Nicol prism as polarizer and analyzer

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.

      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.