MicroscopyPioneers
Figure 1: The principle of Brewster’s angle.
be easily calculated using the following equation for a beam of light traveling through air:
nsinθθ () () ()θθ θ//() ()sinsin== =− ir sintani90i i
where n is the refractive index of the medium from which the light is reflected, θ(i) is the angle of incidence, and θ(r) is the angle of refraction. By examining the equation, it becomes obvious that the refractive index of an unknown specimen can be determined by the Brewster angle. Tis feature is particularly useful in the case of opaque materials that have high absorption coefficients for transmitted light, rendering the usual Snell’s law formula inapplicable. Determining the amount of polariza- tion through reflection techniques also eases the search for the polarizing axis of a sheet of polarizing film that is not marked. Te principle behind Brewster’s angle is illustrated in Fig-
ure 1 for a single ray of light reflecting from the flat surface of a transparent medium having a higher refractive index than air. Te incident ray is drawn with only two electric vector vibration planes but is intended to represent light having vibra- tions in all planes perpendicular to the direction of propaga- tion. When the beam arrives on the surface at a critical angle (Brewster’s angle; represented by the variable θ in Figure 1), the polarization degree of the reflected beam is 100 percent, with the orientation of the electric vectors lying perpendicular to the plane of incidence and parallel to the reflected surface. Te incidence plane is defined by the incident, refracted, and reflected waves. Te refracted ray is oriented at a 90-degree angle from the reflected ray and is only partially polarized. For water (refractive index of 1.333), glass (refractive index
of 1.515), and diamond (refractive index of 2.417), the criti- cal (Brewster) angles are 53, 57, and 67.5 degrees, respectively. Light reflected from a highway surface at the Brewster angle oſten produces annoying and distracting glare, which can be demonstrated quite easily by viewing the distant part of a high- way or the surface of a swimming pool on a hot, sunny day. Modern lasers commonly take advantage of Brewster’s angle to produce linearly polarized light from reflections at the mir- rored surfaces positioned near the ends of the laser cavity.
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