Engineering
Malus's Law Polarizer Intensity & Brewster's Angle optics formulas
Calculate ideal analyzer transmission and the Brewster angle for two transparent dielectric media.
Ideal polarization models with angles in degrees
Malus’s law uses the angle between the incident linear polarization and the analyzer transmission axis. I0 is intensity immediately before the ideal analyzer. Convert degrees to radians for COS. An ideal first polarizer transmits half of unpolarized incident intensity; practical polarizers have additional losses and finite extinction.
Brewster’s formula assumes an interface between transparent, isotropic, nonmagnetic dielectric media with real positive refractive indices at the wavelength used. The incidence angle is measured from the surface normal. The p-polarized reflection vanishes there; an s component may still reflect, so this is not elimination of all glare. If both indices are equal there is no unique Brewster angle because the ideal interface has no reflection at any angle.
| Optics Parameter | Cell | Laser / Glare Setup | Optical Output |
|---|---|---|---|
| Incident Polarized Intensity I0 | B2 = 100 W/m^2 | Collimated polarized beam | 100 W/m^2 at theta = 0 deg |
| Analyzer Angle theta | B3 = 60 deg | COS(RADIANS(60))^2 = 0.25 | Transmitted I = 25.00 W/m^2 |
| Incident Medium n1 & Glass n2 | B4 = 1.00, B5 = 1.50 | DEGREES(ATAN(1.50 / 1.00)) | Brewster Angle = 56.31 deg |
| Crossed Polarizers (90 deg) | B3 set to 90 deg | Ideal cosine-squared limit | Rounded ideal transmission0 |
Malus's Law transmitted intensity I = I0 * COS(RADIANS(theta))^2
Note: unpolarized natural light passing through the FIRST ideal polarizer drops by 50% (0.5 * I_unpol) before hitting the second analyzer.
=IF(OR(COUNT(B2:B3)<>2,B2<0),"Invalid inputs",ROUND(B2 * (COS(RADIANS(B3)) ^ 2), 4))Brewster's Polarization Angle DEGREES(ATAN(n2 / n1))
At Brewster's angle, reflected and refracted rays are perpendicular (theta_B + theta_refracted = 90 deg)!
=IF(OR(COUNT(B4:B5)<>2,MIN(B4:B5)<=0),"Invalid inputs",IF(B4=B5,"No unique angle",ROUND(DEGREES(ATAN(B5/B4)),2)))Try the example
Use the original values or change them to test your understanding.