---
title: "Nicol prism as polarizer and analyzer"
subject: "Engineering Physics"
chapter: 4
key: "semester_1/engineering_physics:nicol-prism-polarizer-analyzer"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/nicol-prism-polarizer-analyzer
site: BCT Engineering
---

# Nicol prism as polarizer and analyzer

Engineering Physics · Chapter 4: Physical Optics

- Asked in: 2069 Asar, 5 marks; 2069 Chaitra, 5 marks; 2067 Asoj, 5 marks (asked 3 times)
- Video: [Nicol Prism: Polarizer and Analyzer](https://www.youtube.com/watch?v=nAJ-aFyjGmM) — MK Sir Physics
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/nicol-prism-polarizer-analyzer
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-4

## Question

Explain the phenomenon of double refraction. Describe the construction and action of Nicol prism and explain how it can be used as a polarizer and analyzer.

## Short answer

Double refraction: in calcite, o-ray (μ_o=1.658) and e-ray (μ_e=1.486) emerge plane-polarized. Nicol prism: calcite cut at 68°/112°, cemented with Canada balsam (μ=1.55), o-ray totally reflected, e-ray transmitted. As polarizer and analyzer, intensity follows I=I₀cos²θ (Malus' law).

## Answer

**Double refraction (birefringence)**: a ray of unpolarized light entering a calcite (or quartz) crystal splits into two rays that travel with different speeds. The **ordinary ray** obeys Snell's law (μ_o = 1.658 for calcite) and the **extraordinary ray** does not (μ_e = 1.486 for light travelling perpendicular to the optic axis). Both rays are plane polarized, with vibrations perpendicular to each other. Along the optic axis there is no splitting.

#### Construction of a Nicol prism
1. Take a calcite crystal whose length is about three times its width. Grind the end faces so that the angles of the principal section become 68° and 112° instead of 71° and 109°.
2. Cut the crystal diagonally along a plane perpendicular to the principal section and to the new end faces.
3. Polish the cut faces and cement them together with a thin layer of **Canada balsam** (μ = 1.55).
4. Blacken the sides and enclose the prism in a tube.

```text
      68°  ____________________
    ____  /  /     (Canada balsam layer)
 o --\--/ / ---> o ray totally reflected
 unpol. \ /  ===> e ray passes through
     ___/_/_____________
```

#### Action
- Canada balsam has μ = 1.55, which lies between μ_e (1.486) and μ_o (1.658).
- The o-ray goes from calcite (denser for it, 1.658) to balsam (rarer, 1.55). Its angle of incidence at the balsam layer is greater than the critical angle, sin⁻¹(1.55/1.658) ≈ 69°, so it is **totally internally reflected** and absorbed by the blackened side.
- The e-ray goes from calcite (1.486) to balsam (1.55), i.e. from rarer to denser, so it is transmitted.
- The emergent beam is plane polarized, with vibrations in the principal section.

#### Use as polarizer and analyzer
Two Nicols are placed in line.
- The first, the **polarizer**, produces plane polarized light.
- The second, the **analyzer**, examines it. The transmitted intensity is **I = I₀ cos² θ** (Malus's law), where θ is the angle between their principal sections.
- Parallel (θ = 0): maximum intensity; crossed (θ = 90°): complete darkness.

Rotating the analyzer therefore shows whether the light is plane polarized.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why is Canada balsam (μ = 1.55) used in the Nicol prism?
   A. Its index lies between μ_e and μ_o, so the o-ray is totally reflected and the e-ray transmitted
   B. It absorbs the e-ray
   C. It has a lower index than both rays
   D. It colours the light
   Answer: A. The o-ray (1.658) meets a rarer medium beyond the critical angle and is totally reflected; the e-ray (1.486) meets a denser medium and passes. (Key point: Role of Canada balsam)

2. The light emerging from a Nicol prism is
   A. the o-ray, unpolarized
   B. both rays
   C. the e-ray, plane polarized in the principal section
   D. circularly polarized
   Answer: C. The o-ray is removed, leaving plane-polarized e-ray light. (Key point: Which ray emerges)

3. When two Nicols have principal sections at angle θ, the transmitted intensity is
   A. I0 sin² θ
   B. I0 cos θ
   C. I0 cos² θ
   D. I0 sin θ
   Answer: C. Malus's law gives I = I0 cos²θ. (Key point: Malus's law)

4. With the polarizer and analyzer crossed (θ = 90°), the output is
   A. maximum
   B. half of maximum
   C. complete darkness
   D. circularly polarized light
   Answer: C. cos²90° = 0, so no light is transmitted. (Key point: Crossed Nicols)

## Related in Engineering Physics

- [Double refraction, linear and circular light](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adouble-refraction-produce-polarized-light) — Engineering Physics, chapter 4

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