Optics Lessons: Part 6 - Diffraction and Refraction

Diffraction

Imagine a child trying to build a wall to prevent the sea from destroying his beloved sandcastle. Unfortunately, he forgets to fill in a segment of his citadel. As the wave strikes the wall, the water does not enter through as a straight stream, but spreads out, submerging the child's entire creation. This analogy can be applied to light.

When one pictures a ray of light, one sees a straight, fast-moving line that travels like a laser. Young performed his double-slit experiment expecting just that. He believed that the light he shined through the slits would travel straight through and reflect as segments upon the screen behind the slits. When he noticed instead was that the light spread out, like a ripple when a stone is cast into water. This effect can also be seen when shining a flashlight, where it forms a cone of slight in darkness. Another term for this deviation of light is diffraction.

In general, the larger the size of the wavelength of the light (for example, red over violet), the greater the diffraction. This makes sense: a large stone would create a greater ripple than a tiny pebble. The same effect occurs for sound, at a more noticeable degree. Sometimes, the slit given is too great for the light waves. In this case, destructive interference occurs, where the opposite occurs and light does not diffract as much.

Two general rules of diffraction are as follows:

a) The narrower the slit through which the wave must pass, the greater the diffraction.
b) The larger the wavelength of the wave, the greater the diffraction.

Diffraction Gratings

Why does a CD look the way it does? The answer lies in diffraction gratings. As light enters through slits and diffracts, it forms fringes. These fringes increase when there are more slits and each individual slit is narrower. A large series of parallel, very thin slits forms something called a diffraction grating. When light passes through it, very interesting properties are formed.

When light passes directly through the slits, it is called transmission grating. However, light is more commonly reflected off these grooves, a procedure known as reflection grating. CDs receive their iridescent nature through such grating. The process is fairly direct, or at least the basics of it. The slits are made on a thin sheet of metal, most commonly aluminum, by lasers, which expose a layer of photo-sensitive material that the light would reflect off of. Diffraction gratings can also be made by an engine-powered diamond stylus.

The use of diffraction gratings has overcome the use of prisms in the study of the spectrum, or spectroscopy. Although both produce the same effects capable of being studied, the use of diffraction gratings is easier and has less chance for error. Wiith prisms a scientist must take into account the nature of the material of the prism.

X-Ray Diffraction

Diffraction can be used to determine any electromagnetic wave's wavelength, through using diffraction gratings. In the late 19th century, the wavelength of an X-ray was experimentally theorized but could not be proven because of the fact that a diffraction grating with a size fitting for the X-ray's wavelength could not be constructed. In 1913, German physicist Max von Laue suggested using molecules as diffraction gratings. He proposed using a crystal such as sodium chloride, whose regular atom pattern seemed to suggets a possible suitable grating. They tested out this new proposition and diffraction patterns were indeed observed.

An equation that is used to calculate wavelength with regards to characteristics of the crystal used, more specifically the spacing between the atoms within the crystal, was derived by W.L. Bragg and is known as Bragg's Law.

2dsin = n

It was thus that the wavelength of X-rays was proven. Today, X-rays are used not only to explore crystals more through diffraction, but also to begin probing into complex biological molecules such as proteins and DNA. Their short wavelengths make X-rays a very ideal diffraction probe for such investigations.

Refraction

To explain refraction, let’s first take the simple example of light traveling through air and hitting a piece of glass. The piece of glass will reflect part of the light and transmit a part of it. But the direction the light is transmitted is different from the direction it came into the glass. In this way, the light is bent or refracted.

But to give a more precise definition, refraction is the alteration of the direction of a wave where it travels to a different surrounding, or medium.

Snell’s Law

Let’s go into Huygen’s principle for more insight. It says that every point on a propagating wave front acts as a root for secondary waves and that if this advancing wave has a certain frequency and is transmitted at certain speed through the medium, then the secondary waves will have the same frequency and speed.

But when the wave enters a denser medium, then the speed is reduced. With this change of speed, there is a change of wavelength but no change in frequency (for particles in the new medium are powered by wave disturbance from the original medium), which can be seen by applying the equationto the right. Also, the change of speed results in a change of direction of the transmitted wave in comparison to the original, or incident wave front.

This change of direction is characterized by the angle of refraction, which can be found using Snell’s law.

Snell’s law states:

   where is speed.

Index of Refraction:

To show how much a certain medium slows down the speed of light, we use the index of refraction, which is calculated using the following formula:

where is the speed of light in a vacuum and is the speed of light in a certain medium

So, if the value of n is higher, the more the medium hinders the speed of light. The closer n is to one, the closer it is to reaching the maximum speed of light, which is c, the speed of it through a vacuum.

We can find in terms of wavelength as well.

Since    

When is divided by , the frequency variables will cancel each other out since they are the same. (Remember, when light travels into another medium, its frequency remains the same.) Wavelength (), however, does change, so we are left with:

We can find another form of Snell’s law using the index of refraction () by substituting the speed components for /, and by canceling out the , which is a constant, we the equation to the right.

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