Concept:
Specific rotation is a property of a chiral chemical compound. It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance-concentration product, as the light passes through a sample of a compound in solution. Glucose exists in an equilibrium of anomers in aqueous solution, resulting in a distinct, constant equilibrium specific rotation.
Step 1: Recall the phenomenon of mutarotation for glucose.
When pure $\alpha$-D-glucose (initial specific rotation $= +112^\circ$) or pure $\beta$-D-glucose (initial specific rotation $= +18.7^\circ$) is dissolved in water, their optical rotations gradually change over time until they reach a constant value. This process is called mutarotation.
Step 2: Identify the equilibrium value.
In an aqueous solution, glucose establishes an equilibrium mixture consisting of approximately 36% $\alpha$-D-glucose, 64% $\beta$-D-glucose, and a trace amount of the open-chain form.
The specific rotation of this stable equilibrium mixture is a known physical constant: $+52.7^\circ$.