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Showing posts from September, 2022

Polarization by scattering.

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When some electromagnetic wave is incident on a scatterer atom, whose size is comparable to wave length of wave, then due to the electric vector of the incident wave the atom starts oscillating.This oscillating atom(acting as small dipole) itself emitts radiations. But the reemission of e.m. wave by the oscillating dipole is such that it emitts e.m. waves in all directions except in the direction of oscillation.This fact can be used for polarization of light.

Photoelasticity.

Photoelasticity is an experimental method to determine stress distribution in various engineering components.The method is mostly used in cases where mathematical methods become quite cumbersome (difficult). Photoelasticity is especially useful for the study of objects with irregular boundaries and stress concentrations, such as pieces of machinery with notches or curves, structural components with slits or holes, and materials with cracks.

Apparent depth.

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Apparent depth is the virtual depth that is observed as a result of the refraction of light.The apparent depth depends upon the refractive index of the medium.In case of viewing other than vertically, the position of the image changes with the angle, which the line of vision makes with the surface of separation of the two media. As the angle increases, the apparent depth decreases.Also, the object appears curved when viewed obliquely through the refracting medium. Look at the following figure

Solve (D²+2D+2)y= sinhx

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Power transmission.

Electrical power transmission through any conductor is always accompanied by energy loss I²R, where I is the current and R is the resistance of the conductor. If superconductors are used, the losses will be eliminated and power transmission can be done at a lower voltage level.

Solve xydx+(x+1)dy=0

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Hydrogen bonding.

With hydrogen atom as the positive end of the dipole, if bonds arise as a result of electrostatic attraction between atoms, it is known as hydrogen bonding.

Miller indices.

The Miller indices of a plane are defined as the reciprocals of the intercepts which the plane makes with the axes when reduced to smallest numbers.

Integration of logx

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Meissner effect.

When a metal becomes superconductor, its thermal conductivity decreases considerably and tends to zero approximately as the cube of the temperature.Superconducting state being a distinct phase of matter having characteristic electrical, magnetic, thermodynamic and other physical properties.Superconductors have zero electrical resistance.In a superconducting state the magnetic permeability is also zero and shows perfect diamagnetism.This phenomenon is known as Meissner effect.

Brownian motion.

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Brownian motion was first observed in 1827  by brown, a botanist.The phenomenon of Brownian movement can be easily observed in a laboratory if a colloidal solution is examined under an ultramicroscope.The non-stop random and haphazard(badly organized) motion of the particles in a medium is called Brownian motion.

Integration of √(a²-x²)dx

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Why electronic orbits are associated with a magnetic moment ?

An electron revolving in an orbit about the nucleus in an atom is equivalent to circular current and behaves like a magnetic shell or tiny magnetic doublet possessing a magnetic moment.Thus electronic orbits are associated with a magnetic moment.

Laser light.

A laser has a unique combination of coherence,monochromaticity, intensity directionality, which distinguishes it from other light sources. The multiplication of photons through stimulated emission results a coherent, powerful, monochromatic and collimated beam of light known as laser light.

Planck's statement.

“It is impossible to extract heat from a single body & convert the whole of heat into work”.

Clausius statement.

“ Heat cannot flow from cold body to hot body without the performance of work by some external agency”.

Equipartition of energy.

In any dynamical system, in thermol equilibrium, the total kinetic energy of the system is equally divided among all it's degrees of freedom & the kinetic energy per molecule per degree of freedom is equal to 1/2 KT, this is called equipartition of energy.

Carnot's engine.

Carnot a french engineer gave an ideal reversible heat engine which went through four strokes.Two strokes are isothermal change & two strokes are adiabatic change.

Nuclear forces.

We know that the nucleus consists of protons and neutrons.Due to the positive charge on proton, there Wii be a repulsive electrostatic force between the two protons and the resulting repulsive force between protons will tend to push the nucleus apart.Therefore, for the nucleus to have a permanent existence, there must be some strong attractive forces between protons and neutrons inside the nucleus.These attractive forces cannot be gravitational because they are much smaller than the attractive force demanded.Moreover, these forces cannot be electrical in nature because the strong repulsive forces between protons will lead to distruption of nucleus. Actually these forces are short range attractive forces known as nuclear forces.

Optical instruments.

The optical instruments can be broadly divided into two groups.One group forms real images of an object, which is projected onto  screen or photographic plate.The image can be viewed simultaneously by many observers.Projectors belong to this category.The other group forms virtual images of an object and only one observer can see the image.The virtual image formed by instrument is transformed by the eye into a real image.Therefore, the optical instrument forming a virtual image are often called optical aids.

Conduction.

Conduction is the process in which heat is transmitted from one point to the other through the substance without the actual motion of the particles.When one end of a metal bar is heated, the molecules at the hot end vibrate with higher amplitude (kinetic energy) and transmit the heat energy from one particle to the next and so on. However, the particles remain in their mean positions of equilibrium.

Convection.

Convection is the process in which heat is transmitted from one place to the other by the actual movement of the heated particles.It is prominent in the case of liquids and gases.Land & sea breezes and trade winds  are formed due to convection.Convection plays an important part in ventilation, gas filled electric lamps and heating of buildings by hot water circulation.

Prevost's theory of heat exchanges.

According to prevost, every body emits radiations continuously to its surroundings at the rate which depends only on the nature of its surface and temperature and at the same time it receives radiations from its surroundings at the rate depending on the surface and the temperature of surroundings.

Electron gas.

Metals are very good conductors.The high conductivity of metals is due to the presence of free electrons.These free electrons inside a metallic conductor move freely inside the metal.They continuously collide with the fixed (localized) atoms and thus behave like an electron gas.Fermi-Dirac derived an expression for the distribution of energies among electrons in the electron gas in a metal on the basis of these assumptions.

Bose-Einstein statistics.

This statistics was developed by S.N. Bose for light quanta, called photons and generalised by A.Einstein to describe the energy distribution among particles, whose spin angular momenta are nh where n=0,1,2,3,..... such particles are called bosons.  wave  functions are symmetric on interchanging two bosons. The pauli exclusion principle which states that in each quantum state there cannot simultaneously be more than one particle, is not applicable to bosons, so that there is no upper limit to the number of bosons in a given quantum state.

Ventilation.

Rooms are provided with ventilators near the ceiling.Air in the room gets warmer due to respiration of people in the room.Warm air containing more of CO2 & water vapour has less density and moves upwards.Fresh air from outside enters the room through the doors & windows.The impure air moves outside through the ventilators.The phenomenon is continuous.

Fission detector.

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Fission reaction may be employed to detect neutrons.A typical detector consists of an ionisation chamber whose walls are coated with fissionable material.The incident neutrons cause Fission in the material.This gives rise to heavy Fission fragments, each having kinetic energy of more than 50MeV.These fission fragments cause ionisation in the gas in ionisation chamber.

Fermions.

Fermions are elementary particles which obey Fermi-Dirac statistics.They have a particle spin equal to half integral.The name fermions is due to Italian physicist Enrico Fermi.These particles follow pauli's exclusion principle.There are two major type of fermions (A) Light weight fermions (leptons) (B) Heavy weight fermions (Baryons)

Cardioid.

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Cardioid is nothing but a heart shaped polar curve. Equation of Cardioid is  r=a(1±sinθ) or r=a(1±cosθ)

Temperature of the sun.

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The sun consists of a central hot portion surrounded by the photosphere.The central portion has a temperature of the order of 10⁷K.The photosphere has a temperature of about 6000K which is calculated  by considering the sun as a perfect black body radiator.

Radiation.

Radiation is the method of heat transfer in which the heat flows from position of higher temperature to that of lower temperature without the aid of medium.In radiation, the heat flows by means of electromagnetic waves.For their propagation, no medium is required.If medium is present, it does not absorb heat. Therefore, radiation may take place in vacuum also.Heat from the sun reaches the earth by radiation.

Uses of cyclotron.

(i) Cyclotron is used in nuclear reactions.High speed particles produced in cyclotron act as bombarding agent to carry out nuclear reactions to produce new particles. (ii) The accelerated charged particles are used in artificial transmutation of elements. (iii) The cyclotron is used to implant the particles in solids to modify their properties. (iv) Cyclotron is used in hospitals to produce different radioactive nuclei.