L-8: Polarization

OBJECTIVE: To study polarization and double refraction of light.

APPARATUS:

Polarization kit plus a polariscope; Brewster angle assembly (laser + mount on M-2 force table, slotted pin & black piece of plastic).

SUGGESTED EXPERIMENTS:

1. Polarization by ABSORPTION: Observe a light source (desk lamp) thru each of two polaroids, and then thru both together. Rotate one of the two about the line of sight. Explain what occurs.

   Orient the two polaroids of the polariscope so no light is transmitted. Then introduce a third polaroid between the first two and rotate it about the line of sight. Explain what happens.
   HINT: there will be an amplitude component $E \cos \theta$ in the direction of the transmission axis.

2. Polarization by REFLECTION from a dielectric: Observe thru the small polaroid (the one with the rim index marks) the light reflected from the black plastic (see figure at right). Rotate the polaroid about the line of sight. Note position of the index marks (i.e. the E vector direction) on polaroid when the transmitted reflected light is a minimum.

   Figure 1: Reflection and transmision of light at Brewster's angle.

   

   Now find an incident angle $\theta_i$ (and reflection angle $\theta_r$) for which this minimum is zero. Then $\theta_i$ is Brewster's angle, $\theta_B$, and $\tan \theta_B = n_2/n_1$. Estimate $\theta_B$ roughly. What is the refractive index $n_2$ of the plastic?

   Alternatively for greater accuracy use a laser plus polaroid to prepare a beam polarized in the plane containing the incident ray and the normal to the reflecting surface. The reflected beam then vanishes at Brewster's angle. Mount laser plus polaroid on the M-2 force table and point it toward a dielectric (plastic or microscope slide) in the slot of the central pin. Rotate the sample until the reflected beam (on the wall) disappears. A thread from the center pin to this point on the wall will help locate the angles on the M-2 table.

   Observe any polarization of light reflected from painted or varnished surfaces, floor tile, clean metal (e.g. aluminum foil) etc.
3. Polarization by SCATTERING: Try to detect the polarization of skylight: one needs a blue sky! Explain (use a diagram) in what direction relative to sunlight should one look to see this polarization best.
4. Polarization by a DOUBLY REFRACTING CRYSTAL: Uniaxial doubly refracting crystals (e.g. calcite) are highly anisotropic and, as such, contain an axis of symmetry (the optic axis) for which the velocity of light depends on whether the $E$-field vector (polarization plane) is $\perp$ to this axis (the ordinary ``$o$'' ray) or parallel to the optic axis (the extraordinary ``$e$'' ray). In the principal plane (i.e. a plane containing the optic axis but $\perp$ to the surface) the new wave front of the ordinary ray involves the usual spherically expanding wavelets, but to construct the front for the extraordinary ray requires ellipsoidally expanding wavelets where the two axes of the ellipse are proportional to the velocities of the parallel and $\perp$ vibrations to the optic axis.

   Calcite (CaCO$_3$) has a large velocity differences between the $o$ and $e$ rays, and its optic axis is the direction at equal angles with the crystal edges at the obtuse corners.

   Observe through the calcite crystal a dot on a piece of paper. Rotate the crystal about the line of sight. Describe the behavior of the two images of the dot. Introduce a polaroid between your eye and the crystal. Note how the appearance of the two images changes as you rotate the polaroid about the line of sight. Explain.

NOTE: For the remaining experiments use the POLARISCOPE. The polaroid next to the light is the ``POLARIZER,'' the other is the ``ANALYZER.'' Place the samples to be studied on top of the polarizer.

5.

CIRCULAR POLARIZATION: A thin doubly refracting crystal cut so that the optic axis is parallel to a surface constitutes a retardation plate. The difference in velocity of the $o$ and $e$ rays then gives a phase difference between the emerging orthogonally polarized rays. If the phase difference is $90^o$, the retardation is $\lambda /4$: hence a ``quarter wave plate''.

Figure 2: Obtaining circularly polarized light from unpolarized light

Set the analyzer of the polariscope to transmit no light. Then place the $\lambda /4$ plate between the polarizer and analyzer and rotate the $\lambda /4$ plate so that extinction again results. You will find two such extinction positions $90^o$ apart. Why?
HINT: When the optic axis is aligned with the polarization direction of the incoming plane polarized wave, will there be any ordinary ray amplitude? Then when you turn the plate (and thus the optic axis) thru $90^o$, will there be any extraordinary ray amplitude.

Rotate the $\lambda /4$ plate to a position halfway between the two extinction positions; thus the optic axis will make a $45^o$ angle to the incident plane of polarization. Explain why the plate now looks bright. Leaving the $\lambda /4$ plate in this position, rotate the analyzer through $2\pi$ radians. Why does the brightness stay approximately constant$^{\ast}$?
HINT: Recall the conditions for a circular Lissajous figure (see E-8 Part B, Fig. 3).

$^{\ast}$

If it doesn't, repeat the preceding operations. You may not have set the $\lambda /4$ plate close enough to the halfway or $45^o$ position. Also remember that a $\lambda /4$ plate is exactly $\lambda /4$ only for a single $\lambda$.

6.

TWO $\lambda /4$ PLATES: Place a $\lambda /4$ plate on the polarizer so as to produce circularly polarized light. Place a second $\lambda /4$ plate on top of the first and similarly oriented. Observe and explain what happens when you now rotate the analyzer. Turn the top $\lambda /4$ through $90^o$ about the line of sight. Observe and explain what happens now when you rotate the analzyer.

7.

COLOR EFFECTS: If the plate is thick enough for retardations of several (but not too many) wavelengths, color effects may result. For a constant refractive index:

$$\lambda _{\mbox{\small red}} \; \sim \; 660 \; \mbox{nm} \; \... ...} (\lambda _{\mbox{\small blue}} \;\sim \; 440 \; \mbox{nm}) .$$

Thus a $\lambda /2$ plate for red is a $3\lambda /4$ plate for blue. [In general, a n($\lambda /2$) plate for red $\sim 3n (\lambda /4$) plate for blue where n is an odd integer.] Hence for white light such a plate at $45^o$ between parallel polaroids would completely extinguish the red but pass the circularly polarized blue light. The resultant color is complementary to that removed. The intensity (hue and saturation) will of course vary with the relative orientation of polarizer, the retardation plate, and the analyzer. As n becomes large the range of $\lambda$ extinguished narrows. Hence that passed is more nearly white.

a)

Place thin mica on the polarizer (with analyzer crossed). Try various mica orientations. Explain.

b)

Repeat a) for the mounted specimen of cellophane tape.

8.

PHOTO-ELASTIC EFFECTS: Strained isotropic materials become doubly-refracting.

With the polariscope set for extinction:

a)

Insert and flex the U-shaped lexan (a polycarbonate resin) sample.

b)

Insert a microscope slide vertically. View the long edge and stress the slide by gently flexing it. Note result. (Glass blowers use polarized light to test for residual glass strains).

9.

LCD APPLICATIONS: Watches and calculators often use LIQUID CRYSTAL DISPLAYS (LCD) in which nematic liquids (thread like molecules arranged nearly parallel to each other) can become optically active, rotate the plane of polarization and thus permit light to pass thru crossed polaroids. A reflector after the analyzer returns the light through the cell.

Figure 3: Construction of a liquid crystal display

To produce the optical rotation: two glass plates, which have been rubbed in one direction to produce invisible scratches, attach aligned nematic molecules. If a few micron thick nematic liquid separates the plates, and if one plate is rotated relative to the other, then the helical arrangement of the nematic liquid produces a rotation of the plane of polarization.

To extinquish the light one applies a voltage between the transparent (but conducting) tin-oxide coated glass surfaces. A sufficient voltage gradient will align the dipole moments of the molecules and thus destroy the optical rotatory power. Voltages applied to segments of the seven segment pattern (see figure) permit display of any numeral 0 to

The power consumption of such an LCD is almost negligible.

OPTIONAL QUESTIONS:

1. How experimentally can one tell whether a light beam is unpolarized? Plane polarized? Circularly polarized?
2. How could you tell whether an object is a gray plastic, a polarizing sheet, a $\lambda /4$ plate or a $\lambda /2$ plate?
3. How could you change right circularly polarized light to left circularly polarized light?
4. Why does the flexed lexan show colors but not the microscope slide?