Final answer:
The axis of the polarizing filter would need to make an angle of approximately 75.5° with the direction of polarized light to reduce the intensity to 10.0 W/m².
Step-by-step explanation:
To find the angle between the axis of a polarizing filter and the direction of polarized light to reduce the intensity, we can use the concept of Malus' law. Malus' law states that the intensity of light transmitted through a polarizing filter is given by the equation I = I0cos2θ, where I is the transmitted intensity, I0 is the initial intensity, and θ is the angle between the axis of the filter and the direction of polarization.
Using this equation, we can solve for θ. We are given the initial intensity I0 as 1.00 kW/m² and the final intensity I as 10.0 W/m². Substituting these values into the equation, we get 10.0 = 1.00cos2θ. Solving for θ, we find θ ≈ 75.5°.
Therefore, the axis of the polarizing filter would need to make an angle of approximately 75.5° with the direction of polarized light to reduce the intensity to 10.0 W/m².