# Optics

## Wavelength, Frequency, And The Speed Of Light

The relationship between the frequency (the number of wave crests that pass by a certain point in a given amount of time) and wavelength for electromagnetic waves is defined by the formula, c = λ f, where c is the speed of light, λ the wavelength in meters, and f equals the frequency in cycles per second. For example, the highest energy wavelength detectable by the human eye is generally determined to be 3.80 x 10-7 m. Rewriting the formula c = λ f as f = c / λ yields (3.00 x 108 m/s / 3.80 x 10-7 m) = 7.9 x 1014 Hz for a frequency of the wave.

The inverse relationship between wavelength and frequency means that as wavelengths increase, frequency decreases. Because the frequency of a photon or electromagnetic wave is directly proportional to the energy of the photon or wave,the higher the frequency of the photon or wave, the greater the energy state of the photon or wave. For this reason, within the visible spectrum, shorter wavelength blue light is more energetic than longer wavelength red light (i.e., photons and em waves with frequencies and wavelengths in the red portion of the spectrum).

Newton was the first scientist to study color. He passed sunlight through a prism and found that it could be separated into beams of light of different colors. He showed that visible light actually consists of red, orange, yellow, green, blue, and violet light. Each of these colors corresponds to a particular frequency and wavelength of light. Newton passed the individual color bands produced by the prism through a second prism. This second prism re-combined the individual bands and the light exited the prism as white light. This showed that white light is actually the combination of all of the colors of the spectrum.

The color of an object is due to the frequencies (and corresponding wavelengths) of light absorbed by the object. Most objects absorb the majority of the frequencies of light. Any frequencies that are not absorbed by the object are reflected, giving the object a particular color. If an object absorbs all light except the frequencies found in the red region of the spectrum, the object appears red. Red light is reflected off of the object. White is actually not a color, but a combination of all colors, occurring when all frequencies of light are reflected. Likewise, black is actually the absence of reflected light, occurring when all frequencies of light are absorbed.

Light waves exhibit constructively and destructive interference patterns. Constructive interference occurs when two or more light waves meet in phase (e.g., wave crests meeting wave crests) and usually results in a more intense or bright resulting light. When the light waves meet out of phase (e.g., when the wave crests of one wave cancel the wave troughs of another wave), destructive interference takes place and light intensity is reduced or the light is negated.

The concept of interference is important for understanding the phenomena of diffraction. Young's double-slit interference experiment is a classic explanation for diffraction, which is the bending of light as it passes around an object. Young made two small slits relatively close to each other on a dark board. When he shined a light through the slits and observed the light on a screen, he noticed that the light did not pass directly though in two straight lines. Instead, there was a pattern of alternating bright and dark bands of light. This resulted from the light waves fanning out-diffracting-as they passed through the barrier slits, much like water ripples when it passes from a small opening into a larger body of water. Because light waves were passing through two slits, two fans were created that overlapped at certain points. Some of these points experienced destructive interference, while others were constructive, thus leading to the alternating bands of light. The dark bands occurred when light waves canceled each other out.