Final answer:
To reduce the intensity of polarized light to one-ninth using a polarizing filter, it should be placed at an angle of approximately 70.5 degrees to the direction of the polarized light, as determined by Malus's law.
Step-by-step explanation:
To determine the angle required to reduce the intensity of polarized light to one-ninth, we can use Malus's law, which states that the transmitted intensity I through a polarizing filter is given by I = I0cos2θ, where I0 is the initial intensity, and θ is the angle between the light's polarization direction and the axis of the filter. If the transmitted intensity needs to be reduced by one-ninth, we have I = (1/9)I0. Substituting this into Malus's law and solving for θ gives cos2θ = 1/9, so θ = cos-1(√(1/9)), which is approximately 70.5 degrees.
To achieve the reduction to one-ninth of the intensity, the polarizing filter should be oriented at an angle of approximately 70.5 degrees to the direction of the polarized light. This specific angle will ensure that the intensity is precisely reduced to one-ninth of its original value, according to the principles of polarization and Malus's law.