Past exam of the physics A course of the University of Cambridge / 2013 / Paper 2 / Section A

The wavelength is $\lambda =c/f\simeq 0.020\mathrm{m}$. The longest interferometric baseline measures the finest angular structure and the shortest-baseline angular scale describes the coarsest:These are order-of-magnitude scales, not sharp cutoffs. A commonly used maximum-recoverable-scale convention is $0.6\lambda /B_{\min }$, giving about $8.2^{\prime }$; reconstruction also depends on baseline coverage and source structure. The individual antenna's primary beam is a separate field-of-view limit.^[ref]

A thin antireflection coating makes reflections from its two interfaces interfere destructively near a chosen wavelength, often in the green part of the visible spectrum. For a single lossless layer at normal incidence, $n_{f}d={\lambda }_0/4$ and ideally $n_f=\sqrt{n_0{n}_s}$ minimize reflection at ${\lambda }_0$. reflection is less completely cancelled in the red and blue, so the residual reflected light can appear purple. This is primarily a reflection colour, not a claim that the transmitted beam is strongly purple. Multilayer coatings can broaden the low-reflectance band.

Sound compressions in air are approximately adiabatic, giving $c_s^2=(\partial p/\partial \rho {)}_s=\gamma p/\rho$. With $p=\rho RT/M$,Here dry air is approximated as a diatomic ideal gas with $\gamma =7/5$ and molar mass $M\simeq 0.029\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$. The ideal-gas law alone is insufficient without this adiabatic response and mean molecular mass; humidity and composition affect a more precise inference.

For conventional cubic cell side $a$, the face-centered cubic lattice has corner and face-centre sites, giving four lattice points per cell; the body-centered cubic lattice has corners and a body centre, giving two. Their primitive unit cells each contain one lattice point. With reciprocal vectors written $\mathbf{G}=(2\pi /a)(h,k,l)$, face-centered cubic lattice allows $h,k,l$ all even or all odd, while body-centred cubic allows $h+k+l$ even. HenceHere $a^{\ast }$ is the side of the reciprocal lattice's conventional cubic cell. The parity conditions describe the reciprocal point sets; reciprocal space contains wavevectors, not a second arrangement of physical atoms.

In the Hall effect, the Lorentz force deflects drifting charge carriers until a transverse electric field balances it: ${\mathbf{E}}_H=-{\mathbf{v}}_d\times \mathbf{B}$. Choose current along $x$, field along $z$ and define $R_H=E_y/(j_x{B}_z)$. Since $j_x=nq{v}_x$,The sign is negative for electrons with this convention. If the sample's mass density is ${\rho }_m$ and its molar mass is $M$, the atomic number density is $n_{\mathrm{at}}={\rho }_m{N}_A/M$, soMeasure the transverse voltage, specimen thickness, current and magnetic field; reversing field and current helps remove longitudinal-voltage pickup and offsets. This free-electron count from a Hall coefficient assumes one approximately free carrier band. Multiple bands, unequal mobilities or a complicated Fermi surface can make a Hall coefficient differ from $-1/(ne)$.