PolarizationPolarization

EM WavesEM Waves Light is an electromagnetic wave. EM waves are Light is an electromagnetic wave. EM waves are

transverse. Thus, the electrical field can vibrate in transverse. Thus, the electrical field can vibrate in any direction perpendicular to the direction of any direction perpendicular to the direction of propagation. Most light sources (candles, propagation. Most light sources (candles, incandescent light bulbs etc..) emit light that is incandescent light bulbs etc..) emit light that is unpolarized – the electric field has all possible unpolarized – the electric field has all possible directions of vibrations.directions of vibrations.

However it is possible to have polarized However it is possible to have polarized light. Polarized light occurs when the light. Polarized light occurs when the vibrations of the electrical field are vibrations of the electrical field are confined to one plane.confined to one plane.

Ways to polarize LightWays to polarize Light 1. 1. Pass the light through a polarizing filter. A Pass the light through a polarizing filter. A

Polaroid sheet has polymers where the Polaroid sheet has polymers where the molecules are aligned in one direction. In molecules are aligned in one direction. In ideal situations, a Polaroid transmits 50% of ideal situations, a Polaroid transmits 50% of the unpolarized light.the unpolarized light.

Two Polaroid SheetsTwo Polaroid Sheets If you pass light through two Polaroid If you pass light through two Polaroid

sheets so that their polarization axes are sheets so that their polarization axes are aligned, light will be transmitted through aligned, light will be transmitted through both of them. both of them.

If their axes are at right angles to each If their axes are at right angles to each other, almost no light will get through. other, almost no light will get through. When Polaroids are used in pairs like this, When Polaroids are used in pairs like this, the first is called the the first is called the polarizerpolarizer and the and the second is called the second is called the analyzeranalyzer..

2. Reflection2. Reflection When an unpolarized wave reflects off a nonmetallic When an unpolarized wave reflects off a nonmetallic

surface, the reflected wave is partially plane surface, the reflected wave is partially plane polarized parallel to the surface. The amount of polarized parallel to the surface. The amount of polarization depends upon the angle (more later).polarization depends upon the angle (more later).

The reflected ray contains more vibrations parallel to the reflecting surface while the transmitted beam contains more vibrations at right angles to these.

ApplicationsApplications Knowing that reflected light or glare Knowing that reflected light or glare

from surfaces is at least partially from surfaces is at least partially plane polarized, one can use Polaroid plane polarized, one can use Polaroid sunglasses. The polarization axes of sunglasses. The polarization axes of the lenses are vertical as the glare the lenses are vertical as the glare usually comes from reflection off usually comes from reflection off horizontal surfaces.horizontal surfaces.

Polarized Lens on a Camera

Reduce Reflections

3. Scatter light3. Scatter light When light(such as that from the sun) shines on When light(such as that from the sun) shines on

particles, they can absorb and then reradiate part of particles, they can absorb and then reradiate part of the light. The absorption and reradiation of light is the light. The absorption and reradiation of light is called scattering. Unpolarized light will be partially called scattering. Unpolarized light will be partially plane polarized after scattering from small particles plane polarized after scattering from small particles of dust etc…The scattered light will be completely of dust etc…The scattered light will be completely plane polarized if scattered light is 90.0plane polarized if scattered light is 90.0oo from from incident light. Thus if you look straight up into the incident light. Thus if you look straight up into the sky and rotate a polarizer, you will see the sky and rotate a polarizer, you will see the transmitted light change in intensity. (Blue light is transmitted light change in intensity. (Blue light is scattered more than red light so the sky appears scattered more than red light so the sky appears blue!!)blue!!)

Mathematics of PolarizationMathematics of Polarization • Two consecutive polarizers. – The first polarizer reduces the intensity by half. – The second polarizer reduces the intensity by another factor of

cos2. This is called Malus’s Law.

Example 1Example 1

Two polarizers are Two polarizers are orientated with orientated with their axes at an their axes at an angle of 35.0angle of 35.0oo, , what proportion of what proportion of the original light the original light remains?remains?

1 o

22 1

22

2

After the first polarizer:

1I I

2After the second polarizer:

I I cos

1cos 35.0

2

0.336

oo

o

I I

I I

Example 2Example 2 Instead of having Instead of having

two polarizers at two polarizers at 9090oo to each other, to each other, what would happen what would happen if the second if the second polarizer is polarizer is replaced by two replaced by two polarizers at polarizers at increasing increasing orientation of orientation of 45.045.0oo??

1 0

2 o2 1

2 o

2 0

2 o3 2

For the first polarizer:

1I

2For the second polarizer:

I I cos 45.0

1note that cos 45.0

21 1 1

2 2 4

For the third polarizer:

1 1 1I I cos 45.0

4 2 8

o

o o

I

I I I

I I

Polarized Reflecting LightPolarized Reflecting Light

When an unpolarized light wave When an unpolarized light wave reflects off a non-metallic surface, it reflects off a non-metallic surface, it can be completely polarized, partially can be completely polarized, partially polarized or unpolarized depending polarized or unpolarized depending on the angle of incidence. A on the angle of incidence. A completely polarized wave occurs for completely polarized wave occurs for an angle called Brewster’s angle an angle called Brewster’s angle (named after Sir David Brewster)(named after Sir David Brewster)

Complete polarization occurs when Complete polarization occurs when the reflected beam and the refracted the reflected beam and the refracted beam are 90beam are 90oo to each other. to each other.

With simple trigonometry this condition can be expressed as:

                   where θ1 is the angle of incidence and θ2 is

the angle of refraction.Using Snell's law,

                              

                                                        Rearranging, we get:

                        

1

2tann

nB

1

2tann

nB

Example 3Example 3

Light is reflected Light is reflected from a smooth ice from a smooth ice surface(n = 1.31) surface(n = 1.31) and the reflected and the reflected wave is completely wave is completely plane polarized. plane polarized. What is the angle What is the angle of incidence?of incidence?

2

1tan

1.31tan

1.0052.6

B

B

B

n

n

Optical ActivityOptical Activity A substance is said to be optically active if A substance is said to be optically active if

it can rotate the plane of polarization of it can rotate the plane of polarization of transmitted light. The angle through transmitted light. The angle through which the light is rotated depends on the which the light is rotated depends on the length of the sample and the length of the sample and the concentration if the substance is in concentration if the substance is in solution. A standard method for solution. A standard method for measuring the concentration of a sugar measuring the concentration of a sugar solution is to measure the rotation solution is to measure the rotation produced by a fixed length.produced by a fixed length.

StressStress Some materials are optically active Some materials are optically active

because of the shape of the molecules. because of the shape of the molecules. Other materials such as glass or plastic Other materials such as glass or plastic become optically active when placed under become optically active when placed under stress. Engineers build plastic models of stress. Engineers build plastic models of various structures such as machine parts. various structures such as machine parts. The model is analyzed under different load The model is analyzed under different load conditions. Polarized light is passed conditions. Polarized light is passed through the plastic and then through an through the plastic and then through an analyzer whose axis is perpendicular to the analyzer whose axis is perpendicular to the polarized light. Regions of greates stress polarized light. Regions of greates stress produce the greatest angles of rotation so produce the greatest angles of rotation so these show up as bright bands.these show up as bright bands.