A slice of quartz is cut with its optic axis lying in the plane of its faces

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 slice of quartz is cut with its optic axis lying in the plane of its faces, so it acts as a wave plate of thickness

d = 49.1\ \mu\text{m}

. It is placed between two crossed polarisers (transmission axes at

0^\circ

and

90^\circ

), with its fast axis set at

45^\circ

to the first polariser. Light of vacuum wavelength

\lambda = 589\ \text{nm}

leaves the first polariser with irradiance

I_0

. Quartz's principal indices at this wavelength are

n_o = 1.544

n_e = 1.553

. ((a)) Compute the plate's retardance

\Gamma

. ((b)) Using the Jones matrix construction

\mathbf{R}(45^\circ)\,\mathrm{diag}(1,e^{i\Gamma})\,\mathbf{R}(-45^\circ)

acting on horizontal input, find the irradiance transmitted by the analyser as a fraction of

I_0