Nicol prism

Nicol prism

1. What Nicol Prism Is

Nicol prism = polarizing beam splitter made from calcite ($CaCO_3$) that transmits $e$-ray (plane polarized) and eliminates $o$-ray by total internal reflection at a Canada balsam cement layer. Invented by William Nicol (1828).

2. Construction (diagram description)

Calcite rhombohedron (length ≈3× breadth) cut diagonally at ~68° to edge, polished, cemented with Canada balsam (μ_b≈1.55)
Natural calcite indices: μ_o≈1.658, μ_e≈1.486 (for Na light, varies with λ)
Optic axis in plane of cut.
Incident ray splits into o (μ_o=1.658) and e (μ_e≈1.486) at entrance.
At balsam layer: μ_o (1.658) → μ_b (1.55): o-ray goes denser→rarer? Actually 1.658→1.55 is rarer ⇒ can TIR if angle > critical angle θ_c = sin^{-1}(1.55/1.658)≈68° (cut angle chosen 68° ensures >θ_c)
e-ray: μ_e≈1.486 → μ_b 1.55 is rarer→denser ⇒ no TIR, transmits.
Reflected o-ray is absorbed by blackened side.

Result: exit beam is linearly polarized $e$-ray only, vibration parallel to principal section.

3. Working Angles

• Must be cut so $o$-ray hits balsam at >$θ_c$ (≈68°) to TIR, while $e$-ray at <θ_c. Length/breadth ratio ~3 gives ~22° incidence at balsam for normal entrance? Exact 68° cut ensures this.

4. Uses and Limitations

• Used as polarizer (produce polarized) and analyzer (test polarization: crossed Nicols extinguish).
• Limitations: narrow field (±~10°) because $θ_c$ sensitive; chromatic (indices vs λ); bulk, expensive vs modern Polaroid/HR polarizers; cannot work at high intensity (balsam absorbs UV). Now replaced by Glan-Thompson, Wollaston, sheet polarizers, but syllabus keeps Nicol as classic.

5. Modern Alternatives (mention for completeness)

Glan-Thompson (cement with different index), Glan-Taylor (air gap), Wollaston (splits both $o$ and $e$ at angle). All use same birefringence + TIR/polarization separation principle.

6. Worked Check

μ_o=1.658, μ_b=1.55 ⇒ θ_c= arcsin(1.55/1.658)=69.2°? Actually sin^{-1}(0.9349)=69.2°; cut ensures o hits at ~75° >69° ⇒ TIR ✓
e: μ_e=1.486 ⇒ 1.486→1.55 is denser ⇒ no TIR ⇒ transmits ✓

7. Exam Points

• Diagram + construction + working of Nicol prism — 7 marks, very frequent (almost certain to ask as "describe Nicol prism").
• Explain why $o$-ray TIR and $e$-ray transmits (critical angle) — 5 marks, very frequent.
• Give $\mu_o, \mu_e, \mu_{balsam}$ and cut angle 68° — 3-5 marks, frequent.
• Use as polarizer/analyzer and crossed Nicols extinction — 3 marks.