고급 광학 숙제 #2 제출기한: 4월 20일, 제출 장소: 담당조교 (강우영, 22-312호) 1. Show that circularly polarized light changes handedness upon reflection from a mirror. 2. Quartz is a positive uniaxial crystal with = 1.553 and = 1.544. (a) Determine the retardation per mm at 0 = 633 nm when the crystal is oriented such that retardation is maximized. At what thicknesses does the crystal act as a quarter-wave plate? (b) Determine the direction of propagation in quartz at which the angle between the propagation vector ⃗ and the Poynting vector is maximum. 3. A right-circularly polarized wave with wavelength λ is incident in the z-direction on a half-wave plate made from a crystal with principal refractive indices (for xand y-polarization) 1 and 2 . (a) What is the thickness of the plate? (b) Show that the wave exits the plate with left-circular polarization. 4. A wave that is linearly polarized in the x direction is transmitted through a sequence of linear polarizers whose transmission axes are inclined by angles ( = 1,2, … , ; = ⁄2) with respect to the x axis. Show that the transmitted light is linearly polarized in the y direction but its amplitude is reduced by the factor . What happens in the limit → ∞? 5. Consider the propagation of light along the axis of twist (the z axis) of a twisted nematic liquid crystal and assume that the twist angle θ varies linearly with z, θ = αz, where α is the twist coefficient (degrees per unit length). The phase retardation coefficient β = ( − )0 is much larger than α. Show that if the incident wave at z = 0 is linearly polarized in the direction of the optic axis (x direction), the liquid crystal works as a polarization rotator with rotation angle αd.

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# 고급 광학 숙제 #2