$$\require{cancel}$$

# 6. Summary

1. We knew how a changing magnetic field causes a changing electric field. We learned that a changing electric field causes a magnetic field.
2. The field lines of an electric field created by a magnetic field form a loop, but the idea that electric field lines only begin or end on charges is still valid.
3. Because the electric and magnetic fields are so intimately related, they're sometimes referred to as one electromagnetic field.
4. The electromagnetic field features wave-like propagation that we call light.
5. Light (electromagnetic waves) can occur at many frequencies.  If the light is visible, this frequency determines the color.
6. Only a small fraction of the total electromagnetic spectrum is visible.  For example, ultraviolet, X-rays, and microwaves are all forms of light at invisible frequencies.  We discuss various applications of different kinds of light.
7. The medium of light waves is the electromagnetic field, which is why we can see through empty space.
8. Electromagnetic waves are transversely polarized because the magnetic field and electric field oscillate perpendicular to the direction of the wave. The polarization of an electromagnetic wave is the direction aligned with the $$\mathbf{E}$$ field.
9. Intensity, defined as power per unit area, is proportional to the square of the wave amplitude ($$I \propto {E_0}^2$$).  Lights with higher intensity appear brighter, lights with lower intensity appear dimmer.

10. "Polarized light" refers to electromagnetic waves that all oscillate in the same direction.  The plane containing the direction of $$\mathbf{E}$$ field oscillation ($$\hat{\mathbf{e}}$$) and the direction of wave motion ($$\hat{\mathbf{k}}$$) is called the plane of polarization.

11. Polarizers work by restricting motion of electrons along the transmission or polarizer axis, allowing a fraction of light to pass through.  All transmitted light is aligned in the same direction.  We learned how to determine the intensity and polarization of light after it passes through a polarizer.

12. Fields are not just mathematical constructions.  Fields must exist to conserve energy and momentum.