIR, critical angle) and distinguish coherentA fibre bundle where each fibre maintains its relative position at both ends, preserving image information. from incoherentA fibre bundle with randomly arranged fibres. Used for illumination only. bundles in endoscopy.
- Describe the principles of MRI: nuclear spin, precession, NMR, gradient fields, and image formation.
- Explain X-ray production via bremsstrahlung and characteristic radiation in a rotating anode tube.
- Apply $I = I_0 e^{-\mu x}$, calculate half-value thicknessThe thickness of material needed to halve X-ray intensity. $x_{1/2} = \ln 2 / \mu$., and explain contrast enhancement with barium and iodine.
- Describe X-ray detection using FTP detectors, photographic film, and image intensifiers.
- Explain how a CT scanner produces 3D images from multiple X-ray slices.
- Describe the properties of common radioactive tracers (Tc-99m, I-131) and the Mo-Tc generator.
- Describe the components and operation of a gamma cameraA device for imaging gamma-emitting tracers. It has a collimator, scintillator, photomultiplier tubes, and computer..
- Explain PET scanning (positron-electron annihilation, 511 keV photons, line of response) and apply $\frac{1}{T_E} = \frac{1}{T_P} + \frac{1}{T_B}$.
- Describe EBRT (LINAC, conformal radiotherapy) and radioactive implants (beta sources).
Notes
01
Converging and diverging lenses
Converging lens, Diverging lens
3.10.1.1
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02
The thin lens equation: 1/f = 1/u + 1/v
$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$
3.10.1.2
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03
Power of a lens and lens combinations
$P = 1/f$
3.10.1.2
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04
Structure and function of the eye
Cornea, Lens, Retina
3.10.1.3
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05
Sensitivity of rods and cones
Rods, Cones
3.10.1.4
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06
Spatial resolution of the eye
Spatial resolution
3.10.1.5
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07
Defects of vision and correction
Myopia, Hyperopia, Astigmatism
3.10.1.6
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08
Structure of the ear
Pinna, Ossicles, Cochlea
3.10.2.1
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09
Sensitivity and frequency response
Closed-tube resonator
3.10.2.2
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10
Intensity and the decibel scale
$\text{IL} = 10\log(I/I_0)$
3.10.2.2
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11
Hearing defects and hearing aids
Audiogram
3.10.2.3
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12
The electrocardiogram (ECG)
P wave, QRS, T wave
3.10.3.1
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13
Ultrasound transducer and acoustic impedance
$Z = \rho c$
3.10.4.1
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14
A-scan and B-scan ultrasound
A-scan, B-scan
3.10.4.2
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15
Endoscopy and fibre optics
Coherent bundle, TIR
3.10.4.3
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16
Magnetic resonance imaging (MRI)
NMR, Gradient field
3.10.4.4
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17
X-ray production and spectrum
Bremsstrahlung
3.10.5.1
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18
X-ray attenuation and contrast
$I = I_0 e^{-\mu x}$
3.10.5.2
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19
X-ray detection methods
FTP, Image intensifier
3.10.5.3
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20
CT scanning
CT scanner
3.10.5.4
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21
Radioactive tracers
Tc-99m, Mo-Tc generator
3.10.6.1
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22
The gamma camera
Collimator, PMTs
3.10.6.2
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23
PET scanning and effective half-life
$1/T_E = 1/T_P + 1/T_B$
3.10.6.3
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24
Radiotherapy
EBRT, Implants
3.10.6.4
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On Data Sheet
Not on Data Sheet
Thin lens equation
$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$
$f$ = focal length, $u$ = object distance, $v$ = image distance. All in metres.
Half-value thickness
$$x_{1/2} = \frac{\ln 2}{\mu}$$
Thickness to halve X-ray intensity.
Intensity level
$$\text{IL} = 10 \log_{10}\left(\frac{I}{I_0}\right)$$
$I_0 = 1 \times 10^{-12}$ W m$^{-2}$. IL in decibels.
X-ray attenuation
$$I = I_0 e^{-\mu x}$$
$\mu$ = linear attenuation coefficient (m$^{-1}$), $x$ = thickness (m).
Power of a lens
$$P = \frac{1}{f}$$
$P$ in dioptres (D), $f$ in metres. Positive for converging, negative for diverging.
Magnification
$$m = \frac{v}{u} = \frac{h_i}{h_o}$$
Ratio of image to object distance, or image to object height.
Acoustic impedance
$$Z = \rho c$$
$\rho$ = density (kg m$^{-3}$), $c$ = speed of sound (m s$^{-1}$). $Z$ in kg m$^{-2}$ s$^{-1}$.
Intensity reflection coefficient
$$\alpha = \frac{(Z_2 - Z_1)^2}{(Z_2 + Z_1)^2}$$
Fraction of ultrasound intensity reflected at a boundary.
Effective half-life
$$\frac{1}{T_E} = \frac{1}{T_P} + \frac{1}{T_B}$$
$T_P$ = physical half-life, $T_B$ = biological half-life. $T_E$ is always the shortest.
Q
Retrieval Practice
Q1. State the thin lens equation and define each term.
- $1/f = 1/u + 1/v$.
- $f$ = focal length, $u$ = object distance, $v$ = image distance.
- Positive $v$ = real image; negative $v$ = virtual image.
Q2. A person is short-sighted. Which type of lens corrects this, and why?
- A diverging (concave) lens.
- It diverges light before it enters the eye, effectively moving the image back onto the retina (from in front of it).
Q3. Why is a coupling gel essential in ultrasound scanning?
- Air has a very different acoustic impedance ($Z \approx 430$) from skin ($Z \approx 1.6 \times 10^6$).
- Without gel, almost all ultrasound would be reflected at the air-skin boundary.
- The gel has $Z \approx 1.5 \times 10^6$, closely matching skin, so most ultrasound is transmitted into the body.
Q4. State the equation for X-ray attenuation and define the half-value thickness.
- $I = I_0 e^{-\mu x}$, where $\mu$ is the linear attenuation coefficient and $x$ is thickness.
- The half-value thickness is the thickness needed to reduce the intensity to half: $x_{1/2} = \ln 2 / \mu$.
Q5. In a PET scan, what happens when a positron meets an electron? What is detected?
- Annihilation occurs: the positron and electron destroy each other.
- Two gamma photons are produced, each with energy 511 keV, travelling in exactly opposite directions.
- A ring of detectors records both photons simultaneously, and the line connecting the two detectors (line of response) locates the event.