Section 10 — Polarization
GE-4 / PHYS7021 unit 10 · 5 solved questions
10.1 Theory you need
- Light is transverse ⇒ its E-vector can be oriented: plane polarized (E in one plane), unpolarized (random planes), circular/elliptical (E rotates with constant/varying magnitude).
- Production: reflection (Brewster), scattering, selective absorption (Polaroid/Nicol), double refraction (calcite).
- Double refraction: in anisotropic crystals one ray splits into ordinary (o, obeys Snell) and extraordinary (e) rays. Huygens: o-wavelet spherical, e-wavelet ellipsoidal; the two tangents give the two refracted wavefronts.
- Quarter-wave plate (QWP): introduces path difference λ/4 between o and e: thickness t = λ/4|μe−μo|. Plane-polarized light at 45° to the axis → circular; at other angles → elliptical.
10.2 Solved past questions — exam-style answers
1. Difference between polarised and unpolarised light.
- Unpolarized light: the E-vector vibrates in all directions perpendicular to propagation with equal probability (ordinary sources).
- Plane polarized light: the E-vector vibrates in one fixed plane only.
- Polarization itself is the proof that light is a transverse wave.
∴ Unpolarized: all planes · Polarized: one plane
2. What is meant by double refraction? Name a double-refracting crystal.
- When a ray enters an anisotropic crystal it splits into two refracted rays: the ordinary ray (obeys Snell's law) and the extraordinary ray (does not); hence an object seen through the crystal shows two images.
- Examples: calcite, quartz, Iceland spar, tourmaline.
∴ Splitting into o-ray + e-ray; e.g. calcite
3. Write Huygens' theory of double refraction.
- In a uniaxial crystal the speed is the same in all directions for the o-wave ⇒ spherical wavelet; for the e-wave the speed depends on direction ⇒ spheroidal (ellipsoidal) wavelet, touching the sphere along the optic axis.
- From each point of an incident plane wavefront AB inside the crystal, draw both wavelets.
- The two common tangent planes to all spheres and all spheroids give two parallel refracted wavefronts — the o-wavefront and the e-wavefront.
- Hence two refracted rays with different speeds and indices (o and e).
∴ Spherical (o) + ellipsoidal (e) wavelets → two refracted rays
4. Thickness of a quarter-wave plate for sodium light (2024: μ0 = 1.544, μe = 1.553, λ = 589.6 nm; 2022 quartz: μ0 = 1.544, μe = 1.535, λ = 5.9×10−5 cm).
Formula: t = λ / (4|μe − μo|); here Δμ = 0.009 in both cases.
- 2024: t = 589.6×10−9/(4 × 0.009) = 1.64×10−5 m ≈ 0.0164 mm.
- 2022: t = 5.9×10−7/(4 × 0.009) = 1.64×10−5 m ≈ 1.64×10−3 cm.
∴ t ≈ 1.64×10⁻⁵ m ≈ 0.0164 mm
5. Prepare elliptically & circularly polarized light using Nicol prism and quarter-wave plate.
- Pass light through a Nicol prism (polarizer) ⇒ plane-polarized beam.
- Let it fall normally on a quarter-wave plate; the beam splits into o and e components with a λ/4 (π/2) phase difference after the plate.
- Circular: set the incident vibration at 45° to the optic axis ⇒ equal o and e amplitudes + π/2 phase ⇒ circularly polarized light.
- Elliptical: at any other angle the amplitudes are unequal ⇒ elliptically polarized light.
- Check with analyser: circular ⇒ intensity unchanged on rotation; elliptical ⇒ intensity varies but never becomes zero.
∴ 45° + QWP → circular ; other angle → elliptical