Unpolarized light passes through three ideal polarizing filters.The first filter is oriented with a horizontal transmission axis,the second one has its transmission axis at 30° from the horizontal,and the third filter has a vertical transmission axis.What percent of the light gets through this combination?
A)9.4%
B)91%
C)50%
D)0%
E)33%

Question

Quizplus · Accepted Answer

When unpolarized light passes through a polarizing filter, the intensity of the transmitted light is reduced to half of the incident light. After passing through the first filter (horizontal), the light is polarized along the horizontal axis. The intensity of light passing through the second filter, oriented at 30° to the first, can be calculated using Malus's law, $I = I_0 \cos^2(\theta)$, where $I_0$ is the intensity of the polarized light before the second filter, and $\theta$ is the angle between the polarization directions of the light and the second filter. Thus, after the second filter, the intensity is $I_0 \cos^2(30°) = 0.5I_0 \times 0.75 = 0.375I_0$, since $\cos(30°) = \sqrt{3}/2$. The third filter is vertical, perpendicular to the first, so the angle between the light from the second filter and the third filter's axis is 60°. Applying Malus's law again, the intensity after the third filter is $0.375I_0 \cos^2(60°) = 0.375I_0 \times 0.25 = 0.09375I_0$, or 9.375% of the original unpolarized light's intensity. This rounds to 9.4%, making the correct answer A.

Unpolarized Light Passes Through Three Ideal Polarizing Filters