# Light: Wave or a Particle?

For centuries, the debate raged as to whether light was a particle or a wave.  The Greeks believed in a particle nature for light.  We were able to see things because our eyes emitted beams of light, which makes me think of Cyclops from the X-Men.  Newton also believed in the corpuscle theory of light.   He saw that light travels in straight lines.   He analyzed geometric objects in terms of momentum and collisions of particles.  Based on this and geometry, Newton wrote Optiks and designed the Newtonian reflecting telescope which differed from most of the lens based telescopes of the time.

However, Young developed his theory that light is actually a wave.  The evidence came in that light exhibited the phenomena of diffraction, refraction, and interference.  In the end, Einstein brought these two theories together and showed that light is both a particle and a wave by explaining photoelectric effect, for which he earned the Nobel Prize.  In this theory, a particle of light is called the photon.

Maxwell developed the idea of electromagnetic waves, which are due to electrons oscillating on an antenna.  He explained how the electromagnetic wave E-fields and B-fields reproduce each other, thus causing the wave to propagate.  By combining Gauss’s Law, Ampere’s Law, and Faraday’s Law, he was able to develop a coherent theory of electromagnetism and its relationship to all forms for electromagnetic radiation, such as radio waves, microwaves, infrared radiation, visible light, ultraviolet light, X-rays, and gamma rays. The only difference between these forms was the wavelength and frequency. It took Einstein to explain that each photon had a frequency, and an energy which was proportional to that frequency as given by

E = hf

Where E is the photon energy, f is the frequency, and h is Plank’s constant.  You can see in the above table the frequency, wavelength, and energy for different forms of electromagnetic radiation.

# Speed of Light

Through the 19th century better estimates were made for the speed of light which we now realize is a constant in all frames of reference.  Photons travel in a vacumn at a speed of approximately  c = 3 x 108 m/s

Galileo realized the speed of light was faster than he could masure. In 1675, Ole Roemer was the first to come up with a good estimate of the speed of light using the moons of Jupiter, of about 2.3 x 108 m/s.   In 1849 Armand Fizeau  used a toothed wheel to estimate the speed at  2.9977 x 108 m/s.  In 1880 Michelson built on this using a rotating octogolnal mirror on a mountain top and got 2.9920 x 108 m/s which is not far from the actual value of 2.99792457 x 108 m/s.  You could easily measure the speed of light yourself by setting of Fizzeu’s experiment in the classroom using a chopper, electric drill, HeNe Laser, mirrors, long focal length converging lenses, phototransistor. diode and an oscilloscope.

# Reflection and transmission of waves.

Earlier we examined how waves traveling down a slinky can be reflected or transmitted when passing from one material to another material.  What happens depends on “boundary conditions,” and is affected by the speed of the wave in both materials.  Similarly, whether an electromagnetic wave is reflected or transmitted depends on the physical properties.  This is also a frequency dependent phenomena.  Certain wavelengths of light will be reflected, transmitted, or even absorbed.  This depends on the resonant frequencies of the material, both on the atomic level and the larger molecular levels.

# Index of Refraction

As an electromagnetic wave passes through a material, it will interact with the charges in that material.  This is a frequency dependent phenomena.

We define the index of refraction, n, as the proportion to which light slows down.

n = c/v

where n is the index of refraction, c is the speed of light in a vacuum, and v is the speed of light in the material

A common example is how glass interacts with electromagnetic waves.  The electrons in glass tend to absorb UV light.  The structure of glass tends to be excited by lower energy infrared light.   One can think of the molecules of visible light as being temporarily absorbed for a microsecond and being remitted.

# Opacity

It is an oversimplification to say a material is opaque, rather we need to discuss the opacity of a material (which depends on wavelength).  As light passes through a substance, a certain percentage of that light will be absorbed, and converted into thermal energy.  The amount of light that is absorbed is actually an exponential function of the depth to which the light penetrates.

We can define the optical depth, t, as the depth after which about 37% of the light is absorbed.  The number 37% is 1/e or 1/(2.71) which is Euler’s number.  This optical depth or  opacity can be related to the electromagnetic properties of a substance as it is actually an imaginary component of the index of refraction.  Again, the optical depth is a wavelength dependent phenomena, and thus is different for various materials. If we define the original intensity as , and I as the Intensity, then after one optical depth, 37% of the light is absorbed.  After a second thickness of optical depth, another 37% of the light will be absorbed.

An object which is red absorbs most colors of light, but reflects red light.  Glass is transparent to visible light, but absorbs a wide range of UV and IR light.  Pure silicon wafers are transparent to infrared light but are “opaque” or have a high optical density in the visible spectrum.

# Inverse Square Law and Intensity of Light

We define the intensity of light as I as

I = P/A

where P is power, and A is area.   So Intensity is Power/Area or watts/meter squared.

Due to the inverse square law, as light is spread out over the surface area of a three dimensional sphere its intensity decreases.

This could easily be measured using a Vernier Optical Sensor on a meter stick optical bench just for distance. You could do a graph of lux as a function of distance.

# Color and the Rainbow

Our friend Ug the Caveman discovered the colors of the rainbow and that white light can be broken up into these colors. Even before Newton’s time, philosophers were using prisms of glass to separate the colors of white light.   Newton, as he wrote in Optiks, discovered that he could take the colors of the rainbow and recombine them into white light. Interestingly, when William Herschel (in 1800) was measuring the temperature of light broken up by a prism, he discovered infrared light.

Despite the fine work of Ug the caveman, our modern sequence ROYGBIV was developed by Newton because he liked 7, which he believed had mystical powers.

In modern physics, we do not consider Indigo a color, and thus the colors of the rainbow are ROYGBV

# Scattering

You have probably observed how beam of light scatters from dust in the air as in passes through your dark living room early in the morning. We can see the same thing is we look at a laser beam or light show at a rock concert.  Even a laser in a classroom scattered off of chalk dust or in a James Bond movie can be exciting.  The scattering of light depends on the size of the dust particles, and thus is a wavelength dependent phenomena.

On the moon, the sky is actually black because there is no atmosphere for light to scatter off of.

Shorter wavelengths scatter easily, so our sky appears blue because of the light scattering off of molecules in the atmosphere.   However, when the sun is low on the horizon, all of the violet, blue, and green light has scattered out, leaving the oranges and reds to penetrate.  Thus, we see red sunsets.