Polarization
By Levi Clancy for Student Reader on
updated
- Physics
- Calorimetrics
- Circuits
- Electricity and Magnetism
- Fluid Dynamics
- Fluid Statics
- Friction
- Human Eye
- Ideal Gas Law
- Interference and Diffraction
- Kinematics
- Mirrors and lenses
- Newton’s Law of Gravitation
- Newton’s laws of motion
- Optics
- Oscillations
- Physics of Breakdancing
- Polarization
- Power
- Thermal expansion
- Thermodynamic Systems
- Vectors
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 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) |
Practice problems
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°