= Solution
A simple <polariscope> contains a fixed <polarizer> and a rotatable <optical analyzer>, with a space for a specimen between them. A historically suitable implementation uses two <Nicol prisms>. Each selects one linearly polarized component from the incident light through the crystal's optical action. A lamp and a collimating arrangement illuminate the first prism, and the observer examines the transmitted field through the second.
With no specimen and ideal elements, <Malus's law> predicts
$$
\boxed{I=I_0\cos^2\theta,}
$$
where $I_0$ is the intensity after the polarizer and $\theta$ is the relative transmission-axis angle. Parallel settings are brightest; crossed settings give extinction. Rotating the analyser supplies an immediate check on the first element's polarization.
Insert a transparent <birefringent> plate between crossed elements with its principal directions oblique to their axes. The two components can acquire different phases, so they need not recombine into the original <linear polarization>; light can then pass the crossed analyser. With white light, wavelength-dependent retardation gives colours. Rotation of the plate, and a check without it, distinguish this response from simple sample opacity or a poor extinction adjustment. An optically active sugar solution can instead rotate the polarization plane, as in <Biot's saccharimeter>. The instrument therefore reveals changes of polarization through an analysed intensity, rather than making polarization directly visible to the eye.
Back to article page
