## Thursday, January 29, 2015

### Polarisation Concepts and Problems

The phenomena of restricting the vibrations of the light to a particular plane is called polarization. It is the property of the transverse wave. A transverse waves can only have vibrations in both the planes. Hence restricting the vibrations of one plane is possible with the transverse wave.

Sound waves in air cannot be polarized because they’re longitudinal in nature.

To explain the concept of polarization we shall depend on an electromagnetic wave theory of light. According to this theory, the varying electric fields particles generate a varying magnetic field around it and the direction of wave motion is perpendicular to both of them.

The magnetic field vibrations are no way responsible for any of the optical properties of light. Electric fields vector is responsible for all optical properties of light. This electric field vector can be resolved into components. The horizontal and vertical components exist in the perpendicular planes. The light that is having both these components is called unpolarized light or natural light. To polarize the light, we shall restrict either horizontal vibrations are vertical vibrations. Horizontal vibrations are represented with arrows and the vertical vibrations are represented with darts.

A unolarised light consists of both the horizontal and vertical vibrations. When the light is polarized, it will have either only the horizontal vibrations or only the vertical vibrations.

The intensity and the amplitude of the polarized light is less than that of the original light. To be more specific intensity of polarized light is half of the original intensity.
Polarization can be done by certain type of crystals like quartz crystal. This crystal is called as polarizer. To check whether the light is actually polarized or not, we can use the same crystal and then it is called as analyzer. Depending on the position of analyzer, the outcome of the light and its intensity can be identified as shown in the diagram.

Problem and solution

Unpolarised light of intensity that the 32 W per meter Squire passes through three Polaroid’s such that the transmission axis of the last polariser is crossed with the first one. If the intensity of the emerging light is 3 W per meter Squire what is the angle between the axes of the first two?

It is given in the problem that the sum of the two angles is equal to 90°. We know the equation further resultant intensity and by writing in this equation and simplifying we can get the answer as shown below.

Problem and solution

A beam of ordinary light is incident and system of four Polaroid’s which are arranged in succession such that each Polaroid is turned through 30° respect to the preceding one. What is the percentage of the incident intensity that emerges out from the system?

We know that when the light is passed through Polaroids its intensity decreases. If it is passing through only one polariser with the parallel axis only half of the intensity is going to remain. When there are good number of the polarisers, to find out the resultant intensity we can use a formula that is shown below and get the intensity.

Problems and solutions

In the following page attached, three problems are solved with a detailed solution. A comment can be made at the end of the post for any kind of further clarifications?

Polarization can be achieved through the process like reflection, refraction and double refraction. When the light strikes the boundary that is separating the two media, for a particular angle of incidence the reflected light is completely polarized. This particular angle of incidence is called the angle of polarization. In this case the refracted light consists of a small number of vertical vibrations and hence the refracted light is not completely polarized.

We can nature the polarization even by refraction. Here a group of plates are arranged one after the other so that each plate to its own polarization up to some extent. As many number of the required plates are placed such that the refracted light is having only horizontal vibrations. This combination is called pile of plates.

We can get the polarization by double refraction also with the help of so special crystals like a calcite crystal. This crystal has a specific property of reflecting the light twice and this property is called the double refraction. It is experimentally observed that both this refracted light’s are completely polarised.

One of the refracted lights follows all the regular rules of light and it is called ordinary light Ray. With the ordinary light Ray refractive index of the medium and the velocity of the light is constant.

The second refracted light Ray doesn’t follow the regular rules and it is called the extraordinary light Ray.

We can identify the ordinary and extraordinary light Ray quite easily. When the calcite crystal is placed in on a point object it makes to point images. With the rotation of the crystal one image reminds in the state of rest and the image is as ordinary. With the rotation of the crystal other image starts rotating and it is called the extraordinary.

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