Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

Optical polarization refers to the orientation of the oscillations of the electromagnetic fields in light waves. In nature, light waves vibrate in many directions, but once they pass through a polarizing filter, they vibrate mainly in one plane, which means they are polarized. Imagine a wave on a rope: without a polarizing filter, the rope moves freely in all directions, but with a filter, it's as if the rope could only move up and down.

When light encounters a polarizing filter, the filter's structure blocks oscillations that are not aligned with its polarization axis. This is similar to how a sieve separates larger objects from smaller ones; the filter 'sieves' out the light waves based on their direction of oscillation. As a result, the light exiting the filter has a reduced intensity because many of its waves have been absorbed or reflected away. The concept of optical polarization is widely utilized in sunglasses to reduce glare, in photography to manage reflections, and in various scientific instruments to analyze materials.

Polarization direction is the orientation of the electric field vector in a polarized light wave, which determines the geometric alignment of the wave's oscillations. This direction is crucial in determining whether the light will pass through a polarizing filter or not.

When a polarizing filter is placed in the path of light, it acts like a gate that either allows or denies passage to light waves depending upon their polarization. For light to effectively pass through, its polarization direction must be parallel to the filter's allowed direction. An understanding of the polarization direction is particularly important when using multiple filters, as the relative angle between their polarization directions determines the overall light intensity.

If two polarizing filters are arranged with their polarization directions at 90 degrees to each other, known as cross-polarization, they will block almost all of the light. This is because the light that manages to get through the first filter is then oriented in such a way that it cannot pass through the second, resulting in a significant reduction in light intensity. This principle is applied in liquid crystal displays (LCDs) and in experiments involving light intensity and wave properties.

Light intensity is a measure of the energy carried by light waves hitting a certain area, and it is a key factor in the behavior of light as it passes through polarizing filters. When light is polarized, its intensity is decreased, translating to a reduction in the energy it carries to the observer.

The process begins with unpolarized light, which contains waves oscillating in all different planes. As this light passes through a polarizing filter, only the waves oscillating in the direction parallel to the filter's polarization axis can pass, while the rest are absorbed. This absorption decreases the light's overall intensity and, consequently, its energy. When a second, crossed polarizing filter is introduced, it allows virtually none of the polarized light from the first filter to pass, which results in an almost complete reduction in the observable light's intensity and energy. This energy doesn't disappear, however; it is transformed, typically into thermal energy, as the filters heat up from the absorbed light.

In practical terms, the manipulation of light intensity via polarization has implications for various technologies, including photography, LCD screens, and even in astronomical observations, where polarizing filters assist in reducing glare and enhancing contrast.