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Polarization of Light

We know that to experiment with light polarization it is necessary to have a rotatable support to hold the polarizing filter, such equipment are really expensive ! But everything changed when we found on eBay a simple rotatable platform for a robotic arm, the following picture shows the”gadget” (search online for rotatable “platform for robotic arm”) :With such a tool we realized that it was possible to assemble a very simple (and cheap) yet precise rotatable support for the filter : the result is shown in the cover image.

Introduction on Light Polarization

Polarization is a property applying to transverse waves that specifies the geometrical orientation of the oscillations, In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves (shear waves) in solids.

An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field which are always perpendicular; by convention, the “polarization” of electromagnetic waves refers to the direction of the electric field. In linear polarization, the fields oscillate in a single direction. In circular or elliptical polarization, the fields rotate at a constant rate in a plane as the wave travels. The rotation can have two possible directions; if the fields rotate in a right hand sense with respect to the direction of wave travel, it is called right circular polarization, while if the fields rotate in a left hand sense, it is called left circular polarization.
The image below shows a wave with linear polarization.

The image below shows a wave with circular polarization : the electric field vector could be thought as the vectorial sum of two vectors, along the two perpendicular axis, oscillating with different phase.

polarizer is an optical filter that lets light waves of a specific polarization pass through while blocking light waves of other polarizations. A polarizer only allows light which is vibrating in a particular plane to pass through it. This plane forms the “axis” of polarization. Unpolarized light vibrates in all planes perpendicular to the direction of propagation. If unpolarized light is incident upon an “ideal” polarizer, only half of the light intensity will be transmitted through the polarizer.

The transmitted light is polarized in one plane. If this polarized light is incident upon a second polarizer, the axis of which is oriented such that it is perpendicular to the plane of polarization of the incident light, no light will be transmitted through the second polarizer.
However, if the second polarizer is oriented at an angle not perpendicular to the axis of the first polarizer, there will be some component of the electric field of the polarized light that lies in the same direction as the axis of the second polarizer, and thus some light will be transmitted through the second polarizer. This is shown in the following image.

If the polarized electric field is called E1 after it passes through the first polarizer, the component, E2, after the field passes through the second polarizer which is at an angle φ with respect to the first polarizer is E1cosφ. Since the intensity of the light varies as the square of the electric field, the light intensity transmitted through the second filter is given by (Malus law) :

I2 = I1 cos2φ

Verification of the Law of Malus

For the verification of the Malus law we used the He-Ne laser, a polarizing filter and the analyzer filter mounted on the rotating support described above. The light intensity transmitted by the filter was measured by a photodiode sensor. In order to exclude the environmental brightness and improve the sensitivity of the measurement, a 633 nm interference filter was used, coinciding with the laser emission wavelength. All placed on our crafted optical table.
More details on the equipment used can be found in the following posts : DIY Optical Table, PSoC based Photometer.
The images below show the setup, with the detail of the sensor + filter.

The following graph shows the results of the measurement obtained by rotating the analyzer filter.

we see how the measure of luminous intensity follows the theoretical prediction fairly faithfully.

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