Double Refraction and Nicol Prism: Polarizer Explained

When unpolarized light passes through certain crystals like calcite, it splits into two refracted beams. This is called double refraction or birefringence. Each beam is polarized, and their vibration planes are perpendicular to each other.

The Nicol prism uses this effect to make a clean polarizer. It removes one of the two beams by total internal reflection, leaving a single plane polarized beam. Understanding it links crystal optics to practical polarizing devices.

Key Concepts

Ordinary ray (O-ray): Obeys the usual law of refraction with a fixed refractive index in all directions inside the crystal.

Extraordinary ray (E-ray): Its refractive index depends on direction; it does not always obey the simple refraction law in the same way.

Optic axis: A special direction in the crystal along which O and E rays travel together without splitting.

Nicol prism: A calcite crystal cut and cemented with Canada balsam. One ray is totally reflected at the cement layer and absorbed; the other is transmitted.

How It Works

1. Unpolarized light enters a calcite crystal and splits into O and E rays that travel at slightly different angles and speeds.
2. Both rays are plane polarized at right angles to each other. Rotating an analyser over each spot extinguishes them alternately.
3. In a Nicol prism, the crystal is cut at a precise angle and joined with Canada balsam (refractive index about 1.55, between the O index 1.658 and E index region).
4. The O-ray hits the balsam at a large angle and undergoes total internal reflection to the side wall, where black paint absorbs it. The E-ray passes through, giving a single polarized beam.

Worked Example

A Nicol prism is used as a polarizer and analyser pair. Unpolarized intensity is 100 units. Estimate the final intensity when the prisms are parallel, assuming ideal transmission for the passed component.

Step 1: First Nicol passes only E-ray: intensity becomes 50 units (half of unpolarized).

Step 2: Second Nicol is parallel, so it passes the incoming polarized light fully: intensity remains 50 units (ideal).

Step 3: If the second Nicol is crossed at 90°, ideal transmitted intensity becomes 0.

In real prisms there are small reflection losses, so the parallel case gives slightly less than 50 units.

Common Misconceptions

• Misconception: Both rays in calcite follow Snell's law in the same simple way. Correct: The E-ray index varies with direction; only the O-ray has a constant index.
• Misconception: A Nicol prism absorbs one ray in the balsam. Correct: The O-ray is removed by total internal reflection at the balsam, then absorbed at the side.
• Misconception: Double refraction happens in all transparent solids. Correct: It needs an anisotropic crystal; glass and water (isotropic) do not show it under normal conditions.

Real-World Applications

Nicol prisms were classic polarizers in microscopes and polarimeters before cheap Polaroid. Double refraction is used in wave plates that change polarization state, in mineral identification under polarizing microscopes, and in optical instruments that measure stress in transparent materials.

Recap: calcite splits light into two polarized rays. The Nicol prism keeps one by reflecting the other away, acting as a neat polarizer.