A telecoms technician wonders whether a scrap of quartz (
PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Polarisation and anisotropic media · Polarisation and anisotropic media
Optics and Photonics, Ch Birefringence and crystal optics
Problem
A telecoms technician wonders whether a scrap of quartz (no=1.544, ne=1.553 at 589 nm) could be cut into a polarising prism like the calcite Glan-Taylor prism of Section 9.3.
((a)) Calculate the critical angle for total internal reflection at a quartz-air interface for the ordinary wave.
((b)) Calculate the critical angle for the extraordinary wave, and hence the angular window between the two critical angles. Compare this window with calcite's (37.1∘ to 42.3∘) and say whether a workshop that can hold a cutting angle to within ±0.5∘ could reliably make a quartz polarising prism.
((c)) Instead, light of vacuum wavelength 589 nm passes through an ideal linear polariser with its transmission axis horizontal, then through a real quartz plate of thickness d=15μm with its fast axis at 30∘ to the horizontal, then through a second ideal polariser (the analyser) with its transmission axis vertical (crossed with the first). Take ∣ne−no∣=0.009. Using the Jones matrix of the plate (Chapter 8's rotation matrices about the plate's own axes) and Malus-type projection onto the analyser, find the fraction of the irradiance leaving the first polariser that emerges from the analyser.