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When we talk about the polarization of light, we are referring to the direction in which the electric field oscillates as the light travels. Natural light is usually composed of waves vibrating in all possible directions perpendicular to its direction of travel. However, we can alter this state to create polarized light, where the waves vibrate in only one direction.

Polarization can be achieved through various means, such as by reflection, scattering, or by passing light through a polarizing material. This process is vital in many everyday applications, including in sunglasses that reduce glare, in liquid crystal displays (LCDs), and in photography to manage reflections and richness of the sky.

Optical polarizers are devices designed to filter light waves, allowing only those with a certain orientation of their electric field to pass through. There are several types of polarizers such as linear polarizers, circular polarizers, and polarizing beam splitters, each serving a unique purpose.

A linear polarizer, for instance, filters out the light waves that do not align with its polarization axis. The angle at which a polarizer is aligned with respect to the incoming light greatly influences how much light it will transmit. This is where Malus's Law becomes indispensable, as it quantitatively describes the amount of light that passes through a polarizer based on the angle between the light's polarization direction and the polarizer's axis.

The Cosine Squared Law, commonly known as Malus's Law, is vital in understanding how polarizers work. It dictates that the intensity of polarized light that passes through a polarizing filter is proportional to the square of the cosine of the angle between the light's polarization direction and the filter's axis. Mathematically, if the initial intensity of the polarized light is I0 and the angle is \theta, the transmitted intensity, I, can be described as:\[ I = I_0 \cos^2(\theta) \]This law helps in predicting the outcome when light passes through one or more polarizers. For example, if vertically polarized light passes through two polarizers, with the first one at an angle of 60 degrees to the vertical and the second at 90 degrees, the fractions of light that pass through can be calculated using Malus's Law. The resulting transmission through each polarizer can be multiplied to get the final fraction that gets through both, which is the essence of the given exercise.