Light: Diffraction, Interference and Young's Experiment

Is light a particle or a wave? The jury has been out on that question for hundreds of years. Physicists have basically come to the agreemeent that light is both a particle and a wave, depending on which experiment you are performing. In this section, we will describe Young's slit experiment, which suggests light is a wave. And waves are just functions, and functions have Fourier Transforms. We'll see a great application of Fourier Transforms in the physical world: the viewing of the Fourier Transform of light for a particular case. Before jumping in, let's discuss light a little bit. Light Light is an electromagnetic wave. This is the same type of wave that the sun heats the earth with, that your microwave warms your food with, and the exact same type of wave that is used by radios, televisions and your personal cell phone to send information. As an electromagnetic wave, light waves have an electric and a magnetic field associated with it. In addition, light waves of all types travel at speed c=300,000 km/s. The frequency f and wavelength (lambda) of light satisfy the following equation: [Equation 1] In addition, we will assume that light behaves as a plane wave. This means that if the light is propagating in the +z-direction, than the E- and H-field will be in the x-y plane. That is, the E-field associated with a plane wave travelling in the +z-direction can be written via the vector: [Equation 2] Equation [2] shows that the E-field is modeled as a vector quantity. The magnitude is given by some constant E_0, and the E-field "points" in the x-direction. The vector is a unit vector in the +x-direction. The complex exponential in Equation [2] represents the phase of the wave. Note that the wave is travelling in the +z-direction, and this is the only spatial dimension that gives rise to phase change. In addition, the E-field is oscillating and a frequency f (hence the time dependence ft). For light, the frequency is very high: 400-800 THz (or 4-8 * 10^14 cycles/second). The only difference between light waves and the waves your cell phone emit is the frequency of the wave (cell phones operate between 800-2100 MHz, or 8-21*10^8 cycles/second). You might question: how good is the plane wave approximation? For light waves, it is fantastic. Electromagnetic waves behave like plane waves when they are many wavelengths from the source, and also the distance from the source is significantly larger than the physical size of the source. Since the wavelength is so small, the first condition is virtually always satisfied. The second condition is true as long as you're not too close to a light source, which is often the case as humans don't like to be right up against their lights. In any event, it is simple to set up a plane wave, and that's what we'll need for our analysis and experiment. What's that? You would like to know more about electromagnetic waves? Feel free to cruise over to antenna-theory.com for more information. In the next section, we'll look at how a plane wave behaves when it hits a small opening in an aperture (a slit).