|Polarization||A property of light is that it can be polarized. Unpolarized light points in all sorts of direction, while polarized light has its E vectors going in the same direction.|
Where I0 is the intensity of unpolarized light, and I is the intensity after polarization:
For polarized light going at angle θ to the polarizer: I = I0 cos2 θ
For unpolarized light, since Since the average value of cos2 θ is ½ then: I = ½ I0
|Brewster's Angle (θP)|
When a ray travelling through a medium with index of refraction n1 strikes a second medium with n2, then the angle θP is when the reflected ray and refracted ray have an angle of 90° between them. The angle θP is formed between the incident ray and the normal to the surface.
n1 sin θP = n2 sin θ2
n1 sin θP = n2 sin ( 90° - θP )
n1 sin θP = n2 cos θP
tan θP = n2 / n1 (Brewster's Law)
Critical angle: sin θc = n2 / n1 Brewster's angle for first material: tan θP = n2 / n1 Brewster's angle for second material: tan θP = n1 / n2
sin 40.0° = n2 / n1 n2 / n1 = tan θP for first material 0.64278761 = tan θP θP = 32.7° for first material
sin 40.0° = n2 / n1 n1 / n2 = tan θP for second material 0.64278761 = 1 / tan θP 1.55572383 = tan θP θP = 57.3° for second material
I = I0 cos2 θ
I0 = Initial intensity I1 = Intensity after first polarizer I2 = Intensity after second polarizer θ1 = 30° is incident light angle to first polarizer θ2 = 50° since the second polarizer is rotated 50° relative to the first polarizer.
I1 = I0 cos2 θ1 = I0 cos2 30° I2 = I1 cos2 θ2 = I0 cos2 30° cos2 50° I2 = I0 0.309881933 I2 / I0 = 0.309881933 = 31% transmitted intensity
I = I0 cos2 θ
I0 = Initial intensity I1 = Intensity after first polarizer I2 = Intensity after second polarizer (10% of I0) θ1 = Incident light angle to first polarizer θ2 = 70° since the second polarizer is rotated 70° relative to the first polarizer.
I1 = I0 cos2 θ1 I2 = I0 cos2 θ1 cos2 70° I2 / I0 = 10% = .10 .10 = cos2 θ1 cos2 70° 0.854863217 = cos2 θ1 0.924588134 = cos θ1 θ1 = 22°