Final answer:
To reduce the transmitted intensity of light by one-ninth using two polarizing filters, one must rotate one filter to approximately 70.5 degrees from the initial alignment where the intensity is maximum. This calculation utilizes Malus's Law, where the final intensity is one-ninth the initial maximum intensity.
Step-by-step explanation:
The subject of this question is Physics, particularly concerning the topic of polarization of light and how the intensity of light is affected by polarizing filters. When two polaroids are aligned such that light passing through them is at its maximum intensity, they are initially aligned parallel to each other. The intensity of unpolarized light passing through a series of polarizing filters can be calculated using Malus's Law, which states that the transmitted light intensity through a polarizing filter is proportional to the cosine squared of the angle between the light's polarization direction and the axis of the filter.
To reduce the transmitted intensity of light by one-ninth, we can use Malus's Law, which is I = I0cos2θ, where I0 is the initial intensity and θ is the angle between the polarization direction of the initial light and the transmission axis of the filter. If the maximum intensity is Imax, the reduced intensity to one-ninth would be Imax/9. Setting this equal to I0cos2θ and solving for θ gives us the angle that reduces the intensity by one-ninth.
To find the angle required, we set up the equation:
I0cos2θ = ⅓I0
This simplifies to:
cos2θ = ⅓
Therefore, θ = cos−1(∙) = ≈ 70.5°
Thus, one must rotate the polarizing filter to approximately 70.5° to reduce the transmitted light intensity by one-ninth of its original value.