Describe polarization of light that is reflected from the sea
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When light encounters a boundary between two media with different refractive indices, some of it is usually reflected as shown in the figure above. The fraction that is reflected is described by the Fresnel equations, and is dependent upon the incoming light's polarization and angle of incidence. The Fresnel equations predict that light with the p polarization (electric field polarized in the same plane as the incident ray and the surface normal) will not be reflected if the angle of incidence is
θB=arctan(n2n1),θB=arctan(n2n1),
where n1n1 is the refractive index of the initial medium through which the light propagates (the "incident medium"), and n2n2 is the index of the other medium. This equation is known as '''Brewster's law''', and the angle defined by it is Brewster's angle.
The physical mechanism for this can be qualitatively understood from the manner in which electric dipoles in the media respond to pp-polarized light. One can imagine that light incident on the surface is absorbed, and then re-radiated by oscillating electric dipoles at the interface between the two media. The refracted light is emitted perpendicular to the direction of the dipole moment; no energy can be radiated in the direction of the dipole moment. That is, if the oscillating dipoles are aligned along the supposed direction of the reflection, no light is reflected at all. In this case, all the light would be refracted in the direction perpendicular to the direction of the dipoles. Thus, if θ1θ1 is the angle of supposed reflection (which is equal in magnitude to the angle of incidence), the angle of refraction θ2θ2would be equal to (90° - θ1θ1).
The above geometric condition can be expressed as
θ1+θ2=90∘θ1+θ2=90∘
where θ1θ1 is the angle of reflection (or incidence) and θ2θ2 is the angle of refraction.
Using Snell's law,
n1sin(θ1)=n2sin(θ2>),n1sin(θ1)=n2sin(θ2>),
one can calculate the incident angleθ1=θBθ1=θB at which no light is reflected:
n1sin(θB)=n2sin(>90∘−θB)=n2cos(θB>)n1sin(θB)=n2sin(>90∘−θB)=n2cos(θB>)
Solving for θBθB gives
θB=arctan(n2n1).
θB=arctan(n2n1),θB=arctan(n2n1),
where n1n1 is the refractive index of the initial medium through which the light propagates (the "incident medium"), and n2n2 is the index of the other medium. This equation is known as '''Brewster's law''', and the angle defined by it is Brewster's angle.
The physical mechanism for this can be qualitatively understood from the manner in which electric dipoles in the media respond to pp-polarized light. One can imagine that light incident on the surface is absorbed, and then re-radiated by oscillating electric dipoles at the interface between the two media. The refracted light is emitted perpendicular to the direction of the dipole moment; no energy can be radiated in the direction of the dipole moment. That is, if the oscillating dipoles are aligned along the supposed direction of the reflection, no light is reflected at all. In this case, all the light would be refracted in the direction perpendicular to the direction of the dipoles. Thus, if θ1θ1 is the angle of supposed reflection (which is equal in magnitude to the angle of incidence), the angle of refraction θ2θ2would be equal to (90° - θ1θ1).
The above geometric condition can be expressed as
θ1+θ2=90∘θ1+θ2=90∘
where θ1θ1 is the angle of reflection (or incidence) and θ2θ2 is the angle of refraction.
Using Snell's law,
n1sin(θ1)=n2sin(θ2>),n1sin(θ1)=n2sin(θ2>),
one can calculate the incident angleθ1=θBθ1=θB at which no light is reflected:
n1sin(θB)=n2sin(>90∘−θB)=n2cos(θB>)n1sin(θB)=n2sin(>90∘−θB)=n2cos(θB>)
Solving for θBθB gives
θB=arctan(n2n1).
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