Determine the angle between a polarizer-analyzer combination that allows 33% of the incident light to pass through.
Light getting thru:
.33=cos(Theta)
theta= arc cos(.33)
Now that is assuming the incident E plane is situated such that the first filter is aligned with it.
To determine the angle between a polarizer-analyzer combination that allows 33% of the incident light to pass through, we can use Malus' Law. According to Malus' Law, the intensity of the transmitted light, I, is given by the formula:
I = I0 * cos^2(θ),
where I0 is the intensity of the incident light and θ is the angle between the transmission axes of the polarizer and the analyzer.
Since we know that 33% of the incident light is transmitted, we can express this as:
I / I0 = 0.33
Substituting the equation for I from Malus' Law, we have:
I0 * cos^2(θ) / I0 = 0.33
cos^2(θ) = 0.33
Taking the square root of both sides, we get:
cos(θ) = √0.33
Now, we can use an inverse cosine function (cos⁻¹) to find the angle θ. Evaluating cos⁻¹(√0.33) using a scientific calculator or math software, we find:
θ ≈ 55.4 degrees
Therefore, the angle between the transmission axes of the polarizer and the analyzer that allows 33% of the incident light to pass through is approximately 55.4 degrees.