Light diffraction pattern

 Light is a wave.  It is the fact that light is a wave that causes it to make a diffraction pattern.  The best way to understand why this works is to do a similar experiment with water in a bathtub.  First side with a small gap in between.  The idea is to block water from moving from one side of the tub to the other, except via the small gap, which should be a couple of inches wide.  Plywood also works great.  Then you can tap the surface of the water with one hand to create waves.  You can also try gently sloshing your hand back and forth.  As the waves go through the opening in the wood, they will create exactly the same types of patterns that light does.  The only difference is that the water will have a wavelength of a few centimeters, whereas light has a wavelength of only a half of a thousandth of a thousandth of a meter (really small!)

Light diffraction pattern

If you tap the water faster, you will see that the wavelength of the water is shorter. If you tap the water slowly, then you will see that the wavelength of the water is longer. Then, what you do is you look at the water pattern that bounces back from the far end of the bathtub. You will see diffraction pattern. It won't glow like light does, but it will have a similar kind of shape, at least until the water bounces around the tub a few times and the waves get confused.
If you do this experiment for a bit, you will notice that the opening is spreading the wave out. But the pattern that is generated depends not only on how the wave is spread out, but also the shape the wave had before it spread. This is because the pattern is caused by some parts of the wave interfering with other parts. That is, at one point the wave is higher than the other. When those two parts touch, then the wave disappears. But when two high points touch, they make a very high point.
 

Fresnel diffraction pattern

Introduction :
Diffraction in the case of waves refers to their bending round the obstacles. The diffraction phenomena is more predominant when the size of he obstacle is small and is comparable with the wavelength of he incident light.

Fresnel diffraction:  In this approach source of light, the obstacle and the screen are relatively close and are at finite distances. The waves are spherical or cylindrical. The wave fronts that reach the obstacle and proceed on to illuminate the screen at any point on it are not plane ones; i.e., the rays involved are not parallel. Therefore Fresnel type of investigation of diffraction is a general one. No lenses are required to observe the diffraction pattern.
Spherical or cylindrical wave fronts are divided into large number of zones, the wavelets emanating from which superimpose to yield the intensity distribution on the screen. The amplitudes and relative phases of all the zones are taken into account to calculate the intensity distribution. So, mathematical treatment for  Fresnel diffraction is  quite complicated.

Fresnel Zones

In the above figure , S is a point source. It ends spherical wavefront in forward direction . Let the radius of the spherical wave front be 'a' after time 't'. The effect of this wavefront at P is determined by dividing the wavefront into annular or ring  shaped zones. The distances from the edges of two successive zones to point P differ by    `(lambda)/(2)`  . The annular zones having this property are known as Fresnel zones. The distance of the zeroth zone from point P is b₀ .
The first zone is at a distance       b₁    =    b₀    +    `(lambda)/(2)`.
The second zone is at a distance  b₂   =   b₀   +    `(2lambda)/(2)` 
The third zone is at a distance        b₃    =    b₀  +  `(3lambda)/(2)`
The m^th  zone is at a distance         b_m  =  b₀  +   `(mlambda)/(2)`

Conclusion to fresnel diffraction pattern:

These zones are also known as half period zones as the path difference of  `(lambda)/(2)`   corresponds to a phase difference of 180⁰  which in turn corresponds to half a period. The areas of Fresnel zones are approximately the same when m in not too great and hence an equal quantity of light energy will be transmitted through each of the zones.

edge diffraction

"Effectively, what is happening is the measurement circumstance is changing from free-field (4-pi) to half-space (2-pi) as the frequency increases and the wavelength decreases to something approaching the overall area of the baffle. This creates a response ‘step’ of about 6 dB, the frequency of the step being dependent upon the baffle area. The effect is most pronounced on-axis, as the baffle causes a beaming phenomenon like a [sic] -automobile headlight reflector."

While what is said is mostly correct, it does make one wonder:
    * How does the wave know how large the baffle is?
    * Why 6 dB?
    * Are there any other effects?
    * Are two baffles equivalent if they have the same area but vastly different dimensions, e.g. a 30 cm X 30 cm baffle vs. a 5 cm X 180 cm baffle?
In my opinion, the key to developing an intuitive or quantitative understanding of cabinet edge diffraction is by studying it primarily the time domain and resorting to the frequency domain only when absolutely necessary. Once the effect is understood in the time domain, it is easily translated to the frequency domain by using the Fourier transform.

Imagine an ideal point source hemispherical radiator mounted on the exact center of the end of a long cylindrical solid. Such a radiator will exhibit a hemispherical radiation pattern that is independent of frequency. In addition, let us suppose it exhibits minimum phase characteristics and has flat frequency response over all frequencies. If we now excite the radiator with a discrete-time impulse of duration 0.025 mS, it will move in response to the impulse and stimulate a hemispherical acoustic impulse moving away from the point source at the speed of sound. Since the radiator is perfect, the acoustic impulse will have a shape identical to the discrete-time impulse.

Everything is very easy to visualize until the edge of the impulse reaches the edge of the cylinder. When the impulse reaches the edge of the cylinder, there is a sudden loss of support as the impulse is now free to radiate behind the face of the cylinder, not just in front of it. In this way, the impulse ‘diffracts’ or ‘scatters’ behind the face of the cylinder. Interestingly, this scattering is frequency independent, but angle dependent. So if we measured the acoustic signal behind the cylinder, we would find that it is an impulse identical to the one formed by the radiator but somewhat diminished in magnitude. Now, few of us set up our favorite listening spot behind our loudspeakers, so it makes sense to try to understand what happens in front of the loudspeaker. Due to the loss of support at the edge of the cylinder, the impulse will partially collapse as some of the pressure ‘leaks’ backwards and this causes a secondary impulse to scatter in the forward direction. Like the impulse scattered behind the cylinder, the forward-scattered impulse will also be frequency independent but angle dependent. Unlike the backward-scattered impulse, though, the forward-scattered impulse will have the opposite polarity as the original impulse. Now imagine a microphone located in front of and on the cylinder axis, far away from the cylinder. What will the microphone measure? First, the impulse from the radiator will be picked up then, delayed by an amount equal to the radius of the cylinder divided by the speed of sound, the forward-scattered impulse will be measured.

Now, as stated previously, neither the forward nor the backward-scattered impulses display frequency dependence. However, taken together, the direct and forward-scattered impulses will result in frequency dependence through constructive and destructive interference. Figure 1 and Figure 2 show the time and frequency domain behavior of the impulse as measured by a microphone located in front of and on the cylinder axis, far away from the cylinder. The radius of the cylinder is 1 meter and the radiator is mounted in the center of the baffle.

anomalous diffraction

An approach to solving the phase problem in protein structure determination by comparing structure factors collected at different wavelengths, including the absorption edge of a heavy-atom scatterer. Also known as multiple-wavelength anomalous diffraction or multiwavelength anomalous dispersion.

The 'normal' atomic scattering factor f0 describes the strength of X-rays scattered from the electrons in an atom assuming that they are free oscillators. Because the scattering electrons are in fact bound in atomic orbitals, they act instead as a set of damped oscillators with resonant frequencies matched to the absorption frequencies of the electron shells. The total atomic scattering factor f is then a complex number, and is represented by the sum of the normal factor and real and imaginary 'anomalous' components:
f = f0 + f' + if''.

A consequence of the wavelength dependence of anomalous dispersion is that the structure factors will be significantly perturbed, both in amplitude and in phase, by resonant scattering off an absorption edge. Hence, if diffraction is carried out at a wavelength matching the absorption edge of a scattering atom, and again at a wavelength away from the absorption edge, comparison of the resulting diffraction patterns will allow information to be extracted about the phase differences. For suitable species, the effect is of comparing a native molecule with a strictly isomorphous derivative (and in such cases phase determination and improvement are similar to isomorphous replacement methods).

The technique, often using tunable synchrotron radiation, is particularly well suited to proteins where methionine residues can be readily replaced by selenomethionine derivatives; selenium has a sufficiently strong anomalous scattering effect that it allows phasing of a macromolecule.
The method of Multiple wavelength Anomalous Diffraction (MAD) is most applicable to problems where there are no available separate native protein diffraction data, e.g. for metallo-proteins where a heavy atom is already bound in the native structure, or to cases where derivative crystals are non-isomorphous and are therefore unsuitable for phasing via isomorphous replacement.

I like to share this diffraction grating definition with you all through my blog.

Check my best blog Diffraction grating.

Diffraction grating

Introduction :
In optics, a diffraction grating is an optical part with a periodic structure, which splits and diffraction light into some beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the brightness so that the grading acts as dispersive element. Because of this, diffraction gradings are generally used in monochromators and spectrometers.

Diffraction grating definition

A photographic slide with a well model of black lines forms a simple grating. For useful applications, diffraction gradings usually have grooves or rulings on their outside rather than dark lines. Such gradings can be moreover transparent or reflective. Gratings which change the phase rather than amplitude of the incident light are also formed, frequently using holography.
                                            (Source : Wikipedia)

Theory of operation

The connection between the grading spacing and the angles of the event and diffracted beams of light is known as the grating equation. According to the Huygens–Fresnel standard, each point on the wave front of a propagating signal can be measured to act as a point source, and the wave front at any following point can be found by calculation together the contributions from every of these individual position sources.
                                                              (Source :Wikipedia)
An idealized diffraction grating is measured here which is made up of a position of long and considerably narrow slits of spacing d. When a level surface signal of wavelength λ is incidence usually on the grating, each slit in the grading acts as a point source propagate in all directions. The light in a exacting direction, θ, is made up of the interfering components from each slit.This occurs at angles θ_m which satisfy the connection dsinθ_m/λ=|m| where d is the division of the slits and m is a digit. Thus, the diffracted light will have maxima at angles θ_m given by

It is basic to show that if a plane wave is event at an angle θ_i, the grating equation becomes

Gratings can be made in which a mixture of the incident light are modulate in a regular example

• Transparency (transmission amplitude gratings)
• Reflectance (reflection amplitude gratings)

• Refractive index (phase gratings)
• Direction of optical axis (optical axis gratings)

The grating equation applies in all these cases.a


Check my best blog Uses of Carbon Compounds.

Uses of Carbon Compounds

 The study of carbon compounds is called organic compounds.Carbon compounds are covalent compounds having low melting points and boiling point. It shows that forces of attraction between their molecules are not very strong. Most of the carbon compounds are non-conductors of electricity. They do not contain ions. Carbon compounds occur in all living things like plants and animals. The number of carbon compounds already known at present is more than 5 million. Many more new carbon compounds are being isolated or prepared in the laboratories everyday. In fact, the number of carbon compounds alone is much more than the number of compound is all other elements taken together. One reason for the existence of a large number of carbon compounds is that carbon atoms can link with one another by means of covalent bonds to form long chains of carbon atoms. This property is called Catenation. Carbon-carbon bonds are strong, and stable. This property allows carbon to form an almost infinite number of compounds; in fact, there are more known carbon-containing compounds than all the compounds of the other chemical elements combined except those of hydrogen.

Uses of Carbon Compounds.

The compounds of carbon with hydrogen are called hydrogen. In addition to hydrogen, carbon compounds may also contain other elements such as oxygen, halogens nitrogen and sulfur. This increases the number of carbon compounds even further. Today, millions of carbon compounds containing a variety of other elements are in our daily life. For example, we use soap for taking bath and detergent powders for washing clothes. The soaps and detergent which are used as cleansing agents in our daily life are carbon compounds. In fact, carbon compounds are being used on our everyday life in the form of medicines, plastics, textiles, dyes, food preservatives, soaps and detergents, sources of energy and many other things.

Stability of Carbon dioxide

Introduction : 

A Scottish chemist and physician JOSEPH BLACK discovered Carbon Dioxide, in 1754. Carbon Dioxide is very popular in Green house effect produced due to human activities, primarily by the combustion of fossil fuels. Carbon Dioxide can be easily found in the earth’s atmosphere, as the main source of carbon dioxide is humans and plants.

About Carbon Dioxide

Carbon Dioxide is a chemical compound composing of two oxygen atoms, which are covalently bonded to the single carbon atom.The chemical formula of carbon dioxide, is CO_2. Carbon dioxide generally exists as gas at room temperature. Carbon Dioxide forms 0.039% of the atmospheric air. Carbon dioxide is also present in liquid and solid forms under some special conditions. It can be solid when temperature will be as low as -78 ⁰C. Liquid carbon dioxide mainly exists when it is dissolved in water. Carbon dioxide is one of the gases, which is easily dissolved in water, when pressure is maintained. Carbon dioxide on leaving water gives bubbles

Properties of carbon Dioxide and its Stability

Carbon dioxide can be found mainly in air, but also in water because of carbon cycle. Some of the important properties of Carbon dioxide are as follows:

• Plants use it during the photosynthesis to make sugars, which will be consumed by them for their essential growth and development.
• It is generated as a byproduct in the combustion of fossil fuels and in the burning of vegetable matter.
• Amount of CO₂ present in the atmosphere changes due to the effect of plant growth.
• CO₂ has no liquid state below 5.1 atm pressure.
• In its solid-state carbon dioxide is known as Dry Ice.
• CO₂ is an acidic oxide; as a result, it turns litmus from blue to pink.
• CO₂ is an anhydride of Carbonic acid.
• CO₂ is toxic in higher concentrations, as a result it make people drowsy
• CO₂ is a colorless and odorless gas having acidic odor.
• It acts as an asphyxiant and an irritant.

The main reason for the stability of carbon dioxide in atmosphere is the carbon cycle, in which human, animals exhale carbon dioxide, and this CO₂ is being taken by plants during day to prepare their food essential for their growth, while in night plants also produce carbon dioxide. This entire process makes the carbon dioxide stable in the atmosphere.

Summary on Stability of Carbon dioxide

Carbon Dioxide is an organic compound used widely in commercial purposes. As it is used in the production of lasers and even in the soft drinks. This compound exists naturally in the earth's environment. Scientists became concerned by the fact that humans are producing too much carbon dioxide for plants to process, if it will continue to follow then it will lead to serious environmental problems.