# Physics Tutorial: Polarization of Light

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In this Physics tutorial, you will learn:

• How do we see objects and their colours?
• What is polarization of light?
• What device do we use to produce polarization?
• How many types of polarization do we have?
• Which are the two types of linear polarization? What are their features?
• How many types of polarizers are there? What are their features?
• What does the Malus Law say on polarization of light?

## Introduction to Polarization of Light

What colours do you see when using green goggles? Why?

Do you think the colour of goggles glass has any effect in the colour of light transmitted through them?

How do we see the colour of objects around us at naked eye?

Do you known what advantage do the polarized sunglasses offer compared to non-polarized ones?

These questions will get answer is this interesting topic that we are going to explain now. You will also learn how light waves of different wavelength (and therefore of different colour) vibrate when they are moving in space and what happens with them after passing through a polarized glass.

## How Do We See the Colours of Objects?

It is a matter of fact that light coming to us from the Sun has white colour. This means the light produced by the Sun includes all possible wavelengths of EM radiation. Most of this radiation (especially high frequency EM waves such as gamma, X and UV radiation) is reflected back by the atmosphere. Therefore, only visible light and below can reach the Earth surface due to their higher amplitudes.

When the white light strikes an object, most of the incident radiation is absorbed by the object itself. This contributes in an increase in object's temperature as EM radiation brings energy with it. As a result, the object becomes hot. Only the light waves that correspond to the object's colour(s) is (are) reflected by the objects surface. As a result, the light waves corresponding to the object's colour comes to our eyes through reflection. This is how we see the objects around us.

In the above figure, leaves reflect only the green light while absorbing all the other colours coming from the sunlight in the form of white light. This is why they look green.

An object appears black when it absorbs all the colours of the spectrum of visible light falling upon it. A black object reflects no light. On the other hand, if an object reflects all the incident light colours falling, it appears white, as white objects absorb none of the colours of the EM spectrum.

## What is Polarization of Light?

As discussed in the Physics tutorial on the Features of Light, EM waves have two components - one electric and the other magnetic -, which oscillate at right angles to each other. However, since the magnetic component of light is much smaller than the electric one (it is smaller by a factor of 3 × 108, i.e. equal to the speed of light in vacuum), we consider only the electric component of EM radiation when dealing with the wave behaviour of light.

However, this description of EM waves' pattern is very helpful in understanding how waves of different wavelength contained in a single beam oscillate in respect to each other. It is proved that light waves oscillate at different angles (depending on their colours) to each other despite propagating through the same axis as shown in the figure.

When we place a coloured glass in the light path, all colours are absorbed by the glass (as explained in the previous paragraph), except one colour - the colour of the glass. In this way, the coloured glass acts like a barrier to the other waves and it allows to pass through only one light wave - the wave that has the same colour to it. This property is known as polarization of light. By definition,

Polarization of light is the restriction of the electric vector oscillation in a single direction (or in simpler words, the restriction of the light wave in a single plane).

This means all the other directions of light oscillation are eliminated except one, as shown in the figure below.

The coloured glass can be substituted by a transparent glass in which parallel gratings at a distance from each other (which is smaller than the waves amplitude) are made. In this case, gratings act like jail bars, i.e. they don't allow the light waves that do not oscillate according their direction to pass through. This kind of glass is known as polarizer.

When we put another polarizer at right angle to the first one, the light is completely blocked as it cannot pass longwise through the narrow gratings as shown in the figure above.

## Types of Polarization

There are three types of light polarization: linear, circular and elliptic. Let's explain the features of each of them.

### a) Linear polarization

In this type of polarization, the electric field is confined to a single plane. This means we obtain a 2-D wave from the original 3-D one. It is called linear polarization because the electric vector oscillates only in one dimension (the other dimension stands for the direction of wave propagation). Look at the figure below in which two incident waves at right angle (one oscillates in the x direction and the other in the y-direction while both propagating in the z-direction) are shown.

After polarization occurs, the oscillation of polarized wave will have a different angle from each single original wave as shown in the figure below, in which the polarized light wave is shown through the dotted line.

The direction of polarized wave changes continuously; thus, at another instant, the polarized wave pattern will be like this:

Linear polarization occurs when the two incident waves oscillate at 900 between them but they don't have any phase difference, i.e. they are at phase.

### b) Circular Polarization

In this kind of polarization the incident waves still have a 900 oscillating direction between them. However, unlike in linear polarization, these incident waves have a phase shift of π/2 between them. As a result, they form a circular polarized wave pattern as shown in the figure.

Therefore, we can say if the two incident waves oscillate according the x and y directions respectively and if one wave is displaced at maximum position when the second one is at the equilibrium position, a circular pattern is produced when polarization occurs. It is true that this circular pattern occurs according the xOy plane, but since all waves propagate in the z-direction, a spring-like pattern is produced in the polarized wave as shown by the dotted line in the above figure.

### c) Elliptic Polarization

Elliptic polarization occurs in two conditions:

• when the amplitudes of the incident waves are not equal, or
• when the angle between the oscillation direction (i.e. of electric vector) of the two incident waves is not 900.

In this case, an elliptic pattern for the polarized wave is produced. Look at the figure.

## P and S Polarization

Among the infinity number of possible linear polarization states, two of them are the most important for reflection and transmission (refraction). The first is called the p-polarization and the later as the s-polarization.

The p-polarization occurs when polarized light has an electric field vector parallel to the plane of incidence. On the other hand, the s-polarization occurs when the electric field vector of the polarized light is perpendicular to the plane of incidence as shown in the figure below.

## Types of Polarizers

Polarizers are tools used to provide a specific polarization of light. There are three types of polarizers available: reflective, dichroic and birefringent.

### Reflective Polarizers

Reflective polarizers provide polarization of the desired light while reflecting (blocking) the rest. Wire grid polarizers are an example of reflective polarizers. In wire grid polarizers, only the light whose electric vector is in the direction of grid lines is allowed to pass through while the light, whose electric vector is perpendicular to those grids, is blocked. Look at the figure in which a wire grid polarizer with four different directions of grid lines is shown.

### Dichroic Polarizers

Dichroic polarizers absorb a specific polarization of light, transmitting the rest. Modern nanoparticle polarizers are examples of dichroic polarizers. The figure below shows a dichroic polarizer.

Most high quality polarized sunglasses in use today have dichroic polarized glasses. This is why only the incidence light is allowed to pass through them, not the reflected one.

### Birefringent Polarizers

Birefringent polarizers operating principle is based on the refractive index of light. Given that different polarizations diffract at different angles, this property is used to choose specific polarizations of light.

Microscopy uses birefringent polarization, as it is very sensible to slight changes of light intensity caused by the elimination of a certain number of electric vectors depending on the situation.

## Malus Law

Non-polarized light can be considered as a continuous switch between p and s polarizations. If we take an ideal linear polarizer for simplicity, it is clear that such a polarizer will transmit only one type of polarization at a time. Therefore, the intensity of polarized light will be half of that of the original light. Thus, if we denote the initial intensity of unpolarised light by I0 and the intensity of polarized light by î(both measured in candela, [cd] which is one of the seven fundamental Sîunits), we obtain

î = I0/2

To describe the relationship between polarized light I, unpolarised light I0 and the angle θ between the incident linear polarization and the polarization axis, we use the so-called Malus Law:

î = I0 × cos2 θ

### Example 1

Calculate the light intensity of the polarized light if the parallel lines of the reflective linear polarizer used for this purpose form an angle of 300 to the electric vector of the incident light. Take the intensity of incident light equal to 20 cd, cos 300 = √3/2 and sin 300 = 1/2 if needed.

### Solution 1

Applying the Malus Law

î = I0 × cos2 θ

we obtain after substituting the values:

î = 20 × cos2 300
= 20 × 3/22
= 20 × 3/4
= 15 cd

## Physics Revision: Polarization of Light Summary

Light waves corresponding to the object's colour comes to our eyes through reflection. Only the light colour representing the colour of objects is reflected to our eyes; the object absorbs the other colours of the (white) sunlight. This is how we see the objects around us.

An object appears black when it absorbs all the colours of the spectrum of

visible light falling upon it. A black object reflects no light. On the other hand, if an

object reflects all the incident light colours falling, it appears white, as white objects absorb none of the colours of the EM spectrum.

Polarization of light is the restriction of the electric vector oscillation in a single direction (or in simpler words, the restriction of the light wave in a single plane).

This means all the other directions of light oscillation are eliminated except one.

Polarizers are transparent objects that allow specific parts of light waves to pass through.

There are three types of light polarization: linear, circular and elliptic.

In linear polarization, the electric field is confined to a single plane. This means we obtain a 2-D wave from the original 3-D one.

In circular polarization, the incident waves still have a 900 oscillating direction between them. However, unlike in linear polarization, these incident waves have a phase shift of π/2 between them. As a result, they form a circular polarized wave pattern.

Elliptic polarization occurs in two conditions:

• when the amplitudes of the incident waves are not equal, or
• when the angle between the oscillation direction (i.e. of electric vector) of the two incident waves is not 900.

Among the infinity number of possible linear polarization states, two of them are the most important for reflection and transmission (refraction). The first is called the p-polarization and the later as the s-polarization.

The p-polarization occurs when polarized light has an electric field vector parallel to the plane of incidence. On the other hand, the s-polarization occurs when the electric field vector of the polarized light is perpendicular to the plane of incidence.

There are three types of polarizers available: reflective, dichroic and birefringent.

Reflective polarizers provide polarization of the desired light while reflecting (blocking) the rest. Wire grid polarizers are an example of reflective polarizers.

Dichroic polarizers absorb a specific polarization of light, transmitting the rest. Modern nanoparticle polarizers are examples of dichroic polarizers.

Birefringent polarizers operating principle is based on the refractive index of light. Given that different polarizations diffract at different angles, this property is used to choose specific polarizations of light.

Microscopy uses birefringent polarization, as it is very sensible to slight changes of light intensity caused by the elimination of a certain number of electric vectors depending on the situation.

To describe the relationship between polarized light I, unpolarised light I0 and the angle θ between the incident linear polarization and the polarization axis, we use the so-called Malus Law:

î = I0 × cos2 θ

## Physics Revision Questions for Polarization of Light

1. The angle between the electric vectors of two incident unpolarised light waves is 600. What kind of polarization is produced in this case?

1. Linear
2. Circular
3. Elliptic
4. Vibrational

2. What kind of polarization does the polarizer shown below provide?

1. Reflective
2. Dichroic
3. Birefringent
4. Chromatic

3. A light ray passes through a reflective polarizer. The electric vector of the incident light wave forms an angle of 370 to the grid lines (cos 370 = 0.8; sin 370 = 0.6). What is the intensity of the polarized light if the intensity of the incident light is 20 cd?

1. 7.2 cd
2. 12 cd
3. 12.8 cd
4. 16 cd