SPH3UW/SPH4UI Unit 10.1 Polarization of Light Page 1 of 5

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1 SPH3UW/SPH4UI Unit 0. Polarization of Light Page of 5 Notes Physics Tool box Longitudinal waves: In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. Transversal waves: In a transverse wave the particle displacement is perpendicular to the direction of wave propagation Polarization of light can be achieved in the following ways: double refraction, reflection, scattering, and a polarization filter. Polarization provided the proof that light is a transverse wave. Scattering occurs when light from the Sun passes through our atmosphere and encounters small particles that scatter light. Polarization filters have many uses, including glare reduction, stress analysis, and photography. Young s experiment demonstrated that wave properties of light, but it did not give any indication if the light waves are transverse of longitudinal. If we assume that vibrations are transverse and that they vibrate in all directions, perpendicular to the direction in which the light is travelling. Then if the transverse wave passed through a filter that allowed vibrations to occur in only one direction. Then the wave would be polarized in that direction (plane-polarized) The vertically polarized waves below pass through a vertical slit but are stopped by a horizontal polarizing slit. Thus when light is passed through a polarization filter, the light waves are polarized in one plane (only light vibrating in that direction can pass through the slit). Now if you have another polarizer (called an analyzer) that is perpendicular to the first, then almost all the light will be blocked (absorbed, reflected).

2 SPH3UW/SPH4UI Unit 0. Polarization of Light Page of 5 If light was a longitudinal wave, then polarizing filters would not stop them. Thus light is a transverse wave (or acts like transverse waves). Polarization can be achieved in 4 ways: ) Double refraction ) Reflection 3) Scattering 4) Polarization Filter Materials such as glass and Lucite, which become doubly refractive when subjected to mechanical stress, are said to have photo-elasticity. When you place a photo-elastic material between two polarizers, the stress patterns are revealed. Polarized Light An ordinary light beam is composed of a large number of waves that where emitted by the atoms of the light source. Each atom produces a light wave having some particular orientation of the electric field vector E, corresponding to the direction of atomic vibration (recall that the magnetic, B, field vibrates perpendicular to this direction). The direction of the polarization of each individual light wave is defined to be the direction in which the electric field (E) is vibrating. In the Figure above where the light wave is travelling in the x direction, the polarization lies along the y axis. However, an individual electromagnetic wave could have its E vector in the yz plane, making any possible angle with the y axis. Because all directions of vibration from a wave source are possible, the resultant electromagnetic wave is a superposition of waves vibrating in many different directions. The result is an unpolarized light beam represented in the Figure to the right. The direction of wave propagation in this figure is perpendicular (out or in) to the page. The arrows show a few possible directions of the electric field vectors for the individual waves making up the resultant beam. At any given point and at some instant of time, all these individual electric field vectors add to give one resultant electric field vector.

3 SPH3UW/SPH4UI Unit 0. Polarization of Light Page 3 of 5 A light wave is said to be linearly polarized if the resultant electric field E vibrates in the same direction at all times at a particular point. The plane formed by E and the direction of propagation is called the plane of polarization of the wave. It is possible to obtain a linearly polarized beam from an unpolarized beam by removing all waves from the beam except those whose electric field vectors oscillate in a single plane. This process will provide us with polarized light that now has a single axis of polarization. Malus s Law Malus' law, which is named after Etienne-Louis Malus, says that when a perfect polarizer is placed in a polarized beam of light, the intensity, I, of the light that passes through is given by: I Io cos Note: If unpolarized light passes through a polarizer, then ½ the intensity passes through. Where I o represents the initial intensity and represents the angle between the light's initial polarization direction and the axis of the polarizer. Intensity= I o Intensity= I o Intensity = I o cos

4 SPH3UW/SPH4UI Unit 0. Polarization of Light Page 4 of 5 Example Determine the intensity of I 3 I I Solution I : Since random light passes through a polarizer we have: I I0 I : Apply Malus s Law : I Icos 45 Difference between 0 0 I0 cos 45 and 45 0 I0 I0 4 I 3 : Apply Malus s Law: I I cos 45 3 I 4 I0 4 I0 8 0 cos 45 Difference between 90 0 and 45 0 The final intensity is 8 of the original intensity.

5 SPH3UW/SPH4UI Unit 0. Polarization of Light Page 5 of 5 Extra Notes and Comments