Unpolarized light is shown through two polarizing filters that are at 90 degrees. What fraction of light will pass through both filters?
To determine the fraction of light that will pass through two polarizing filters that are at a 90 degree angle, we need to consider the properties of polarized light and Malus's law.
Polarized light refers to light waves that vibrate in a specific direction, instead of vibrating in all directions randomly. A polarizing filter is a material that transmits light waves vibrating in a specific direction and blocks or absorbs light waves vibrating in other directions.
When unpolarized light passes through the first polarizing filter, it becomes polarized in the direction of the filter's transmission axis. However, when this polarized light passes through a second polarizing filter, the filter's transmission axis is perpendicular (at 90 degrees) to the polarization of the light, resulting in obstruction of most of the light.
According to Malus's law, the intensity (brightness) of the light that passes through the second filter is proportional to the cosine squared of the angle θ between the transmission axes of the two filters.
In this case, the angle between the transmission axes of the two filters is 90 degrees, so θ = 90 degrees. The cosine of 90 degrees is 0, so the intensity of the light that passes through the second filter is zero.
Therefore, no light will pass through both filters. The fraction of light that passes through both filters is 0.