Question

In an experiment, light is passed through two polarizing filters. The image below shows the first filter and axis of polarization.
The intensity of the resulting light (after the first filter) is recorded as I. Three configurations (at different angles) are set up for the second filter, and the intensity of light is recorded for each configuration. The results are shown in the table below:
Complete the table by calculating $\theta_1$, $\theta_2$, and $\theta_3$.

Question Image

**Figure 27.58**

**Table 27.2**

$\theta_1 = 0^\circ$

$\theta_2 = 45^\circ$

$\theta_3 = 90^\circ$

$\theta_2 = 45^\circ$

$\theta_3 = 90^\circ$

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This is College Physics Answers with Shaun Dychko. Some unpolarized light travels through this polarizing filter and the intensity after passing through this first filter is

*I*and then the light goes through a second polarizing filter and the intensity after the second filter is measured in this column here and the question is what are the angles of the axis of polarization of this second filter in each of these three scenarios— configuration A, configuration B and configuration C? So configuration's A and C we can figure out without calculation; in configuration A, the intensity of light after the second filter is the same as it was before the second filter that means the second filter makes no difference to the intensity and that means that its axis must be parallel to the axis of the first polarizing filter— it could be because it has no effect on the intensity— and so that means the angle is zero degrees. In configuration C, the final intensity after the second polarizing filter is zero and so these polarizing films must be crossed they have their axis at 90 degrees with respect to each other and so the direction of polarization of light between the filters is perpendicular to the axis of polarization of the second filter and so nothing gets through it and so the angle then is 90 degrees in that case. For configuration B, the intensity is half of what it was between the polarizing films and for that we have to do some calculation. So we have this formula here, which says that the final intensity after a polarizing film equals the initial intensity before it times*cos*of the angle between the direction of polarization of the light and the axis of polarization of the film squared. So we have 0.5 times the intensity— it's final intensity after the second film— equals the intensity before the second film*I*times*cos squared Θ*, divide both sides by*I*and you get*cos squared Θ*is 0.5, take the square root of both sides and you have*cos Θ*then is square root of 0.5. Inverse*cos*of both sides solves for*Θ*and so*Θ*then is the inverse*cos*of the square root of 0.5, which is 45 degrees and that's*Θ 2*.