High Monochromaticity of Laser Light

High Monochromaticity:

A laser beam is highly monochromatic. The monochromaticity of the laser beam is much more than that of any traditional monochromatic source. The line spread of a laser beam is very small in comparison to the light from a traditional source. This difference arises because conventional sources emit wave trains of very short duration and length, whereas, laser emit continuous waves of very long duration. The random spontaneous emission in the laser cavity is one of the mechanisms that determine a laser's ultimate spectral line width. It should be noted that no light source including laser light source, is perfectly monochromatic but a better approximation to the ideal condition may be considered in the case of the laser beam. The spread of light from a normal monochromatic source range over a wavelength of the order of $100 -1000 \overset{\circ}{A}$ while in lasers it is of the order of few angstroms $(\lt 10 \overset{\circ}{A})$ only.

The high spectral purity of laser radıation leads directly to applications in basic scientific research including photochemistry, luminescence excitation spectroscopy absorption, Raman spectroscopy, and also in communication. The degree of non-monochromaticity $\xi$ of light is characterized by the spread in frequency of a line by the line width $\Delta \nu $ and is expressed as:

$\xi=\frac{\Delta \nu}{ \nu_{\circ}}$

where $\nu_{\circ}$ is the central frequency. If $\Delta \nu $ approaches zero the degree of non-monochromaticity tends to zero which is an ideal condition. Absolute monochromaticity $(\Delta \nu =0)$ is not attainable in practice even with laser light. The spreads of two light sources, laser light, and normal light, are shown in the figure above. The degree of non-monochromaticity may also be written in terms of coherence time $(\tau_{C})$ or coherence length $(L_{C})$ as follows:

$\xi=\frac{1}{\tau_{C} \: \nu_{\circ}}$

$\xi=\frac{c}{L_{C} \: \nu_{\circ}}$

This relation shows that the monochromaticity will be large for higher values of coherence time or coherence length. The bandwidth of a laser light from a high-quality He-Ne gas laser is of the order of $500Hz$ $(\Delta \nu =500 Hz)$ corresponding to coherence length of the order of $600 km$ $(\tau_{C} = 2 \times l0^{-3} sec)$.

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Conversion of Galvanometer into a Voltmeter

What is a voltmeter?

A voltmeter is an instrument used to measure potential differences between two points in an electric circuit directly in volts. The instrument measuring the potential difference of the order of millivolt $(mV)$ is called a millivoltmeter. An ideal voltmeter has infinite resistance.

Galvanometer used as voltmeter:

To use the galvanometer as a voltmeter in the circuit, The resistance of the galvanometer should be very high or almost infinite as compared to the other resistance of the circuit. Because the internal resistance of an ideal voltmeter is infinity.

So a high resistance is connected in series with the galvanometer (pivoted-type moving-coil galvanometer).

When a high resistance is connected in series to the galvanometer then the resultant resistance increases as compared to the other resistance of the circuit and it can be easily used as an ammeter and the actual potential difference can be measured through it.

Mathematical Analysis:

Let us consider, $G$ is the resistance of the coil of the Galvanometer, and the $i_{g}$ current, passing through it, produces full-scale deflection. If $V$ is the maximum potential difference that exists between two points $a$ and $b$ in the circuit. On connecting the galvanometer across the points $a$ and $b$, a current $i_{g}$ passes through the galvanometer and a high resistance $R$ is connected in series with galvanometer then

$i_{g}= \frac{V}{G + R}$

$G + R= \frac{V}{i_{g}}$

$R= \left(\frac{V}{i_{g}}\right ) - G$

If the current $i_{g}$ in the coil produces a full-scale deflection, then for the potential difference $V$ between the points $a$ and $b$, there will be a full scale deflection. Thus, on connecting a resistance $R$ of the above valve in series with the galvanometer, the galvanometer will become a voltmeter of range $0$ to $V$ Volt.

Note:

For the voltmeter, a high resistance is connected in series with the galvanometer and so the resistance of a voltmeter is very high compared to that of a galvanometer.

Resistance of voltmeter

$R_{v}=R+G$

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Light Detection And Ranging (LIDAR)

LIDAR (Light Detection And Ranging):

The laser system used for monitoring the environment is known as LIDAR. LIDAR is an acronym that stands for "Light Detection And Ranging".

Before the discovery of the laser, the study of the atmosphere was carried out using an optical beam, the source being the search light. One such experiment was performed by Hulbert in 1937 to study the turbidity of the atmosphere. After the discovery of the laser as a source of an optical highly coherent beam, the study of the atmosphere was revolutionised.

A pulsed laser beam is transmitted into the atmosphere. It is scattered by the particles present in the atmosphere. The scattered radiations are picked up by a receiver. The receiver removes the background sunlight by using different filters. The scattered light gives information regarding the particles present in the atmosphere. Although microwaves can also give these characteristics, the results from laser beams are better in resolution and clarity. The different particles present in the atmosphere in colloidal form can be studied by a LIDAR. A schematic diagram of such a setup is shown in the Figure Below.

A photo detector is used to measure the time dependence of the intensity of the back-scattered laser beam. The time variation can be easily converted into the height (range) from which the laser beam has been back scattered the figure below shows a plot of time dependence of back scattered laser beam, which corresponds to height in the case of clear atmosphere with no aerosols, i.e., back scattering is by pure molecular gases such as $N_{2}$, $O_{2}$, $Ar$ etc. These molecules have dimensions much smaller than optical wavelength.

The scattering is of Rayleigh type. The figure below shows a plot of time dependence of backscattered light in the atmosphere contained aerosols (colloidal particles). These particles have dimensions comparable with the wavelength of laser light. This is Mie scattering. The curve in the figure below has kinks at points A and B between heights h and h. These kinks are due to the fact that between points $A$ and $B$, there are aerosols that are responsible for a greater intensity than that for a clear atmosphere. This implies the presence of aerosols between heights $h_{1}$ and $h_{2}$. With LIDAR, it is also possible to study the concentration and sizes of the aerosols present in the atmosphere. These are very important in atmospheric pollution studies.

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Comparison between electric charge and mass

Electric Charge:

1.) An electric charge can be positive, negative, or neutral.

2.) The electric charge of a body is always quantized and follows the equation: $q=ne$

3.) The electric charge of a body remains unaffected by its speed.

4.) Charge is strictly conserved.

5.) Electrostatic forces between two charged bodies can be either attractive or repulsive.

6.) Electrostatic forces between multiple charges can sometimes cancel each other out.

7.) A charged body always carries some mass.

Mass:

1.) The mass of a body is always positive.

2.) Unlike charge, mass quantization has not yet been established.

3.) The mass of a body increases with its speed.

4.) Mass is not conserved by itself as some of the mass may get changed into energy or vice versa.

5.) Gravitational forces between two masses are always attractive.

6.) Gravitational forces between multiple bodies never completely cancel out.

7.) A body with mass may not necessarily have a net charge.

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