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 𝑛𝑒 = 1.553 and 𝑛𝑜 = 1.544.
(a) Determine the retardation per mm at 𝜆0 = 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 𝑘⃗ and the Poynting vector 𝑆 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) 𝑛1 and 𝑛2 .
(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 𝑁 linear polarizers whose transmission axes are inclined by angles
𝑚𝜃 (𝑚 = 1,2, … , 𝑁; 𝜃 = 𝜋⁄2𝑁) 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 𝑐𝑜𝑠 𝑁 𝜃. What happens in the limit 𝑁 → ∞?
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 = (𝑛𝑒 − 𝑛𝑜 )𝑘0 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.