Quartz at 589 nm has and (a positive uniaxial crystal
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
Quartz at 589 nm has no=1.544 and ne=1.553 (a positive uniaxial crystal, so the extraordinary wave is the slower, higher-index one and the ordinary axis is the fast axis).
((a)) A quartz-air interface is cut so that a beam inside the crystal can strike it at a variable angle. Using Snell's law and the definition of the critical angle (Chapter 6), find the critical angle for the ordinary wave and for the extraordinary wave at this interface. Explain in one or two sentences, referring to how a Glan-Taylor prism works (Section 9.3), why these two numbers make quartz a poor material for a polarising prism, in contrast to calcite (no=1.658, ne=1.486).
((b)) A quartz plate of thickness d=15μm is cut with the optic axis in its face and placed with its fast axis at 45∘ to the transmission axis of an ideal linear polariser. Light of vacuum wavelength λ=589nm passes through the polariser, then the plate, then a second ideal linear polariser crossed with the first (transmission axis at 90∘ to the first). Using the Jones matrix methods of Chapter 8 and the retardance formula of Section 9.4, find the fraction of the irradiance leaving the first polariser that emerges from the second.