Electromagnetic Radiation Cont.…

Lecture 3

Dispersion of Radiation

If we look carefully at the equation ni = c/vi and remember that the speed of radiation in vacuum is constant and independent on wavelength, and since the velocity of radiation in medium i is dependent on wavelength, therefore the refractive index of a substance should be dependent on wavelength. The variation of the refractive index with wavelength is called dispersion.

Refraction of Radiation

When a beam of radiation hits the interface between two transparent media that have different refractive indices, the beam suffers an abrupt change in direction or refraction. The degree of refraction is quantitatively shown by Snell's law where:

n1 sin 1 = n2 sin 2

Reflection of Radiation

An incident beam hitting transparent surfaces (at right angles) with a different refractive index will suffer successive reflections. This means that the intensity of emerging beam will always be less than the incident beam.

Scattering of Radiation

When a beam of radiation hits a particle, molecule, or aggregates of particles or molecules, scattering occurs. The intensity of scattered radiation is directly proportional to particle size, concentration, the square of the polarizability of the molecule, as well as the fourth power of the frequency of incident beam. Scattered radiation can be divided into three categories:

1. Rayleigh Scattering

Rayleigh Scattering is scattering of electromagnetic radiation by particles much smaller than the wavelength of the radiation. Rayleigh Scattering usually occurs in gasses. The scattering of solar radiation by earth’s atmosphere is one of the main reasons why the sky is blue. Rayleigh Scattering has a strong dependence on wavelength having a -4 relationship.

2. Mie scatteringMie scattering is caused

by dust, smoke, water droplets, and other particles in the lower portion of the atmosphere. It occurs when the particles causing the scattering are close in dimension to the wavelengths of radiation in contact with them. Mie scattering is responsible for the white appearance of the clouds.

3. Tyndall Effect (nonspecific scattering)

It occurs in the lower portion of the atmosphere when the particles are much larger than the incident radiation. This type of scattering is not wavelength dependent and is the primary cause of haze.

Quantum Mechanical Description ofRadiation

All the previously mentioned properties of radiation agrees with the wave model of radiation. However, some processes of interest to us, especially in this course, can not be explained using the mentioned wave properties of radiation. An example would be the absorption and emission of radiation by atomic and molecular species. Also, other phenomena could not be explained by the wave model and necessitated the suggestion that radiation have a particle nature. The familiar experiment by Heinrich Hertz in 1887 is the corner stone of the particle nature of radiation and is called the photoelectric effect.

The Photoelectric Effect

When Millikan used an experimental setup like the one shown below to study the photoelectric effect, he observed that although the voltage difference between the cathode and the anode was insufficient to force a spark between the two electrodes, a spark occurs readily when the surface of the cathode was illuminated with light. Look carefully at the experimental setup:

It is noteworthy to observe the following points:

1. The cathode was connected to the positive terminal of the variable voltage source, where it is more difficult to release electrons from cathode surface.

2. The anode was connected to the negative terminal of the voltage source which makes it more difficult for the electron to collide with the anode for the current to pass.

3. The negative voltage was adjusted at a value insufficient for current to flow. The negative voltage at which the photocurrent is zero is called the stopping voltage.

At these conditions, no current flows through the circuit as no electrons are capable of completing the circuit by transfer from cathode to anode. However, upon illumination of the cathode by radiation of suitable frequency and intensity, an instantaneous flow of current takes place. If we look carefully at this phenomenon and try to explain it using the wave model of radiation, it would be obvious that none of the wave characteristics (reflection, refraction, interference, diffraction, polarization, etc. ) can be responsible for this type of behavior.

What actually happened during illumination is that radiation offered enough energy for electrons to overcome binding energy and thus be released. In addition, radiation offered released electrons enough kinetic energy to transfer to the anode surface and overcome repulsion forces with the negative anode.

If the energy of the incident beam was calculated per surface area of an electron, this energy is infinitesimally small to be able to release electrons rather than giving electrons enough kinetic energy. When this experiment was repeated using different frequencies and cathode coatings the following observations were collected:

Conclusions

1. The photocurrent is directly proportional to the intensity of incident radiation.

2. The magnitude of the stopping voltage depends on both chemical composition of cathode surface and frequency of incident radiation.

3. The magnitude of the stopping voltage is independent on the intensity of incident radiation.