Optical Rotation: Polarimetry of Chiral Solutions

Solution

Compound

Concentration c 0.20 g/mL

Tube length l 1.0 dm

Light

Analyzer

Analyzer angle θ_a 0°

Rotate the analyzer until the exit beam goes darkest — extinction happens 90° away from the true rotation angle α.

Readouts

Rotation α

0.0°

[α]_λ

0.0°

Transmitted intensity (Malus's law)

100.0%

How it works

Plane-polarized light entering a solution of chiral molecules has its polarization plane rotated because left- and right-circularly-polarized components (the two halves the plane wave decomposes into) travel at slightly different speeds through a chiral medium — circular birefringence. The total rotation follows Biot's law:

α = [α]_λ^T · l · c

α       observed rotation (degrees)
[α]     specific rotation of the compound at wavelength λ, temperature T
l       path length through the cell, in decimetres
c       concentration, in g/mL

[α] itself depends on wavelength (optical rotatory dispersion). Far from any absorption band this follows the single-term Drude equation used here:

[α](λ) = A / (λ² − λ_c²)

with λ_c an ultraviolet transition of the molecule — this is why violet light rotates more than red for the same solution. A racemic 50/50 mixture of the two enantiomers shows zero net rotation: their equal-and-opposite contributions cancel exactly, even though every individual molecule is still chiral.

Compound — switches sign and magnitude of the reference rotation (dextro-/levorotatory/racemic).
Concentration & tube length — both enter Biot's law linearly.
Wavelength buttons — recompute [α] from the Drude dispersion relation and recolor the beam.
Analyzer angle — a second polarizer whose transmission follows Malus's law, I = I₀cos²(θ_a − α); this is exactly how a real polarimeter reads off α by finding the extinction angle.

Real-world relevance: this is the working principle behind saccharimeters used in the sugar industry, and behind pharmaceutical QC checks that confirm a drug is the correct enantiomer.

Dextrorotatory (D) molecule Levorotatory (L) molecule

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