# Polarization

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. | |
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Malus' Law | Where I For polarized light going at angle θ to the polarizer: I = I For unpolarized light, since Since the average value of cos | |

Brewster's Angle (θ_{P}) | When a ray travelling through a medium with index of refraction n n n n tan θ |

## Practice problems

Critical angle: sin θ_{c} = n_{2} / n_{1}
Brewster's angle for first material: tan θ_{P} = n_{2} / n_{1}
Brewster's angle for second material: tan θ_{P} = n_{1} / n_{2}

sin 40.0° = n_{2} / n_{1}
n_{2} / n_{1} = tan θ_{P} for first material
0.64278761 = tan θ_{P}
θ_{P} = 32.7° for first material

sin 40.0° = n_{2} / n_{1}
n_{1} / n_{2} = tan θ_{P} for second material
0.64278761 = 1 / tan θ_{P}
1.55572383 = tan θ_{P}
θ_{P} = 57.3° for second material

I = I_{0} cos^{2} θ

I_{0} = Initial intensity
I_{1} = Intensity after first polarizer
I_{2} = Intensity after second polarizer
θ_{1} = 30° is incident light angle to first polarizer
θ_{2} = 50° since the second polarizer is rotated 50° relative to the first polarizer.

I_{1} = I_{0} cos^{2} θ_{1} = I_{0} cos^{2} 30°
I_{2} = I_{1} cos^{2} θ_{2} = I_{0} cos^{2} 30° cos^{2} 50°
I_{2} = I_{0} 0.309881933
I_{2} / I_{0} = 0.309881933 = 31% transmitted intensity

I = I_{0} cos^{2} θ

I_{0} = Initial intensity
I_{1} = Intensity after first polarizer
I_{2} = Intensity after second polarizer (10% of I_{0})
θ_{1} = Incident light angle to first polarizer
θ_{2} = 70° since the second polarizer is rotated 70° relative to the first polarizer.

I_{1} = I_{0} cos^{2} θ_{1}
I_{2} = I_{0} cos^{2} θ_{1} cos^{2} 70°
I_{2} / I_{0} = 10% = .10
.10 = cos^{2} θ_{1} cos^{2} 70°
0.854863217 = cos^{2} θ_{1}
0.924588134 = cos θ_{1}
θ_{1} = 22°