A sample of 5CB at some temperature below has a measured birefringence at

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Condensed Matter, Materials & Soft Matter · Polarisation and anisotropic media

Soft Matter at the Thermal Scale, Ch Nematic order and the isotropic-nematic transition

Problem

A sample of 5CB at some temperature below TNIT_{\rm NI} has a measured birefringence Δn=0.135\Delta n = 0.135 at 633 nm633\,\mathrm{nm}. The fully aligned value is Δn0≈0.30\Delta n_0 \approx 0.30, inferred from 5CB's room-temperature birefringence Δn≈0.18\Delta n \approx 0.18 at Sn≈0.6S_{\rm n}\approx 0.6 through Δn≈Δn0Sn\Delta n \approx \Delta n_0 S_{\rm n}. ((a)) Estimate the nematic order parameter SnS_{\rm n} of the sample. ((b)) This nematic is placed as a planar cell of thickness d=3 μmd = 3\,\mu\mathrm{m} between crossed polarisers with the director at ψ=45∘\psi = 45^\circ to the polariser axis, at the same wavelength 633 nm633\,\mathrm{nm}. Calculate the fraction of incident intensity transmitted.

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