Optics

Light is pure energy stored in the form of a travelling electromagnetic wave.

The energy of a light particle is stored in the electromagnetic oscillation. During one moment, light is a “pulse” of electric field in space, and during the next instant it is a “pulse” of pure magnetic energy. Think of sending a “wrinkle pulse” down a long rope – where the pulse of mechanical energy is traveling along the rope. Light is like that, but without the rope. Light is just an electro-magnetic pulse and such pulses happen even in empty space. Thus, unlike most other waves you may have seen until now, light does not need a medium to travel in: empty space will do just fine.

The understanding of light as a manifestation of electro-magnetic energy (electromagnetic radiation) is some deep stuff, which is not the subject of this section. We will get to this, after we cover the concept of electric and magnetic fields, electric and magnetic energy and Maxwell's equations. For the moment, when I say “oscillating energy”, I want you to think of a mechanical mass-spring system in which the energy oscillates between the potential energy of the spring and the kinetic energy of the mass. A photon is a similar oscillation between a “magnetic system” part and the “electric system” part, which travels through space at the speed of light.

In this section, we focus on light rays. The vector $\hat{k}$ in the figure describes the direction of travel of the light ray.

  Oh light ray, light ray! 
  Where art thou, on this winter day.

Light is made up of “light particles” called photons:

• $p$: a photon.
• $E_p$: the Energy of the photon.
• $\lambda$: the wavelength the photon.
• $f$: the frequency of the photon. (Denoted $\nu$ in some texts.)
• $c$: the speed of light in vacuum. $c=2.9979\times 10^{8}$[m/s].

NOINDENT The speed of light depends on the material in which it travels:

• $v_x$: the speed of light in material $x$.
• $n_x$: the diffraction index of material $x$,

which tells you how much slower light is in that material

  relative to the speed of light in vacuum. 
  $v_x=c/n_x$.
  Air is pretty much like vacuum, 
  so $v_{air} \approx c$ and $n_{air}\approx 1$. 
  There are different types of glass used in 
  lens-manifacturing with $n$ values ranging from 1.4 to 1.7.

Like all travelling waves, the propagation speed of light is equal to the product of its frequency times its wavelength. In vacuum we have \[ c = \lambda f. \]

For example, red light of wavelength $\lambda=700$n[m], has frequency $f=428.27$THz since the speed of light is $c=2.9979\times 10^{8}$[m/s].

The energy of a beam of light is proportional to the intensity of the light (how many photon per second are being emitted) and the energy carried by each photon. The energy of a photon is proportional to its frequency: \[ E_p = \hbar f, \] where $\hbar=1.05457\times 10^{-34}$ is Plank's constant. The above equation is a big deal, since it applies not just to light but to all forms of electromagnetic radiation. The higher the frequency, the more energy per photon there is. Einstein got a Nobel prize for figuring out the photoelectric effect which is a manifestation of the above equation.

The speed of light in a material $x$ with refractive index $n_x$ is \[ v_x = \frac{c}{n_x}. \]

Here is a list of refractive indices for some common materials: $n_{vacuum}\equiv 1.00$, $n_{air} = 1.00029$, $n_{ice}=1.31$, $n_{water}=1.33$, $n_{fused\ quartz}=1.46$, $n_{NaCl}=1.54$, Crown glass 1.52-1.62, Flint glass 1.57-1.75, $n_{sapphire}=1.77$, and $n_{diamond}=2.417$.

Our eyes are able to distinguish certain wavelengths of light as different colours.

Note that units of wavelength are tiny numbers like: nanometers $1[\textrm{nm}]=10^{-9}[\textrm{m}]$ or Armstrongs $1[\textrm{A}]=10^{-10}[\textrm{m}]$.

Visible light is only a small part of the electromagnetic spectrum. Waves with frequency higher than that of violet light are called ultraviolet (UV) radiation and cannot be seen by the human eye. Also, frequencies lower than that of red light (infrared) are not seen, but can sometimes be felt as heat.

The EM spectrum extends to all sorts of frequencies (and therefore wavelengths, by $c=\lambda f$). We have different names for the different parts of the EM spectrum. The highest energy particles (highest frequency $\to$ shortest wavelength) are called gamma rays ($\gamma$-rays). We are constantly bombarded by gamma rays coming from outer space with tremendous energy. These $\gamma$-rays are generated by nuclear reactions inside distance stars.

Particles with less energy than $\gamma$-rays are called X-rays. These are still energetic enough that they easily pass through most parts of your body like a warm knife through butter. Only your bones offer some resistance, which is kind of useful in medical imaging since all bone structure can be seen in contrast when taking an X-ray picture.

The frequencies below the visible range (wavelengths longer than that of visible light) are populated by radio waves. And when I say radio, I don't mean specifically radio, but any form of wireless communication. Starting from 4G (or whatever cell phones have gotten to these days), then the top GSM bands at 2.2-2.4GHz, the low GSM bands 800-900MHz, and then going into TV frequencies, FM frequencies (87–108MHz) and finally AM frequencies (153kHz–26.1MHz). It is all radio. It is all electromagnetic radiation emitted by antennas, travelling through space and being received by other antennas.