PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Polarisation and anisotropic media
Optics and Photonics, Ch Reflection and transmission at interfaces
Problem
A sailor watches a calm, horizontal harbour (refractive index of water n=1.33) at dusk, when the Sun is only 10.0∘ above the horizon. Glare reaches the eye from the point on the water where a ray from the low Sun reflects into the line of sight; for a horizontal surface the angle of incidence θi (from the vertical normal) is 90∘ minus the Sun's elevation. Treat sunlight as unpolarised (equal s and p power), the water as a perfect plane mirror for this ray, and any polarising filter used below as ideal: it transmits all the power in the component aligned with its axis and none in the orthogonal component.
((a)) Find θi for this ray, and compute Brewster's angle θB for the air-water interface. Say how far θi is from θB.
((b)) Use Snell's law to find θt, then use the Fresnel formulas to compute Rs and Rp.
((c)) State which direction is s and which is p for this reflection, find the fraction of the glare's power passed by an ideal filter with its axis vertical and with its axis horizontal, and say whether polarising sunglasses work as well here as they do when the Sun is higher.