A mica retarder lies between two ideal linear polarisers on an optical bench

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 mica retarder lies between two ideal linear polarisers on an optical bench, illuminated at normal incidence by monochromatic light of vacuum wavelength λ=589\lambda = 589 nm. The first polariser's transmission axis is taken as 0∘0^\circ; the light leaving it has irradiance I1I_1. The plate's fast axis is at 30∘30^\circ to this axis; mica's birefringence is ∣ne−no∣=5.0×10−3|n_e-n_o| = 5.0\times10^{-3} (Section 9.1) and the plate's thickness is d=100 μmd = 100\ \mu\text{m}. The second polariser (the analyser) is parallel to the first, also at 0∘0^\circ. ((a)) Compute the plate's retardance Γ\Gamma, in radians. ((b)) Write the plate as R(30∘) diag(1,eiΓ) R(−30∘)\mathbf{R}(30^\circ)\,\mathrm{diag}(1,e^{i\Gamma})\,\mathbf{R}(-30^\circ) acting on the horizontal light leaving the first polariser (Section 9.5), and find the irradiance leaving the analyser as a fraction of I1I_1. ((c)) The mica plate is now replaced by an unknown sample Y, and the analyser is turned to be crossed with the input polariser for this test. With the input polariser at 0∘0^\circ and the analyser at 90∘90^\circ, sample Y gives full extinction. Turning the input polariser to 20∘20^\circ, no analyser angle restores extinction; the darkest setting found while sweeping the analyser still transmits a small non-zero irradiance. Using the two-measurement test of Section 9.7, state what kind of element Y must be, and give the one other input angle, between 0∘0^\circ and 180∘180^\circ, at which full extinction would again be recoverable for some analyser setting.

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