When two pieces of Polaroid are placed in succession along the path of a light wave, the intensity of light received behind the two Polaroids is described by Malus’ Law. The law expresses light intensity, I, as a function of the angle θ which is the angle between the directions of polarization of the two filters. The law can be expressed as follows:
I = Imax cos2θ
where, Imax is the light intensity between the two sheets of Polaroid.
In 1808 Malus from his experiment found that if polarized light, obtained by reflection from a plain glass surface, falls on another reflecting surface at polarizing angle, intensity of reflected light from the lattersurface is directly proportional to the cosine of angle between the two reflecting surfaces (say λ). When the two surfaces are parallel, the intensity is maximum (say Io). Similarly when the surfaces are normal to each other, the intensity is a minimum. Malus found that the output is directly proportional to the irradiance (that is, intensity) of incident light that is Malus Law express as
I = Io cos2θ
Where, I is the intensity obtained after transmission through analyzer, I0 is the intensity of polarized light obtained through polarizer and θ is the angle between the optic axes of polarizer and analyzer.
Figure demonstrates Malus law using two polaroids for any orientation θ between polarizer and analyzer axes. Figure demonstrates the minimum or zero transmission case for θ = 90º. Similarly transmission will be maximum for θ = 0º. Through direct vision, these positions of maximum and minimum intensity are most readily detectable. The orientation of polarized light can be read using a photo detector.
Figure shows polarization of natural light propagating along the x-direction. The analyzer and the polarizer are identical Polaroids, differing only in their orientation. If the electric field vector passing through the polarizer has maximum amplitude Eo, then Eo cosθ is simply the component of electric field that transmits through the analyzer. It means that electric field vector of light passed by the polarizer is oscillates in a plane that makes an angle θ relative to the optic axis of polarizer.
The Law of Malus is a fundamental principle in optics that describes the intensity of polarized light after passing through an analyzer. This crucial experiment helps students understand the behavior of polarized light and its applications in modern optics and photonics.
To verify the Law of Malus by studying the variation of intensity of polarized light with the angle of the analyzer.
The Law of Malus states that when completely plane-polarized light is incident on an analyzer, the intensity of the transmitted light varies as the square of the cosine of the angle between the transmission directions of the polarizer and analyzer.
Mathematical Expression: I = I₀ cos²θ
Where:
When unpolarized light passes through a polarizer, it becomes plane-polarized. The analyzer then filters this polarized light based on its orientation relative to the polarizer.
| Sl. No. | Angle θ (degrees) | cos θ | cos²θ | Intensity I (units) | I₀ × cos²θ |
|---|---|---|---|---|---|
| 1 | 0 | 1.000 | 1.000 | 95 | 95.0 |
| 2 | 10 | 0.985 | 0.970 | 92 | 92.2 |
| 3 | 20 | 0.940 | 0.884 | 84 | 84.0 |
| 4 | 30 | 0.866 | 0.750 | 71 | 71.3 |
| 5 | 40 | 0.766 | 0.587 | 56 | 55.8 |
| 6 | 50 | 0.643 | 0.413 | 39 | 39.2 |
| 7 | 60 | 0.500 | 0.250 | 24 | 23.8 |
| 8 | 70 | 0.342 | 0.117 | 11 | 11.1 |
| 9 | 80 | 0.174 | 0.030 | 3 | 2.9 |
| 10 | 90 | 0.000 | 0.000 | 0 | 0.0 |
Note: Values are sample data. Actual readings may vary.
The graph between intensity (I) and angle (θ) produces a characteristic cosine-squared curve:
Key Features of the Graph:
The experiment successfully verifies the Law of Malus. The intensity of transmitted light through the analyzer varies as cos²θ, where θ is the angle between the transmission axes of polarizer and analyzer.
Verification Evidence:
A: Polarization of light refers to the phenomenon where light waves vibrate in a particular direction perpendicular to their direction of propagation. Unpolarized light becomes polarized when it passes through a polarizing filter.
A: The Law of Malus states that the intensity of plane-polarized light transmitted through an analyzer varies as the square of the cosine of the angle between the transmission axes of the polarizer and analyzer: I = I₀ cos²θ.
A: A polarizer converts unpolarized light into polarized light, while an analyzer is used to analyze the polarization state of already polarized light by rotating it to measure intensity variations.
A: At 90°, the transmission axes of polarizer and analyzer are perpendicular to each other. According to the Law of Malus, cos²(90°) = 0, hence no light is transmitted.
A: Monochromatic light (such as from a sodium lamp or laser) is preferred to obtain clear and consistent results without chromatic aberrations.
A: If unpolarized light is used directly, no variation in intensity would be observed as the analyzer is rotated, since unpolarized light has vibrations in all directions.
A: Brewster's angle is the angle of incidence at which light reflected from a surface becomes completely polarized. It is given by tan θB = μ, where μ is the refractive index.
A: At 0° and 180°, the transmission axes of polarizer and analyzer are parallel, allowing maximum light transmission. cos²(0°) = cos²(180°) = 1, giving maximum intensity.
A: Applications include:
A: The graph between intensity (I) and cos²θ would be a straight line passing through the origin, confirming the direct proportionality I ∝ cos²θ.
This experiment successfully demonstrates and verifies the Law of Malus in polarization optics. The theoretical relationship I = I₀ cos²θ is experimentally validated through systematic measurements and graphical analysis. Understanding this fundamental principle is essential for applications in modern optics, laser technology, and optical communications.
The experiment not only reinforces theoretical concepts but also develops practical skills in optical measurements and data analysis, making it a cornerstone experiment in polarization studies for physics students.
Related Topics: Brewster's Law, polarization of light, optical experiments, wave optics, Malus law applications
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