Unpolarized light with an average intensity of 750.0W.m^2 enters a polarizer with a vertical trasmission 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 orintation angle of the second polarizer relative to the first one?
The actual angle depends upon the losses of the polarizers. For sheet Poloroid film, these losses are about 50% per sheet, in addition to the fraction that is lost due to polarization.
Only crystal prism polarizers (Nicol, Glan-Thompson, Wollaston etc.) are lossless. They are actually beam separaters, and are based on double refraction.
I will assume there are no losses in the preferred plane of polarization. Call the orientation angle theta. It is the rotation angle between the two preferred planes of polarization.
In your case, 1/6 of the light gets through the pair.
Cos(theta)^2 = 1/6
Cos theta = 0.408
theta = 66 degrees.
To find the orientation angle of the second polarizer relative to the first one, we can use the Malus' Law equation.
Malus' Law states that the intensity of light transmitted through a polarizer is given by the equation:
I = I₀ * cos²(θ)
Where:
I is the transmitted intensity,
I₀ is the initial intensity,
θ is the angle between the transmission axis of the polarizer and the initial polarization direction.
Since the first polarizer has a vertical transmission axis, the initial polarization direction is also vertical.
Let's assume that the initial intensity (I₀) is the average intensity of unpolarized light, which is 750.0 W/m^2.
So, we have:
I = 125 W/m^2
I₀ = 750.0 W/m^2
θ = ?
Using Malus' Law, we can rearrange the equation to solve for θ:
cos²(θ) = I / I₀
Now substitute the known values:
cos²(θ) = 125 / 750.0
cos²(θ) = 1/6
Taking the square root of both sides:
cos(θ) = √(1/6)
Now we can solve for θ:
θ = arccos(√(1/6))
Using a calculator, we find:
θ ≈ 67.21 degrees
So, the orientation angle of the second polarizer relative to the first one is approximately 67.21 degrees.
To determine the orientation angle of the second polarizer relative to the first one, we need to consider the concept of polarized light and Malus's law.
Here's how we can solve the problem step by step:
Step 1: Understand Malus's Law
Malus's law states that the intensity of polarized light transmitted through a polarizer is proportional to the square of the cosine of the angle between the transmission axis of the polarizer and the polarization direction of the incident light.
Mathematically, Malus's law is expressed as:
I = I₀ * cos²(θ)
Where:
I is the transmitted intensity through the polarizer,
I₀ is the incident intensity of light, and
θ is the angle between the polarizer's transmission axis and the polarization direction of the incident light.
Step 2: Find the incident intensity
In the problem, it is mentioned that the unpolarized light has an average intensity of 750.0 W/m².
Step 3: Determine the transmitted intensity through the first polarizer
Since the first polarizer has a vertical transmission axis and the light entering it is unpolarized, the average intensity of the transmitted light remains the same. Therefore, the transmitted intensity through the first polarizer will also be 750.0 W/m².
Step 4: Calculate the angle between the first polarizer and the polarization direction of the transmitted light
We can rearrange Malus's law to find the angle θ. Since the transmitted intensity through the first polarizer is equal to the incident intensity, we can substitute these values into the equation:
I₂ = I₀ * cos²(θ)
125 = 750 * cos²(θ)
Step 5: Solve for θ
Divide both sides of the equation by 750:
cos²(θ) = 125/750
cos²(θ) = 1/6
Taking the square root of both sides:
cos(θ) = √(1/6)
θ = arccos(√(1/6))
Using a calculator, find the inverse cosine (arccos) of √(1/6) to obtain θ. The result will be the angle in radians.
Finally, convert the angle to the desired unit (degrees or radians) depending on the instructions or context of the problem.
By following these steps, you should be able to determine the orientation angle of the second polarizer relative to the first one.