Past exam of the optics and electrodynamics course of the University of Cambridge / 2012 / Paper 1 / 1

The electric field of the reflected beam is perpendicular to the vertical plane of incidence, hence parallel to the water surface. At Brewster's angle the reflected p-polarization amplitude vanishes; only the s-polarization component remains. For incidence from air, approximated by refractive index one,Incidence is measured from the surface normal, whereas solar elevation is measured from the horizontal. The Brewster solar elevation is thereforeThis assumes an ideally flat, transparent, nonmagnetic interface; ripples, absorption and diffuse light would spoil complete polarization.

For a Hertzian dipole of length $\ell$ driven at peak electric current $I_0$, the electric dipole moment amplitude is $p_0=I_0\ell /\omega$. ConsequentlyThe Hertzian dipole fixed-current power scaling is thus $\overline{P}\propto I_0^2{\ell }^2/{\lambda }^2$, givingThe inverse-fourth-power wavelength scaling would hold at fixed electric dipole moment, not at the fixed electric current specified here.

During the time light crosses a telescope of length $L$, Earth moves sideways by approximately $vL/c$. The telescope must tilt towards Earth's motion so that both ends intercept the ray. Thus the annual stellar aberration amplitude at a transverse sightline is $\delta \simeq v/c$.

Taking one orbital year as $365.25$ days and treating the orbit as circular,This is the instantaneous shift relative to a stationary heliocentric observer, not the doubled peak-to-peak annual excursion. The exact Lorentz transformation for a ray transverse in that frame gives $\sin \delta =v/c$, with the same first-order result.