# 1.7 Polarization  (Page 7/20)

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## 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?

plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
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