Electromagnetic Spectrum The electromagnetic radiation covers a vast spectrum of frequencies and wavelengths. This includes the very energetic gamma-rays radiation with a wavelength range from 0.005 1.4 A o to radiowaves in the wavelength range up to meters (exceedingly low energy). However, the region of interest to us in this course is rather a very limited range from 180-780 nm. This limited range covers both ultraviolet and visible radiation. 1
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Mathematical Description of a Wave A sine wave can be mathematically represented by the equation: Y = A sin (ωt + φ) Where y is the electric vector at time t, A is the amplitude of the wave, ω is the angular frequency, and φ is the phase angle of the wave. The angular frequency is related to the frequency of radiation by the relation: ω= 2πν This makes the wave equation become: Y = A sin (2πν πνt + φ) 4
Superposition of Waves When two or more waves traverse the same space, a resultant wave, which is the sum of all waves, results. Where the resultant wave can be written as: Y = A 1 sin (2πν t+ φ ) + A 2 sin (2πν 2 t + φ 2 ) +... + A n sin (2πν n t + φ n ) 5
Constructive Interference The resultant wave would have a greater amplitude than any of the individual waves which, in this case, is referred to as constructive interference. The opposite could also take place where lower amplitude is obtained. 6
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The decrease in the intensity is a result of what is called a destructive interference. When the multiple waves have the same wavelength, maximum constructive interference takes place when φ 1 -φ 2 is equal to zero, 360 deg or multiple of 360 deg. Also maximum destructive interference is observed when φ 1 φ 2 is equal to 180 deg, or 180 deg + multiples of 360 deg. 8
The blue and yellow shaded waves interfere to give the brown shaded wave of less amplitude, a consequence of destructive interference of the two waves. 9
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The Period of a Beat When two waves of the same amplitude but different frequencies interfere, the resulting wave exhibit a periodicity and is referred to as beat (see figure below). The period of the beat can be defined as the reciprocal of the frequency difference between the two waves: P b = 1/( ν) 12
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Fourier Transform The resultant wave of multiple waves of different amplitudes and frequencies can be resolved back to its component waves by a mathematical process called Fourier transformation. This mathematical technique is the basis of several instrumental techniques like Fourier transform infrared, Fourier transform nuclear magnetic resonance, etc. 15
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Diffraction of Radiation Diffraction is a characteristic of electromagnetic radiation. Diffraction is a process by which a parallel beam of radiation is bent when passing through a narrow opening or a pinhole. Therefore, diffraction of radiation demonstrate its wave nature. Diffraction is not clear when the opening is large. 17
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Coherence of Radiation Two beams of radiation are said to be coherent if they satisfy the following conditions: 1. Both have the same frequency and wavelength or set of frequencies and wavelength. 2. Both have the same phase relationships with time. 3. Both are continuous. 20
Transmission of Radiation As mentioned before, the velocity of radiation in any medium is less than that in vacuum. The velocity of radiation is therefore a function of the refractive index of the medium in which it propagates. The velocity of radiation in any medium can be related to the speed of radiation in vacuum ( c ) by the relation: n i = c/v i Where, v i is the velocity of radiation in the medium i, and n i is the refractive index of medium i. 21
The decrease in radiation velocity upon propagation in transparent media is attributed to periodic polarization of atomic and molecular species making up the medium. By polarization we simply mean temporary induced deformation of the electronic clouds of atoms and molecules as a result of interaction with electric field of the waves. 22