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 photographer stands at the shore of a calm, horizontal alpine lake (refractive index of water n=1.33) at sunrise, when the Sun is 20.0∘ above the horizon. The glare that reaches her eye comes from the point on the water where a ray from the Sun reflects into her line of sight; for a horizontal surface the angle of incidence θi (measured from the vertical normal) is 90∘ minus the Sun's elevation. Treat sunlight as unpolarised (equal s and p power), the surface as a perfect plane mirror for this ray, and any polarising filter used below as ideal: it transmits all of the power in the component aligned with its axis and none of the power in the orthogonal component.
((a)) Find θi for this ray, and compute Brewster's angle θB for the air-water interface. Say whether θi is above or below θB.
((b)) Use Snell's law to find the transmission angle θt, then use the Fresnel formulas to compute Rs and Rp for this reflection.
((c)) State which direction (vertical or horizontal) is s and which is p for this reflection, and hence find the fraction of the glare's power passed by a filter held with its transmission axis vertical, and by the same filter turned horizontal. Say which orientation a pair of sunglasses should use.