equations for light intensity in polarizer

During his experiments, Bartholin also observed a quite unusual phenomenon. The first clues to the existence of polarized light surfaced around 1669 when Erasmus Bartholin discovered that crystals of the mineral Iceland spar (a transparent, colorless variety of calcite) produce a double image when objects are viewed through the crystals in transmitted light. The concept of using two polarizers oriented at right angles with respect to each other is commonly termed crossed polarization and is fundamental to the concept of polarized light microscopy. The wave passing through the first polarizer is subsequently blocked by the second polarizer, because this polarizer is oriented horizontally with respect to the electric field vector in the light wave. The polarizing direction of the first polarizer is oriented vertically to the incident beam so it will pass only the waves having vertical electric field vectors. Only the incident light that is vibrating in the same plane as the oriented polymer molecules is absorbed, while light vibrating at right angles to the polymer plane is passed through the first polarizing filter.

The polarizers illustrated in Figure 1 are actually filters containing long-chain polymer molecules that are oriented in a single direction. In reality, the incident light electric field vectors are vibrating perpendicular to the direction of propagation with an equal distribution in all planes before encountering the first polarizer. Electric field vectors are depicted in the incident light beam as sinusoidal waves vibrating in all directions (360 degrees although only six waves, spaced at 60-degree intervals, are included in the figure).

The basic concept of polarized light is illustrated in Figure 1 for a non-polarized beam of light incident on two linear polarizers. In effect, humans cannot differentiate between the high contrast real images observed in a polarized light microscope and identical images of the same specimens captured digitally (or on film), and then projected onto a screen with light that is not polarized. The human eye lacks the ability to distinguish between randomly oriented and polarized light, and plane-polarized light can only be detected through an intensity or color effect, for example, by reduced glare when wearing polarized sun glasses.

Equations for light intensity in polarizer