$2.$ Certain materials can give us very fine control over the polarization of light. These are called polarizers, and act a bit like this: All the light which emerges from the other side has the same polarization. The intensity of transmitted light is given by Malus$$s Law: I $=$ I$0$ cos$2$ where I$0$ is the intensity of the incident light, and is the angle between the polarizer and the polarization of the incoming light. $($a$)$ Randomly$-$polarized light with an intensity of $500$ W m$2$ is directed onto a polarizer, which is oriented $30$ relative to a second polarizer. Determine the final intensity of the light. $($Note: The intensity of randomly$-$polarized light is halved when passing through a polarizer.$)$