Brewster's observed that when unpolarised light is incident on the material, reflected and refracted rays are at the angle of 90o as shown in Figure given below. By using Snell's law, we know that refractive index of the material is provided by relation
μ = sin ip/sin r
Here ip is the polarizing angle. It is stated as angle of incidence when reflected light is almost entirely polarized. μ is refractive index of material.
But from the Figure, one can see that r = 90 - ip
μ = sin ip /sin (90 - ip) = sin ip /cos ip = tan ip
Therefore Refractive index μ = tan ip................Eq.1
Eq.1 is known as Brewster's law. Thus, refractive index of the transparent medium is equal to tangent of the polarizing angle ip. Therefore Eq.1, (Brewster law) can be utilized to determine refractive index of materials.
Percentage of Polarization:
When light passes through the Polaroid (or polarizer), light that has vibration along specified direction of crystal above is transmitted. If transmitted light intensity is estimated using the photocell, current measured remains constant in whatever direction polarizer is rotated. If there is any variation in intensity, it illustrates that incident light is partly polarized. I.e., vibration of the incident beams is not uniform in all directions.
P = [(Imax - Imin)/(Imax x Imin)] x 100.............................Eq.2
Where Imax = maximum light intensity
Imin = minimum light intensity
The Analyzer is introduced between the polarizer and photo cell. Specified direction of polarizer makes an angle Θ with an analyzer being oriented vertically. Polarized light transmitted by polarizer can be resolved into 2 components, thus, Eocos Θ vertically and Eo sin Θ horizontally, as shown in Figure given above, where Eo is an amplitude vector of th incident beam. Only component of amplitude Eo cos Θ that is parallel to transmission direction, would be transmitted by an analyzer. The transmitted light is maximum when Θ is 0o and is zero (minimum) when Θ is 900. At intermediate angles, intensity is proportional to amplitude, and we have
I0 α E02 and I α E2
Therefore I/I0 = E2E0 = E02 cos2Θ/ E02
Therefore I = I0cos2Θ.....................Eq.3
The Eq.3 is called as Malu's law
Thus from Eq.3, it can be observed that intensity of emergent light differs as square of the cosine of angle between polarizer and the analyzer.
Application of Polarization:
(i) Use of Polaroids in Sunglasses:
Unpolarised light is injurious to human eye, but with the use of Polaroid this can be avoided. They protect our eyes from glare. They assisted to decrease intensity of sunlight.
(ii) In Film Industries:
Polarized light is utilized in films to generate illusion of three dimensional pictures.
The rotation of plane of polarization by sugar solution is utilized as a method of finding the concentration of sugar solution in the given sample.
(d) Photoelectric Stress Analysis:
Few substances like glass and plastic, which are not usually double refracting, may become so if subjected to stress. If such stressed materials are put between the polarize and analyzer, bright and dark areas which are seen give information about strains. Technology of photo-elasticity is based on double refraction generate by stresses.
(e) Utilized in window pares:
Window panes of airplane and trains utilized polaroids to manage light entering through them.
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