Step 1: Understanding the Concept:
Optical physics of polarimetry in sugar analysis: a Nicol prism (Iceland spar calcite $ ext{CaCO}_3$ crystal cut at 68° and cemented with Canada balsam) splits unpolarized light by double refraction and total internal reflection to produce plane-polarized light.
Key Formula or Approach:
\[ \text{Unpolarized Monochromatic Light} \xrightarrow{\mathbf{Nicol \text{ } Prism \text{ (Polarizer)}}} \text{Plane-Polarized Light (Single Plane of Oscillation)} \]
Step 2: Detailed Explanation:
In polarimetry and optical instrumentation for carbohydrate determination:
1. Nicol Prism (Polarizer) (A): A specialized optical polarizing prism invented by William Nicol (1828) constructed from a rhomb of Iceland spar (crystalline calcite, $\text{CaCO}_3$). It utilizes birefringence (double refraction) to eliminate the ordinary ray by total internal reflection at the Canada balsam junction while transmitting the extraordinary ray as a beam of pure Plane-Polarized Light through the sample tube containing optically active lactose ($[\alpha]_D^{20} = +55.4^\circ$).
2. Sodium Vapour Lamp: Provides monochromatic yellow light (D-line, $589.3\text{ nm}$).
3. Photocell Eye Piece with Analyzer Prism: Detects optical rotation angle.
Step 3: Final Answer:
Hence, the component producing plane-polarized light is Nicol prism, matching option (A).