The angle between the polarizer transmission axis and the plane of polarization of the incoming light is 30 +/- 2 deg. If the incident light intensity Io is 100 W/cm2 what would be the intensity I after the light is transmitted through the polarizer? What would be the percent error in intensity?
I = 100 cos30 = 86.6
Max = 100 cos28 = 88.3
Min = 100 cos32 = 84.8
Percent error: +/- 2%
This assumes a lossless polarizer (when aligned in the proper plane), such as a Wollaston or Nicol prism type. Polaroid sheet film has large losses, even in the plane of polarization.
It also assumes that the incoming radiation is perfectly plane-polarized.
To calculate the intensity of the light after it is transmitted through the polarizer, we need to take into account the angle between the polarizer transmission axis and the plane of polarization of the incoming light.
The transmitted intensity (I) can be calculated using Malus's law, which states that the transmitted intensity is equal to the incident intensity (Io) times the square of the cosine of the angle between the transmission axis and the plane of polarization. Mathematically, it can be written as:
I = Io * cos²(θ)
Where:
- I is the transmitted intensity
- Io is the incident intensity (given as 100 W/cm²)
- θ is the angle between the polarizer transmission axis and the plane of polarization (given as 30° +/- 2°)
Substituting the given values into the equation, we have:
I = 100 W/cm² * cos²(30°)
To calculate the percentage error in the intensity, we first need to calculate the intensity at the upper limit of the angle (32°) and the lower limit of the angle (28°). Then we can calculate the percentage error using the formula:
Percentage error = (|I_upper - I_lower| / I_avg) * 100
Where:
- I_upper is the transmitted intensity at the upper limit of the angle
- I_lower is the transmitted intensity at the lower limit of the angle
- I_avg is the average intensity [(I_upper + I_lower) / 2]
Calculating the transmitted intensity at the upper limit of the angle:
I_upper = 100 W/cm² * cos²(32°)
Calculating the transmitted intensity at the lower limit of the angle:
I_lower = 100 W/cm² * cos²(28°)
Calculating the average intensity:
I_avg = (I_upper + I_lower) / 2
Then, substituting the calculated values into the percentage error formula, we can find the percent error in intensity.
Note: Remember to convert the angle to radians before taking the cosine.
Hope this explanation helps!