The Wave Nature of Light

The speed of the wave, the distance traveled per unit time (in units of meters per second), is the product of its frequency (cycles per second) and its wavelength (meters per cycle)  

In a vacuum, all types of electromagnetic radiation travel at 2.99792458X10 m/s (3.00x10 m/s to three significant figures), which is a physical constant called the speed of light (c)  

As Equation 7.1 shows, the product of v and X. is a constant. Thus, the individual terms have a reciprocal relationship to each other radiation with a high frequency has a short wavelength, and vice versa. 

Gamma i ray 1 X-ray 1 Ultra- 1 violet 1 0) co 1 1 Infrared i 1 1 Microwave Radio frequency 

For the radio signal Combining steps to calculate the frequency. 

A wire loop containing a sample ofa metal compound is placed in a flame.Leff to right flames of lithium (red),sodium (yellow), strontium (red),and calcium (orange). 

Each element, in fact, has a characteristic line spectrum because of the emission of light from atoms in the hot gas. The spectra can be used to identify elements. How is it that each atom emits particular colors of light What does a line spectrum tell us about the structure of an atom If you know something about the structures of atoms, can you explain the formation of ions and molecules We will answer these questions in this and the next few chapters. 

In Chapter 2 we looked at the basic structure of atoms and we introduced the concept of a chemical bond. To understand the formation of a chemical bond between atoms, however, you need to know something about the electronic structure of atoms. The present theory of the electronic structure of atoms started with an explanation of the colored light produced in hot gases and flames. Before we can discuss this, we need to describe the nature of light. 

If you drop a stone into one end of a quiet pond, the impact of the stone with the water starts an up-and-down motion of the water surface. This up-and-down motion travels outward from where the stone hit it is a familiar example of a wave. A wave is a continuously repeating change or oscillation in matter or in a physical field. Light is also a wave. It consists of oscillations in electric and magnetic fields that can travel through space. Visible light, x rays, and radio waves are all forms of electromagnetic radiation. 

You characterize a wave by its wavelength and frequency. The wavelength, denoted by the Greek letter A (lambda), is the distance between any two adjacent identical points ofa wave. Thus, the wavelength is the distance between two adjacent peaks 

There are many types of electromagnetic radiation in addition to visible light. These different types—radio waves that carry music to our radios, infrared radiation (heat) from a glowing fireplace. X-rays—may seem very different from one another, but they all share certain fundamental characteristics. 

A cross section of a water wave ( FIGURE 6.2) shows that it is periodic, which means that the pattern of peaks and troughs repeats itself at regular intervals. The distance between two adjacent peaks (or between two adjacent troughs) is called the wavelength. The number of complete wavelengths, or c) cles, that pass a given point each second is the frequency of the wave. 

Just as with water waves, we can assign a frequency and wavelength to electromagnetic waves, as illustrated in FIGURE 6.3. These and all other wave characteristics of electromagnetic radiation are due to the periodic oscillations in the intensities of the electric and magnetic fields associated with the radiation. 

TABLE 6.1 Common Wavelength Units for Electromagnetic Radiation  

How do the wavelength and frequency of an X-ray compare with those of the red light from a neon sign  

Frequency is expressed in cycles per second, a unit also called a hertz (Hz). Because it is understood that cycles are involved, the units of frequency are normally given simply as per second, which is denoted by s or /s. For example, a frequency of 698 megahertz (MHz), a typical frequency for a cellular telephone, could be written as 698 MHz, 698,000,000 Hz, 698,000,000 s or 698,000,000/s. 

Our bodies are penetrated by X rays but not by visible light. Is this because X rays travel faster than visible light  

Is the wavelength of a microwave longer or shorter than the wavelength of visible light By how many orders of magnitude do the two waves differ in wavelength  

Two electromagnetic waves are represented in the margin, (a) Which wave has the higher frequency (b) If one wave represents visible light and the other represents infrared radiation, which wave is which  

Radiation Electromagnetic radiation can be described as a wave composed of oscillating electric and magnetic fields. The fields oscillate in perpendicular planes. 

Wavelength and amplitude are independent properties. The wavelength of light determines its color. The amplitude, or intensity, determines its brightness. 

Like all waves, Ught is also characterized by its frequency (v), the number of cycles (or wave crests) that pass through a stationary point in a given period of time. The units of frequency are cycles per second (cycle/s) or simply s. An equivalent unit of frequency is the hertz (Hz), defined as 1 cycle/s. The frequency of a wave is directly proportional to the speed at which the wave is traveling—the faster the wave, the more crests will pass a fixed location per unit time. Frequency is also inversely proportional to the wavelength (A)—the farther apart the crests, the fewer that will pass a fixed location per unit time. For light, therefore, we can write the equation  

Calculate the wavelength (in nm) of the red light emitted by a barcode scanner that has a frequency of 4.62 X 10 s  

You are given the frequency of the light and asked to find its wavelength. Use Equation 7.1, which relates frequency to wavelength. You can convert the wavelength from meters to nanometers by using the conversion factor between the two (1 nm = 10 m). 

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The Schrodinger equation cannot be subjected to firm proof but was put forward as a postulate, based on the analogy between the wave nature of light and of the electron. The equation was justified by the remarkable successes of its applications. 

This section reviews the evidence for the wave nature of light and of X-rays, and then puts these two forms of radiation into the context of electromagnetic radiation in general. 

Point spread function (PSF) If a tiny population of 100 nm fluorescent beads sandwiched between a coverslip and a microscope slide are examined at high resolution (i.e. at 100x objective magnification, 1.4 NA. and in a correctly matched refractive index of oil), it can actually show a tiny set of rings in the horizontal (XY) view (also called an airy disk (see Fig. below). This airy disk cannot be avoided due to diffraction and the wave nature of light. If a specimen is optically sectioned and projected in a vertical (XZ) view (see Fig. xx), a set of concentric rings will flare from the center. When a three-dimensional image of this specimen is collected, a complete point spread function is said to be recorded for each bead. The (PSF)... 

If one considers the wave nature of light, one may think that the photon size is roughly equal to its wavelength (say 500 nm) however, when the photon is absorbed by an atom, it "disappears" within a body of radius 0.5 nm this is a manifestation of the intricacies of the wave-particle duality, which are discussed in Section 3.39. 

The ray model of light is of limited usefulness. If we are to understand the fundamental processes involved in the formation of an image by a lens, we must consider the wave nature of light. The simplest form of the wave theory of light is based on a geometrical construction known as Huygens principle, which is usually stated as follows ... 

Early hints of the wave nature of light included the seventeenth-century discovery of diffraction by Hooke and other manifestations of interference. It was obvious that dropping a rock into a pond created waves, and Boyle showed that air was necessary for the transmission of sound waves. Thus, it appeared that there had to be a medium for transmitting light waves and it was thought to be a kind... 

By 1900 the success of Maxwell s electromagnetic theory had firmly established the wave nature of light. One puzzle that remained was the distribution of wavelengths in a cavity, or blackbody the observed distribution had eluded explanation on accepted principles. In 1900 Max Planck calculated the distribution, within the experimental error, in a completely mysterious way. Planck s work proved ultimately to be the key to the entire problem of atomic structure yet at first glance it seems to have little bearing on that problem. 

Owing to the wave nature of light, diffraction at the particles aperture must be accounted for and added to the geometrical part described above. 

By the end of the 19th century, the wave nature of light and its diffraction was understood. A strip of transparent film, uniformly scored... 

Young, Thomas (1773-1829) was an English physician physicist. He could read fluently by age two and presented his first paper to the Royal Society at the young age of 20. By 1801 he was a professor at the Royal Institution in London. He was probably best known for his classic double slit experiment, which demonstrated the wave nature of light. 

In 1905, the accuracy of experimental data was too poor to conlirmEinstein s theory as the only one which could account for the experimental results. Besides, the wave nature of light was supported by thousands of crystal clear experiments. Einstein s argument was so breathtaking (... particles ), that Robert Millikan decided to disprove experimentally Einstein s hypothesis. However, after ten years of investigations, Millikan acknowledged that he is forced to support Einstein s explanation, however absurd it nmy looK (Rev. Modem Phys., 21, 343 (1949)). This conversion of a skeptic inclined the Nobel Committee to award Einstein the Nobel Prize in 1923 for his work on the elementary charge of electricity and on the photo-electric effecf . 

The fundamental ideas of interferometry are treated, at various levels of mathematical rigor, in standard optical texts (Hecht 2003 Bom et al. 1999). Conceptually, interferometry is most easily understood in terms of the wave nature of light, an electromagnetic wave (following Maxwell s equations) with a phase that changes by 2n radians every wavelength. A wavefront is a surface of constant phase (e.g., the peak, valley, or any other phase in Fig. 1). 

THE WAVE NATURE OF LIGHT We learn that light (radiant energy, or electromagnetic radiation) has wave-like properties and is characterized by wavelength, frequency, and speed. 

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