The average intensity of light emerging from a polarizing sheet is 0.807 W/m2, and the average intensity of the horizontally polarized light incident on the sheet is 0.972 W/m2. Determine the angle that the transmission axis of the polarizing sheet makes with the horizontal.
Malus's Law
I=Io•(cosφ)^2,
cos φ =sqrt(I/Io),
φ =19.19o
To determine the angle that the transmission axis of the polarizing sheet makes with the horizontal, we can use Malus's law. Malus's law relates the intensity of transmitted light to the incident light when passed through a polarizing sheet.
The formula for Malus's law is:
I = I₀ * cos²θ
where I is the transmitted intensity, I₀ is the incident intensity, and θ is the angle between the transmission axis of the polarizing sheet and the direction of polarization of the incident light.
In this case, we are given the transmitted intensity (0.807 W/m²) and the incident intensity (0.972 W/m²), so we need to solve for θ.
Rearranging the formula, we have:
cos²θ = I / I₀
Taking the square root of both sides, we get:
cosθ = √(I / I₀)
Now, plug in the given values:
cosθ = √(0.807 / 0.972)
cosθ = 0.932
To find the angle θ, we can take the inverse cosine (arccos) of 0.932:
θ = arccos(0.932)
Using a scientific calculator, we find that θ ≈ 23.5 degrees.
Therefore, the angle that the transmission axis of the polarizing sheet makes with the horizontal is approximately 23.5 degrees.