Polarization by Reflection

When an unpolarized light beam is reflected from a surface, the reflected light may be completely polarized, partially polarized, or unpolarized, depending on the angle of incidence. If the angle of incidence is 0°, the reflected beam is unpolarized. For other angles of incidence, the reflected light is polarized to some extent, and for one particular angle of incidence, the reflected light is completely polarized. Let us now investigate reflection at that special angle.

Suppose that an unpolarized light beam is incident on a surface, as in Figure 3.8a. Each individual electric field vector can be resolved into two components: one parallel to the surface (and perpendicular to the page in Fig. 3.8, represented by the dots), and the other (represented by the brown arrows) perpendicular both to the first component and to the direction of propagation. Thus, the polarization of the entire beam can be described by two electric field components in these directions. It is found that the parallel component reflects more strongly than the perpendicular component, and this results in a partially polarized reflected beam. Furthermore, the refracted beam is also partially polarized.

Figure 3.8 (a) When unpolarized light is incident on a reflecting surface, the reflected and refracted beams are partially polarized. (b) The reflected beam is completely polarized when the angle of incidence equals the polarizing angle θ_p, which satisfies the equation n = tanθ_p. At this incident angle, the reflected and refracted rays are perpendicular to each other.

Now suppose that the angle of incidence θ₁ is varied until the angle between the reflected and refracted beams is 90°, as in Figure 3.7b. At this particular angle of incidence, the reflected beam is completely polarized (with its electric field vector parallel to the surface), and the refracted beam is still only partially polarized. The angle of incidence at which this polarization occurs is called the polarizing angle θ_p.

We can obtain an expression relating the polarizing angle to the index of refraction of the reflecting substance by using Figure 3.8b. From this figure, we see that

Θ_p + 90° + θ₂ = 180°; thus θ₂ = 90° – θ_p.

Using Snell’s law of refraction and taking n₁ = 1.00 for air and n₂ = n, we have

n =

Because sinθ₂ = sin(90° – θ_p) = cosθ_p, we can write this expression for n as n = sin θ_p/cosθ_p, which means that

n = tan θ_p (3.7)

This expression is called Brewster’s law, and the polarizing angle θ_p is sometimes called Brewster’s angle, after its discoverer, David Brewster (1781–1868). Because n varies with wavelength for a given substance, Brewster’s angle is also a function of wavelength.

We can understand polarization by reflection by imagining that the electric field in the incident light sets electrons at the surface of the material in Figure 3.8b into oscillation. The component directions of oscillation are (1) parallel to the arrows shown on the refracted beam of light and (2) perpendicular to the page. The oscillating electrons act as antennas radiating light with a polarization parallel to the direction of oscillation. For the oscillations in direction (1), there is no radiation in the perpendicular direction, which is along the reflected ray. For oscillations in direction (2), the electrons radiate light with a polarization perpendicular to the page. Thus, the light reflected from the surface at this angle is completely polarized parallel to the

surface.

Polarization by reflection is a common phenomenon. Sunlight reflected from water, glass, and snow is partially polarized. If the surface is horizontal, the electric field vector of the reflected light has a strong horizontal component. Sunglasses made of polarizing material reduce the glare of reflected light. The transmission axes of the lenses are oriented vertically so that they absorb the strong horizontal component of the reflected light. If you rotate sunglasses through 90 degrees, they are not as effective at blocking the glare from shiny horizontal surfaces.

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