# 1.7 Polarization  (Page 7/20)

 Page 7 / 20 Birefringent materials, such as the common mineral calcite, split unpolarized beams of light into two with two different values of index of refraction.

## Summary

• Polarization is the attribute that wave oscillations have a definite direction relative to the direction of propagation of the wave. The direction of polarization is defined to be the direction parallel to the electric field of the EM wave.
• Unpolarized light is composed of many rays having random polarization directions.
• Unpolarized light can be polarized by passing it through a polarizing filter or other polarizing material. The process of polarizing light decreases its intensity by a factor of 2.
• The intensity, I , of polarized light after passing through a polarizing filter is $I={I}_{0}\phantom{\rule{0.2em}{0ex}}{\text{cos}}^{2}\phantom{\rule{0.2em}{0ex}}\theta$ , where ${I}_{0}$ is the incident intensity and $\theta$ is the angle between the direction of polarization and the axis of the filter.
• Polarization is also produced by reflection.
• Brewster’s law states that reflected light is completely polarized at the angle of reflection ${\theta }_{\text{b}}$ , known as Brewster’s angle.
• Polarization can also be produced by scattering.
• Several types of optically active substances rotate the direction of polarization of light passing through them.

## Key equations

 Speed of light $c=2.99792458\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{8}\phantom{\rule{0.2em}{0ex}}\text{m/s}\approx 3.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{8}\phantom{\rule{0.2em}{0ex}}\text{m/s}$ Index of refraction $n=\frac{c}{v}$ Law of reflection ${\theta }_{\text{r}}={\theta }_{\text{i}}$ Law of refraction (Snell’s law) ${n}_{1}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta }_{1}={n}_{2}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta }_{2}$ Critical angle ${\theta }_{\text{c}}={\text{sin}}^{-1}\left(\frac{{n}_{2}}{{n}_{1}}\right)\phantom{\rule{0.5em}{0ex}}\text{for}\phantom{\rule{0.2em}{0ex}}{n}_{1}>{n}_{2}$ Malus’s law $I={I}_{0}\phantom{\rule{0.2em}{0ex}}{\text{cos}}^{2}\phantom{\rule{0.2em}{0ex}}\theta$ Brewster’s law $\text{tan}\phantom{\rule{0.2em}{0ex}}{\theta }_{\text{b}}=\frac{{n}_{2}}{{n}_{1}}$

## Conceptual questions

Can a sound wave in air be polarized? Explain.

No. Sound waves are not transverse waves.

No light passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original two, some light can pass. Why is this? Under what circumstances does most of the light pass?

Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

Energy is absorbed into the filters.

When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to $\frac{1}{\lambda }$ . Does this mean there is more scattering for small $\lambda$ than large $\lambda$ ? How does this relate to the fact that the sky is blue?

Using the information given in the preceding question, explain why sunsets are red.

Sunsets are viewed with light traveling straight from the Sun toward us. When blue light is scattered out of this path, the remaining red light dominates the overall appearance of the setting Sun.

When light is reflected at Brewster’s angle from a smooth surface, it is $100\text{%}$ polarized parallel to the surface. Part of the light will be refracted into the surface. Describe how you would do an experiment to determine the polarization of the refracted light. What direction would you expect the polarization to have and would you expect it to be $100\text{%}$ ?

If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well. Why not?

The axis of polarization for the sunglasses has been rotated $90\text{°}$ .

## Problems

What angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?

#### Questions & Answers

in the wave equation y=Asin(kx-wt+¢) what does k and w stand for.
derivation of lateral shieft
Hi
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ALFRED
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Imran
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ALFRED
total binding energy of ionic crystal at equilibrium is
How does, ray of light coming form focus, behaves in concave mirror after refraction?
Refraction does not occur in concave mirror. If refraction occurs then I don't know about this.
Sushant
What is motion
Anything which changes itself with respect to time or surrounding
Sushant
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Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
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Chemist
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DHEERAJ
These substance create harmful radiation like alpha particle radiation, beta particle radiation, gamma particle radiation
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
as a free falling object increases speed what is happening to the acceleration
of course g is constant
Alwielland
acceleration also inc
Usman
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normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
give any fix value to wave length
Rafi
40 cm into change mm
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends​.
Prema
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because is the study of mater and natural world
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because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
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tahreem
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Buvanes
all living things are matter
Buvanes
why rolling friction is less than sliding friction
tahreem
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tahreem
is this a physics forum
explain l-s coupling   By Eric Crawford  By   By Subramanian Divya  By