Properties of Light

Light is a unique thing. We can think of it terms of both waves and particles called photons. In this post, we are going to look at only the wave nature of light, or in general, all electromagnetic radiation of which light is only a small subset.


 


Electromagnetic radiation is made up of both electric fields and magnetic fields which propagate perpendicular to each other. The wave itself, moves in the third direction, perpendicular to the fields.

where B is the strength of the magnetic field, E is the strength of the electric field, and c is the speed of light (3x10⁸ m/s)

 

So what exactly is a wave? Waves have maxima (crests), minima (troughs), and zero points (nodes).

We can also take a measure of a wave by looking at the distance between successive crests (or troughs) which we call the wavelength, represented by the Greek letter lambda (λ). This can be measured in meters, nanometers (10^-9 m), or Ångstroms (10^-10 m symbolized by Å).

Or we can look at a point in space and how long it takes two successive crests (or troughs) to pass that point in space. This is called the frequency, symbolized as either f or ν (Greek letter nu). This value can be measured in the inverse of seconds (1/s) or Hertz.

The cool thing about the wavelength and the frequency is that you can multiply them together to get the speed of the wave. In our case, for light, the speed is just c.

c= λ*ν

 

Lastly, when we are talking about visible light, we are talking about all light that can be seen by the human eye. They range in color from red to violet (ROY G. BIV), with the longer wavelengths and shorter frequencies closer to the red end of the spectrum and the shorter wavelengths with higher frequencies near the violet end.

For visible light, red is approximately 7000 Å and 430 terahertz (10¹² Hertz). Violet is around 3000 Å and 1 petahertz (10¹⁵ Hertz). 

These will become important later on.

 

 

Olbers' Paradox

In the early 1800's, there was a quandary. Scientists did not know about the size of the universe or the speed of light. There was an assumption that the universe was infinite in size, age, and mass. Not only that, they assumed that light itself travelled instantaneously from place to place. They did not know about the Big Bang, or Hubble's Law, or even Relativity. So from these assumptions, there arose a question: why is the night sky dark?


They believed the universe was infinite and static. Because of this, they wondered where all the stars were. Imagine looking in any direction in the sky. If the universe is infinitely populated with stars, no matter where you look, you will see a star, despite the great distances involved (remember, light is instantaneous). Therefore, you should see light from that star. Because of this, at night, when the Sun is not dominating the sky, the sky itself should be lit up like daytime. Though this question has been posed before, Heinrich Olbers was the first to formulate the question and try to answer it, and we call this question, Olbers' Paradox.






He came up with a few reasons why the night sky is not dark. I'm only going to mention two for simplicity.

1. The universe is not infinite. There is a limit to the size as well as the age of the universe, though the size may be larger than the age of the universe. We still don't know exactly how big the universe really is since we can only see about 14 billion light-years in any direction.
2. The speed of light is not infinite. He didn't know how fast it was, but he could conclude that light travelled at a finite speed. Therefore, light from stars that are farther away from us than the age of the universe have not had enough time to reach us since the star/galaxy/whatever was formed.

From these two reasons, we can see the night sky is dark because the light from most of the stars in the universe has not had enough time since the light left the star to reach us.

Special Relativity

Previously, we briefly discussed General Relativity and how it expands Newtonian Mechanics to include the interaction between mass and space(time). Today, we are going to talk a little bit about Special Relativity in that what happens to physics when we approach velocities near the speed of light.

There are two postulates that Albert Einstein proposed make up Special Relativity.

1.      All Laws of Physics are invariant in all inertial systems - basically, the laws of physics must remain the same for all reference frames that are not accelerating.

2.      The speed of light in a vacuum is the same for all observers, regardless of the motion of the observers. In other words, the speed of light, c, is the same for a stationary person and a person moving at any speed, up to the speed of light (which is impossible).

One of the amazing things about Special Relativity is the idea of time dilation. It means that for any body travelling at any speed, time is not constant. To a stationary observer, it would appear that the clock for the moving object slows down, but for the observer in motion, the clock of the stationary person speeds up. In both cases, each observer sees the clock in his or her reference frame as moving normally. How does this work?

We have to use math to show this. There is an equation that describes how time is relative using the Lorentz transformation:

Where  is the time for the moving observer,  is the time for the stationary observer, and  is the Lorentz factor given by , where v is speed of the moving observer and c is the speed of light (3x10⁸ m/s). Since v is always less than the speed of light, is always greater than one, therefore Δt’ > Δt. For the stationary observer, the clock of the moving person is slow, while for the moving observer, the stationary person has a fast clock. For velocities much smaller than the speed of light, γ is virtually 1 and the times are equivalent. However, we have seen for objects moving near the speed of light (particles with little mass), this actually holds true. An example is a muon. A stationary muon would decay in only 2.2 μsec; however, when a muon is travelling near the speed of light will last much longer than 2.2 μsec (to a stationary observer).

Another strange feature of special relativity is the idea of length contraction. In other words, a moving object will appear shorter than it would be if it were stationary.

Where Δx’ is the length of the moving object and Δx is the length of the stationary object. This again leads to another strange phenomenon: relativity of simultaneity.

Relativity of simultaneity means that something that happens simultaneously in one inertial frame is not necessarily simultaneous in another. The best example given is called the ladder paradox.

Imagine a ladder and a barn. The ladder is just a little bit longer than the length of the barn. Now imagine that the ladder is moving at a relativistic speed. Someone in the barn reference frame will see the ladder shorter than its stationary length, and can close doors at both ends with ladder inside simultaneously. However, to keep the ladder from crashing through the end door, the doors must open up again. For the ladder, however, it sees the end door close first, then the front door close secondly, with the end door opening up before the ladder reaches it. The ladder does not see both doors closed at the same time.

A third phenomenon of special relativity is the idea of infinite mass. For a moving mass, Δm’=γΔm. As v approaches c, you can see that γ nears infinity (v/c approaches 1 and the denominator in the Lorentz factor approaches 0). This is why nothing can reach the speed of light as its mass will become infinite, which leads to another famous equation: E=mc², the energy-mass equivalency. This means in order to accelerate a mass to the speed of light, the amount of energy required goes to infinity.