Unpolarized light whose intensity is 1.95 W/m2 is incident on the polarizer in the drawing. (a) What is the intensity of the light leaving the polarizer? (b) If the analyzer is set at an angle of θ = 76.0° with respect to the polarizer, what is the intensity of the light that reaches the photocell?
To answer these questions, we need to understand the concept of polarization and the behavior of polarizers and analyzers.
(a) Intensity of light leaving the polarizer:
A polarizer is an optical filter that allows the transmission of light waves vibrating only in a specific direction. When unpolarized light passes through a polarizer, it becomes partially or completely polarized in the direction perpendicular to the polarization axis of the polarizer.
In this case, the unpolarized light with an intensity of 1.95 W/m2 is incident on the polarizer. Let's assume the polarizer transmits 50% of the incident intensity. So, the intensity of light leaving the polarizer will be:
Intensity = (Transmittance) x (Incident Intensity)
= 0.5 x 1.95 W/m2
= 0.975 W/m2
Therefore, the intensity of light leaving the polarizer is 0.975 W/m2.
(b) Intensity of light reaching the photocell:
An analyzer is another polarizer that can be oriented at different angles with respect to the polarizer. It only allows the transmission of light waves oscillating in a specific direction parallel to the analyzer's polarization axis.
In this case, the analyzer is set at an angle of θ = 76.0° with respect to the polarizer. To find the intensity of light reaching the photocell, we need to determine the component of light parallel to the polarization axis of the analyzer.
By applying Malus' law, the intensity of light reaching the photocell can be calculated as:
Intensity = (Transmittance) x (Incident Intensity) x (cosθ)²
Since the light leaving the polarizer is already polarized in the direction perpendicular to the polarization axis of the polarizer, the transmittance when passing through the analyzer will depend on the angle (θ) between the two polarization axes.
Assuming the analyzer transmits 80% of the incident intensity (transmittance = 0.8), the intensity of light reaching the photocell will be:
Intensity = (0.8) x (0.975 W/m2) x (cos(76.0°))²
Now, plug in the values and calculate the result.
Note: Make sure to convert the angle from degrees to radians for the cosine function if you're using a calculator.