# The Wave Nature of Light

The fundamental question of the nature of light: Does light travel as particles that emanate from a source and move in a straight line (except when they are bent by a force such as gravity), or is light a wave that spreads out from the source? The answer is, yes! We will find in subsequent studies, both in optics and in modern Physics, that light has the nature of both a particle and a wave. Let's start with a little history to get into the theory.

Sir Isaac Newton believed in a corpuscular, or particle theory of light, even though at times he observed phenomena that would support a wave theory. But I don't think Newton ever really made the intellectual leap that light behaves as a wave. The Dutch physicist, Christiaan Huygens, theorized that light was made of waves and not out of particles. Huygens and Newton were contemporaries and often at odds with each other, and the history of the interaction between these two is fascinating. (For more on this, try: http://www.studyphysics.ca/newnotes/20/unit04_light/chp1719_light/lesson57.htm or do your own search!) Let's go with Huygens' Principle. Take a moment to follow this link, http://www.mathpages.com/home/kmath242/kmath242.htm, which does a very nice job of explaining Huygens' Principle in terms of the propagation of little wave packets. Note also that it took some additional work by others, notably Augustin Fresnel, to complete the theory to a usable form. So let's establish, in this lesson, some basics.

Light is an electromagnetic wave (a wave consisting of alternating electric and magnetic fields perpendicular to
each other), and is a part of the electromagnetic (EM) spectrum. EM waves travel through a vacuum at the speed of 3.00 x 108 m/s. We call this value c, the speed of light. We relate speed (c), frequency (f) and wavelength (
l) by the formula

c = fl

But visible light is only one kind of electromagnetic wave. Take a look at the chart below - we see that visible light falls into a very narrow band of wavelengths from 400 nm to 750 nm.

Newton had observed the dispersion of white light into the color spectrum when it passed through a prism. Long wavelength light (750 nanometers) is the red end. At the short end (400 nm) is violet light. We see spectacular examples of dispersion when we look at rainbows. The spectrum of colors within visible light are

750nm                                                                  400nm

RED ORANGE YELLOW GREEN BLUE VIOLET

4x1014 Hz                                                            7.5x1014 Hz

Here is where we get into a little trouble. In kindergarten, we learned that the primary colors were red, yellow, and blue. In physics, we talk about primary additive and primary subtractive colors. What does this mean? Well, it depends upon whether we are talking about light or about pigments.  When talking about light, we talk about colors adding. All of the colors together make up white light, and there are three primary colors that make up all colors: red, blue, and green. If you look closely at the screen on your computer or TV, you will see that it is made up of tiny red, green, and blue dots that make all the other colors. Or, open a drawing program on your computer and go to the utility that allows you to change colors. The newest software will allow you to select a specific shade by mixing various combinations of red, green, and blue.

Red and Green combine to make Cyan, Blue and Red combine to make Magenta, and Red and Green combine to make Yellow. Yellow, Cyan, and Magenta are the three secondary additive colors. Additionally, when two primary colors add to make a secondary color, that color is considered to be the complimentary color to the third primary color. That is to say, when added to the third color, it will make white.

When white light reflects on an object, the color of the object is the light we see reflected from the object. The other colors are absorbed. Pigments are subtractive colors. They filter out light. The subtractive primary colors are red, blue, and yellow. Red and yellow mix to produce orange, blue and yellow mix to produce green, and red and blue mix to produce violet. All of the pigments mixed produce black.

Once we have stated that light is a wave, then we are going to have to acknowledge that light behaves like a wave. In other words, light is going to exhibit the same characteristics of reflection, refraction, and diffraction that any other wave does. Let's review:

Reflection is the bending back of a wave as it bounces against the surface of another object or medium. Recall our earlier lessons on the Law of Reflection, where the incident angle is equal to the reflected angle. We'll make use of this property when we start to talk about mirrors.

Refraction is the bending of the direction of a wave as it passes from one medium to another and changes speed. We will use Snell's Law to determine the relation (angle) between the incident wave and the refracted wave (or more precisely, the relation of those two waves to the perpendicular of the surface of the media interface. Snell's Law states:

n1sinq1=n2sinq2

where n1 and n2 represent the indices of refraction for the two materials and q1 and q 2 represent the incident and refracted angles. Again, more on this later.

Finally, light exhibits the characteristics of diffraction, or the bending of a wave as it passes around or through an object. For this, we need to spend some time with Thomas Young and our lessons on diffraction.

The NTNU Virtual Physics Laboratory provides several excellent applets that demonstrate principles of Physics. Click Here to play with an applet that shows how light is reflected and refracted in a prism. Additionally, check out these links to see how colors are mixed.

http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=56

http://www.yorku.ca/eye/colormix.htm