Chapter 5

Polarization of Light Waves

Polarization of Light Waves Each atom produces a wave with its own orientation of

All directions of the electric field vector are equally possible and lie in a plane perpendicular to the direction of propagation

This is an unpolarized wave

A wave is said to be linearly polarized if the resultant electric field vibrates in the same direction at all times at a particular point

Polarization can be obtained from an unpolarized beam by selective absorption reflection scattering

Polarization by Selective Absorption

The most common technique for polarizing light Uses a material that transmits waves whose electric

field vectors in the plane are parallel to a certain direction and absorbs waves whose electric field vectors are perpendicular to that direction

E. H. Land discovered a material that polarizes light through selective absorption He called the material Polaroid The molecules readily absorb light

whose electric field vector is parallel to their lengths and transmit light whose electric field vector is perpendicular to their lengths

The intensity of the polarized beam transmitted through the second polarizing sheet (the analyzer) varies as

I = Io cos2 θ Io is the intensity of the polarized wave

incident on the analyzer This is known as Malus’ Law and

applies to any two polarizing materials whose transmission axes are at an angle of θ to each other

The intensity of light transmitted through two polarizers depends on the relative orientation of their transmission axes. (a) The transmitted light has maximum intensity when the transmission axes are aligned with each other. (b) The transmitted light intensity diminishes when the transmission axes are at an angle of 450 with each other. (c) The transmitted light intensity is a minimum when the transmission axes are at right angles to each other.

Polarization by Reflection When an unpolarized light beam is reflected

from a surface, the reflected light is Completely polarized Partially polarized Unpolarized

It depends on the angle of incidence If the angle is 0° or 90°, the reflected beam is

unpolarized For angles between this, there is some degree

of polarization For one particular angle, the beam is

completely polarized

The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θp

θp + 90o + θp = 180°, so that θ = 90° - θp .

Using Snell’s law and taking n1 = 1.00 and n2 = n, we have

  Because sin θ2 = sin(90° - θp) = cos θp , the

expression for n can be written as

θp may also be called Brewster’s Angle

sintan

cosp

pp

n

Polarization by Double Refraction When light travels through an amorphous

material, such as glass, it travels with a speed that is the same in all directions.

That is, glass has a single index of refraction. In certain crystalline materials, however, such as calcite and quartz, the speed of light is not the same in all directions. Such materials are characterized by two indices of refraction. Hence, they are often referred to as double-refracting or birefringent materials.

When unpolarized light enters a calcite crystal, it splits into two plane-polarized rays that travel with different speeds, corresponding to two angles of refraction

One ray, called the ordinary (O) ray, is characterized by an index of refraction, nO that is the same in all directions.

The second plane-polarized ray, called the extraordinary (E) ray, travels with different speeds in different directions and have an index of refraction, nE, that varies with the direction of propagation.

there is one direction, called the optic axis, along which the ordinary and extraordinary rays have the same speed, corresponding to the direction for which

nO = nE . The difference in speed for the two rays is a

maximum in the direction perpendicular to the optic axis.

Polarization by Scattering When light is incident on a system of

particles, the electrons in the medium can absorb and reradiate part of the light This process is called scattering

An example of scattering is the sunlight reaching an observer on the earth becoming polarized

The horizontal part of the electric field vector in the incident wave causes the charges to vibrate horizontally

The vertical part of the vector simultaneously causes them to vibrate vertically

Horizontally and vertically polarized waves are emitted

Optical Activity Certain materials display the property of

optical activity A substance is optically active if it

rotates the plane of polarization of transmitted light

Optical activity occurs in a material because of an asymmetry in the shape of its constituent materials

The angle through which the light is rotated by a specific material depends on the length of the sample and on the concentration if the substance is in solution.

One optically active material is a solution of common sugar dextrose.

A standard method for determining the concentration sugar solutions is to measure the rotation produced by a fixed length of the solution.

photoelastistity materials, such as glass

and plastic, become optically active when stressed

If the plastic is stressed, regions of greatest stress rotate the polarized light through the largest angles.

a series of bright and dark bands is observed in the transmitted light;