Final answer:
A beam of partially polarized light can be considered a mixture of polarized and unpolarized light. The fraction of intensity associated with polarized light can be found using the formula I = Io * cos^2(θ), where I is the transmitted intensity, Io is the incident intensity, and θ is the angle between the direction of polarization and the axis of the filter. In this case, the transmitted intensity varies from a minimum value to a maximum value, with the maximum value being 9.7 times the minimum value. By equating the maximum transmitted intensity to 9.7 times the minimum value and solving for θ, we can find the fraction of intensity associated with polarized light to be approximately 3.12.
Step-by-step explanation:
When a beam of partially polarized light is sent through a polarizing filter, it can be considered a mixture of polarized and unpolarized light. The transmitted intensity varies from a minimum value to a maximum value as the filter is rotated through 360 degrees. In this case, the maximum transmitted intensity is 9.7 times the minimum value.
To find the fraction of the intensity associated with polarized light, we can use the formula for the intensity of polarized light after passing through a polarizing filter: I = Io * cos^2(θ), where I is the transmitted intensity, Io is the incident intensity, and θ is the angle between the direction of polarization and the axis of the filter.
Let's assume the minimum transmitted intensity (imin) corresponds to an angle of 0 degrees, and the maximum transmitted intensity (9.7 * imin) corresponds to an angle of 90 degrees. Using the formula, we can solve for the fraction of intensity associated with polarized light:
9.7 * imin = imin * cos^2(θ)
Dividing both sides by imin, we get:
9.7 = cos^2(θ)
Taking the square root of both sides, we have:
sqrt(9.7) = cos(θ)
Therefore, the fraction of the intensity associated with polarized light is equal to the square root of 9.7, which is approximately 3.12.