Describe what happens to unpolarized light incident on a birefringent material w
ID: 1522759 • Letter: D
Question
Describe what happens to unpolarized light incident on a birefringent material when the optical axis (OA) is oriented as shown below. You will want to comment on the following considerations: Single or double refracted rays? Any phase retardation? Any polarization of refracted rays? Which orientation(s) would you use to make a quarter-wave plate? Why? What minimum thickness should a piece of quartz have to act as a quarter-wave plate for a wavelength of 589.3 nm in vacuum? Will other thicknesses work? Explain.(n_0 = 1.5443, n_e = 1.5534)Explanation / Answer
b) Quarter-wave plates are used to turn plane-polarized light into circularly polarized light and vice versa. To do this, we must orient the wave plate so that equal amounts of fast and slow waves are excited. We may do this by orienting an incident plane-polarized wave at 45° to the fast (or slow) axis.
c)
Let the refractive indices for the two waves be n1 and n2
speed of light in vacuum = c
speed of light in quartz = s1, s2
wavelength of light in vacuum = L
frequency of light = f
time = t
s = c/n
time taken for a wave to traverse thickness T is t = T/s = Tn/c
t1 - t2 = (T/c)(n1 - n2) ... (1)
for a 1/4 wave phase difference on emergence from the plate -
t1 - t2 = N/(4*f) = N*L/(4*c) where N is 1, 5, 9 etc i.e 4a + 1, a being any integer
t1 - t2 = (4a +1)*L/(4*c) = (T/c)(n1 - n2) ... from (1)
T(n1 - n2) = (4a +1)*L/4 ...(2) let a be 1.
T = (4a +1)*L/{4*(n1 - n2)} = 0.0809 micrometers