A 20 cm tube containing cane-sugar solution rotates the plane of polarization by +13.3° for sodium light. Specific rotation of cane sugar S = +66.5° dm⁻¹ (g/cm³)⁻¹. (a) Find the concentration. (b) If the same solution is diluted to half concentration, what rotation would a 10 cm tube give? Solution: (a) θ = S·l·c → c = θ/(S·l) = 13.3 / (66.5 × 2.0 dm) = 13.3/133 = 0.10 g/cm³ (i.e. 10 g per 100 mL). (b) New c = 0.05 g/cm³, l = 1.0 dm: θ = 66.5 × 1.0 × 0.05 = 3.325°. Halving both length and concentration quarters the rotation: 13.3°/4 = 3.325°. ✓