Question 9.20: QUARTZ HALF-WAVE PLATE What should be the thickness of a hal...

QUARTZ HALF-WAVE PLATE What should be the thickness of a half-wave quartz plate for a wavelength λ ≈ 707 nm given the extraordinary and ordinary refractive indices are n_{o} = 1.541 and n_{e} = 1.549?

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Half-wavelength retardation is a phase difference of \pi, so from Equation 9.81

\phi=\frac{2 \pi}{\lambda}\left(n_{e}-n_{o}\right) L=\pi

giving

L=\frac{\frac{1}{2} \lambda}{\left(n_{e}-n_{o}\right)}=\frac{\frac{1}{2}\left(707 \times 10^{-9}  m \right)}{(1.549-1.541)}=44.2  \mu m

This is roughly the thickness of a sheet of paper.

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