Optional Modules: Astrophysics, Medical Physics, Engineering Physics and Turning Points
Choosing the optional module
You sit one optional module. The common exam skill is to identify the governing equation and check units; the content differs sharply.
Astrophysics and cosmology
- Parallax: d(pc) = 1/p(arcsec).
- Distance modulus m − M = 5 log10(d/10).
- Wien λmaxT = 2.9 × 10^-3 m K; Stefan L = 4πr²σT⁴; flux F = L/(4πd²).
- Hubble v = H0d, redshift z = Δλ/λ ≈ v/c for low z.
Medical physics
- Attenuation I = I0e^(−μx); half-value layer x½ = ln2/μ.
- Ultrasound reflection depends on acoustic impedance Z = ρc; Doppler shift for blood flow.
- Gamma camera: collimator, scintillator, photomultiplier; tracer half-life chosen short.
Engineering physics
Rotational dynamics τ = Iα, angular momentum conservation; materials and thermodynamics; fluid flow continuity A1v1 = A2v2 and Bernoulli.
Turning points
Photoelectric effect, Millikan's oil-drop, Rutherford scattering, Michelson–Morley, and the development of quantum and relativity ideas.
Worked example
A star has parallax 0.025 arcsec, so d = 40 pc. With apparent magnitude m = 6.0, m − M = 5 log(4) = 3.01, so M = 2.99. If its peak wavelength is 500 nm, surface temperature T = (2.9 × 10^-3)/(500 × 10^-9) = 5800 K.
Traps
Using arcminutes in parallax; log base e in distance modulus; mixing luminosity and flux; forgetting that medical attenuation is exponential, not linear; quoting optional-module facts without linking them to the equation.