is incident on a polarizer whose transmission axis makes an angle of 30o with respect to the horizontal. What is the average intensity of the light that is transmitted through the polarizer

Let the incident intensity of light on the polariser is Io.

Let the angle of transmission is θ.

According to the law of Malus,

The intensity of light coming out form the polariser is given by

I = IoCos²θ

The mean or the average value of Cos²θ is 1/2

So, the intensity of light coming out from the polariser is

I = Io/2

Thus, the 50% of light is transmitted by the polariser.