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EMR

Electromagnetic Radiation (EMR) is radiation in the form of waves. These waves are divided into little packets called photons. Electromagnetic Radiation gets its name from the fact that it is made up of electrical and magnetic fields.

The electromagnetic spectrum consists of radio, microwaves, infrared radiation, visible light, ultaviolet, x-rays and gamma radiation. Radio waves have the longest wavelengths, lowest frequencies, and the least energy. Gamma rays have the shortest wavelengths, the highest frequencies and the highest energy.

Visible light is approximately halfway through the EMR spectrum, with UV (ultraviolet) and x-rays with higher frequencies than visible light. Infrared and microwaves have lower frequencies than visible light.

EMR spectrum
Properties of EMR
Speed

All EMR travels at the speed of light in a vacuum. When EMR enters a medium, like glass, air, and water, it slows down proportionally to the medium's index of refraction: $n = c/{v}$, where c is the speed of light in vacuum, $3.0 x 10^8 m/s$, and $v$ is the speed of light in the medium.

Wave behaviour

EMR behaves as waves. EMR waves experience reflection, refraction, and diffraction just like light.

No medium necessary

EMR does not need a medium to propagate. The Sun sends us light and heat across space, even though space is nearly completely empty. We can send and receive radio signals from the surface of the Moon, and communicate with satellites with microwaves.

EMR Waves

  • Radio
  • Radio waves have very long wavelengths, and low frequencies.

    Radio is used for communication and radar.

    Radio telescopes can detect very distant objects in the unverse due to the radio signals they emit.

  • Microwaves
  • Microwaves have shorter wavelengths than radio.

    Microwaves are also used for communication, such as to satellites in orbit.

    Microwaves can excite water molecules, so are useful for heating food quickly.

  • Infrared
  • Infrared radiation carries heat. It is infrared that we sense when our skin feels that something is hot.

    Infrared is a broad bandwidth, and can be used as an alternative to visible light for things like remote control devices.

    Using infrared glasses or cameras, people can see in the dark, reading an object of person's 'heat signature'.

  • Visible light
  • Eyes detect a narrow band of EMR. An inverted image is formed on the retina, which stimulates nerve cells according to the frequency and intensity of the light. This is assembled into a message, and sent to the brain by the optic nerve.

    The different frequencies of visible light form the colours we perceive. When these are superimposed, we see 'white light'.

    White light is absorbed by a material. We see a colour when the material re-radiates only that colour frequency, and absorbs the others.

  • Ultraviolet
  • UV is a dangerous wavelength of EMR for living cells. Its high-energy radiation can cause damage to DNA and cause cancer.

    The statosphere is a layer of the atmosphere above the troposphere, which contains ozone. The ozone layer forms a shield against the Sun's dangerous UV, and protects all life from its radiation. Until the 1980s, industries used chemicals (such as CFCs) which were destroying the ozone layer. Luckily, CFCs are banned in most countries.

    A small amount of UV still reaches the Earth's surface. It is what causes our skin to tan, which is a protection against intense sunlight.

    UV light is used to kill bacteria on the surfaces of medical equipment, as well as to see writing and codes which are invisible to the naked eye.

  • X-rays
  • X-rays have short wavelengths and high frequencies. This allows them to penetrate skin tissue, so can be used to 'photograph' bones and hard tissue.

    X-rays are high energy and are dangerous to living cells. That is why x-rays are done very carefully and as little as possible. In particular, delicate parts of the body, especially the reproductive organs, must never be exposed to x-rays.

    X-rays from space (cosmic rays) are studied by astronomers, because they bring information about distance objects, like supernovae and black holes.

    Meanwhile, back on Earth, x-rays are used to examine the structures of crystals, as well as for looking inside containers for security, such as at airport check-in.

  • Gamma rays
  • Gamma rays have very short wavelengths and very high frequencies, and pack a lot of energy. They are extremely dangerous to living tissue.

    Nuclear bombs release gamma radiation (γ-rays) as part of the decay of uranium atoms.

    Astronomers study gamma ray bursts to understand distant events, like supernovae explosions.

    Gamma rays are absorbed by the atmosphere, and do not reach the ground.

    Gamma rays are used to look inside metallic objects, when x-rays cannot penetrate.

    Irradiation is the use of high-energy radiation, such as gamma, to kill bacteria in food.

    Radio and Communications

    Communication involves a source, a carrier and a receiver. For example, a person talking is the source of sound waves, the air is the carrier, in this case compression or longitudinal waves, and a listener is the receiver, modifying the incoming pressure waves on his inner ear to an electrical signal, which his brain interprets as sound information.

    Modulation

    To include information in a signal, there must be some variation which can be interpreted by the receiver. This is known as modulation.

    Morse code modifies the length of the electrical signal to send sequences of long and short pulses. computer modems do something similar with binary code, sending a stream of zeroes and ones, or bits, which can be interpreted as characters (8 bits make a byte).

    Carrier Wave

    The carrier wave does what its name suggests: it is the means by which information is transmitted. It can be an electromagnetic wave, like radio or microwave, or an alternating current down an electrical wire.

    Signal Wave

    The signal wave contains the information to be communicated. This may take the form of changing frequencies for audio information, or pixel colouring for video, or any other form of data.

    Power Spectrum

    A plot of the power of a signal against its frequency. The power of a signal is the amplitude squared.

    A harmonic wave has the form y = sin(2πft) or y = cos(2πft), where y is the displacement (or voltage), f is the frequency, and t the time.

    AM: amplitude modulation

    The amplitude of the carrier wave is modulated by a signal wave, causing instantaneous displacement.

    $$y_s = A_ssin(2πf_st)$$ $$y_c = A_csin(2πf_ct)$$

    where $y_s$ is a sinusoidal signal wave, and $y_c$ is a sinusoidal carrier wave.

    $$y_M = [A_c + A_ssin(2πf_st)]sin(2πf_ct)$$

    where $y_M$ is the modulated carrier wave.

    Now the clever bit: the amplitude modulated carrier wave formula may be rewritten as:

    $$y_M = A_csin(2πf_ct) + 1/2A_s[cos(2π(f_c - f_s)t) - cos(2π(f_c + f_s)t)]$$

    where $A_csin(2πf_ct)$ is the original carrier wave, and there are two other components waves to the signal. These waves have an amplitude of $1/2A_s$, and respective frequencies of $(f_c - f_s)$, and $(f_c + f_s)$.

    These frequencies, $(f_c - f_s)$ and $(f_c + f_s)$, are the lower and upper side frequencies.

    The difference between the lower and upper side frequencies is known as the bandwidth:

    $$Δf = (f_c + f_s) - (f_c - f_s) = 2f_s$$

    If the information signal wave carries a range of frequencies (which frankly it must if it is to be carrying information), then the bandwidth can be defined in terms of the highest frequency in the range, $f_H$:

    $$Δf = = 2f_H$$

    In short, in amplitude modulation, the bandwidth is equal to two times the highest signal wave frequency.

    FM: frequency modulation

    In this form of radio transmission, the frequency of the carrier wave is modulated by the instantaneous displacement of the signal wave. The amplitude stays constant.

    $$β = {Δf}/{f_I}$$

    where β is the modulation index, and Δf is the greatest deviation of the modulated carrier's frequency f from the unmodulated carrier frequency $f_c$, and $f_I$ is the highest frequency of the information signal wave.

    The FM bandwidth is: ≈ $2(Δf + f_I)$

    Black Body Radiation

    Wien Displacement Law: the wavelength $λ_0$ and surface temperature $T$ of a black-body is related by: $λ_0T = 2.90 × 10^{-3}$ K m.

    e.g. Use the Wien displacement law to calculate the wavelength of the cosmic background radiation (T = 2.7 K).

    $λT = 2.90 × 10^{-3}$ K m

    $λ = {2.90 × 10^{-3}}/{2.7} = 1.07 × 10^{-3}$ m.

    1.07 mm is just within the microwave bandwidth (1-300 mm).

    Content © Andrew Bone. All rights reserved. Created : March 5, 2014 Last updated :April 16, 2016

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