unpolarized light with an average intensity of 750.0W/m^2 enters a polarizer with a vertical transmission axis. the transmitted light then enters a second polarizer. the light that exits the second polarizer is found to have an average intensity of 125 W/m^2. what is the orientation angle of the second polarizer relative to the first one?
54.7 degrees
To determine the orientation angle of the second polarizer relative to the first one, we need to understand the behavior of polarized light when it passes through polarizers.
When unpolarized light passes through a polarizer, it becomes linearly polarized, meaning it vibrates in only one plane, perpendicular to the transmission axis of the polarizer. In this case, the incident light is unpolarized, and its average intensity is given as 750.0 W/m^2.
In the first polarizer, with a vertical transmission axis, it allows only the component of light that vibrates vertically to pass through. Therefore, the intensity of the light that exits the first polarizer will be reduced and become vertically polarized.
The vertically polarized light then enters the second polarizer. The orientation angle of the second polarizer relative to the first one determines how much of the vertically polarized light can pass through it.
The intensity of the light that exits the second polarizer is given as 125 W/m^2. Since the intensity changes between the two polarizers, we can use Malus's law to relate the intensities to the angle between their transmission axes.
According to Malus's law, the intensity of the transmitted light is proportional to the square of the cosine of the angle (θ) between the transmission axes of the polarizers:
I₂ = I₁ * cos²(θ)
where I₁ is the initial intensity (750.0 W/m^2) and I₂ is the final intensity (125 W/m^2).
Solving the equation for θ, we get:
cos²(θ) = I₂ / I₁
cos(θ) = sqrt(I₂ / I₁)
θ = arccos(sqrt(I₂ / I₁))
Now we can substitute the given values into the equation:
θ = arccos(sqrt(125 W/m^2 / 750.0 W/m^2))
θ ≈ arccos(sqrt(1/6)) ≈ 54.7 degrees
Therefore, the orientation angle of the second polarizer relative to the first one is approximately 54.7 degrees.