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) $50 \%$
B) $33 \%$
C) $0 \%$
D) $9.4 \%$
E) $91 \%$

Question

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) $50 \%$
B) $33 \%$
C) $0 \%$
D) $9.4 \%$
E) $91 \%$

Quizplus · Accepted Answer

When unpolarized light passes through a polarizing filter, the intensity of the transmitted light is reduced to 50% of the original intensity. After passing through the first filter, 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 initial intensity, $I$ is the final intensity, and $\theta$ is the angle between the light's polarization direction and the axis of the filter. Thus, after the second filter, the intensity is $0.5 \times \cos^2(30°) = 0.5 \times (0.75) = 0.375$ of the original intensity. The third filter is vertical, perpendicular to the first, and would theoretically block all light polarized horizontally. However, since the light is now polarized at 30° to the vertical axis (90° - 30° = 60° from the horizontal), using Malus's law again, the intensity after the third filter is $0.375 \times \cos^2(60°) = 0.375 \times (0.25) = 0.09375$ or 9.375% of the original intensity, which rounds to 9.4%.

Unpolarized Light Passes Through Three Ideal Polarizing Filters 50%50 \%50% B) 33%33 \%33%

Unpolarized Light Passes Through Three Ideal Polarizing Filters $50 \%$ B) $33 \%$