A beam of partially polarized light can be considered to be a mixture of polarized and unpolarized light. Suppose a beam of partially polarized light is sent through a polarizing filter. The polarization direction of the filter can be changed by rotating it. As the filter is rotated through 360 degrees, we observe that the transmitted intensity varies from some minimum value Imin to a maximum value of 9.7 times Imin. What fraction of the intensity of the original beam is associated with polarized light?
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To determine the fraction of the intensity of the original beam associated with polarized light, we can use the concept of the degree of polarization.
The degree of polarization (P) is defined as the ratio of the polarized intensity (Ip) to the total intensity (It):
P = Ip / It
Given that the transmitted intensity varies from a minimum value (Imin) to a maximum value (Imax = 9.7 * Imin), we can express the degree of polarization in terms of these values:
P = (Imax - Imin) / (Imax + Imin)
Since the partially polarized light is a mixture of polarized and unpolarized light, the total intensity (It) can be written as the sum of the intensities of the polarized light (Ip) and the unpolarized light (Iu):
It = Ip + Iu
However, since the transmitted intensity varies from Imin to Imax, the minimum value of the transmitted intensity (Imin) is associated with the unpolarized light (Iu). Therefore, the fraction of the intensity of the original beam associated with polarized light is:
Fraction of polarized intensity = Ip / It
= Ip / (Ip + Iu)
= Ip / Imin
Substituting the expression for the degree of polarization (P) in terms of Imin and Imax:
Fraction of polarized intensity = (Imax - Imin) / (Imax + Imin) * 1 / Imin
Given that Imax = 9.7 * Imin:
Fraction of polarized intensity = (9.7 * Imin - Imin) / (9.7 * Imin + Imin) * 1 / Imin
= (8.7 * Imin) / (10.7 * Imin) * 1 / Imin
= 8.7 / 10.7
Therefore, the fraction of the intensity of the original beam associated with polarized light is approximately 0.813.
To determine the fraction of the intensity of the original beam associated with polarized light, we need to understand the behavior of partially polarized light passing through a rotating polarizing filter.
When a beam of partially polarized light is incident on a polarizing filter, the intensity of the transmitted light depends on the angle between the polarization direction of the incident light and the transmission axis of the filter. When the polarization direction of the incident light is parallel to the transmission axis of the polarizing filter, maximum intensity is transmitted; while when the polarization direction is perpendicular (orthogonal) to the transmission axis, zero intensity is transmitted.
In this case, as the polarizing filter is rotated through 360 degrees, we observe that the transmitted intensity varies from some minimum value Imin to a maximum value of 9.7 times Imin. Let's denote the transmitted intensity at any arbitrary angle α as It.
To find the fraction of the intensity associated with polarized light, we need to consider the maximum and minimum transmitted intensities.
At the minimum intensity, Imin, the transmitted light consists purely of unpolarized light. Unpolarized light has equal intensities in all possible polarization directions. Therefore, the fraction of intensity associated with polarized light at this minimum value is zero.
At the maximum intensity, 9.7 times Imin, the transmitted light consists purely of polarized light. The intensity of polarized light is maximum when the polarization direction of the incident light is parallel to the transmission axis of the filter. Therefore, the fraction of intensity associated with polarized light at this maximum value is 1 (or 100%).
By observing that the transmitted intensity varies from Imin to 9.7 times Imin, we can conclude that the fraction of intensity associated with polarized light varies from 0% to 100%.
Hence, we cannot determine a specific fraction of the intensity of the original beam that is associated with polarized light based on the given information.