Question

Unpolarized light passes through two polaroid sheets. The axis

of the first is vertical, and that of the second is at 22.0 ∘ to
the vertical. What fraction of the initial light is
transmitted?

Answer 1

To find the fraction of initially unpolarized light transmitted through two polaroid sheets at a 22-degree angle, we apply Malus's Law, resulting in a transmission of 50% of the light after the first polarizer and then cos²(22°) of that after the second polarizer.

Step-by-step explanation:

The student is asking about the fraction of unpolarized light transmitted through two polaroid sheets when the angle between their axes is 22 degrees. To solve this, we use Malus's Law, which states that the intensity of light passing through a polarizing filter is given by I = I0 cos2 θ, where I0 is the initial intensity and θ is the angle between the light's polarization direction and the filter's axis. Since unpolarized light can be considered as having half its intensity polarized in any direction, after passing through the first polarizer, its intensity is reduced to 50%. Upon passing through the second polarizer, which is at a 22.0° angle to the first, the intensity is further reduced by the factor of cos2(22.0°). Hence, the fraction of light transmitted is (0.50)(cos2(22.0°)).