Malus's Law Polarizer Transmitted Intensity
Malus's Law Polarizer Transmitted Intensity
Malus's law describes what happens when already-polarized light passes through a second polarizing filter (an "analyzer") set at some angle to the first: the transmitted intensity depends on the square of the cosine of the angle between them. This is the principle behind polarized sunglasses, LCD screens, and photographic polarizing filters.When the analyzer is aligned with the incoming polarization, all the light passes through; when it is rotated to 90°, essentially no light gets through at all — the basis for the "crossed polarizers block all light" demonstration common in physics classrooms and used deliberately in some optical instruments and camera filters to cut reflected glare.
Malus's law gives the transmitted intensity as I = I_0·cos²θ. where I_0 is the incident (already polarized) light intensity, theta_pol is the angle between the polarizer axis and the incoming polarization direction, and I_trans is the transmitted intensity.
Inputs
I_0 := 100 W/m^2=100 kg/s^3
theta_pol := 0.5236=0.52
Apply Malus's law: squaring the cosine means the intensity falls off faster than the angle itself as the polarizer rotates away from alignment.
I_trans := I_0·cos(theta_pol)^2=75 kg/s^3
Results
At a 30° misalignment, about 75% of the incident intensity still gets through, since cos²(30°) = 0.75 — a reminder that transmission drops off gently near perfect alignment but very steeply as the angle approaches 90°. At exactly 90° (crossed polarizers) the transmitted intensity would go to zero, and at 0° it would equal the full incident intensity I_0.
Assumptions & limitations
- Incoming light is already fully (linearly) polarized.
- Ideal polarizer with no absorption losses beyond the cos²θ projection.
- Monochromatic or broadband light treated the same (no wavelength dependence of the polarizer).