Osm Physics by Ashish

Rotating Frame of Reference and Coriolis Force Let the coordinates of any point P are $(x,y,z)$ and unit vectors are $(\hat{i},\hat{j},\hat{k})$ along the axes of the stationary reference frame S. The position vector of point P is $$ \overrightarrow{OP}=\vec r =\hat{i}x+\hat{j}y+\hat{k}z \tag{1} $$ Fig. (1): Rotating reference frame R If another reference frame R which is initially at $t=0$ coincident with the frame S, is rotating with an angular velocity $\vec{\omega}$. After $t$ seconds all the axes of frame R will be inclined by an angle ($\theta=\omega t $) with the respective axes of frame S. In this state if the coordinates of the same point P are $(x',y',z')$ and unit vectors are $(\hat{i}',\hat{j}',\hat{k}')$ along the axes of the rotating reference frame R, then the position vector of point P is $$ \overrightarrow{OP}=\vec r' =\hat{i}'x'+\hat{j}'y'+\hat{k}'z' \tag{2} $$ Since the dir...

Invariance of physical laws means that the fundamental laws of physics have the same mathematical form in all inertial frames of reference. The laws of physics do not depend on the uniform motion of the observer. If two observers are moving with constant velocity relative to each other, both should obtain the same physical laws. This principle is called the principle of relativity. For example, Newton’s laws of motion have the same form in all inertial frames. In classical mechanics, this invariance is associated with Galilean transformations. In special relativity, physical laws are invariant under Lorentz transformations. Example: An experiment performed inside a smoothly moving train gives the same physical results as when the train is at rest, provided the train moves with constant velocity. Key point: The laws of physics are universal and do not depend on the choice of inertial reference frame.    1. Newton’s First Law — Law of Inertia A body remains ...

  A pseudo force (also called a fictitious force or inertial force) is an apparent force that is observed only when viewing motion from a non-inertial (accelerating or rotating) reference frame. It does not arise from a physical interaction but is introduced to apply Newton's laws in an accelerating frame. Definition A pseudo force acts on an object when the observer is in an accelerating frame of reference. Its magnitude is F = -ma where: m = mass of the object a  = acceleration of the reference frame The negative sign indicates the pseudo force acts opposite to the acceleration of the frame. Example Suppose you are standing in a lift that suddenly accelerates upward: You feel heavier then your actual weight. Similarly, if lift is moving downward, then you feel lighter .

  Unit-I Nuclear Properties: Rutherford’s scattering and Nucleus model of atom, Properties of Nuclei, Mass, Charge, Estimation of charge density, size, density, spin, parity, statistics, magnetic dipole moment, Electric Quadrupole Moment, Mass Defect and concepts of Binding energy, Constituents of nucleus, Discovery of neutron and proton-neutron hypothesis, Nuclear potential, Nuclear Force, Liquid drop model, Semi Empirical Mass formula and its applications; 1. Alpha decay, 2. Mass Parabola, 3. Mirror Nuclei, Nuclear Mass measurements, Aston's Mass Spectrograph, Double Focussing Mass Spectrograph and Doublet method. Unit-II Nuclear Fission:- The Discovery of Nuclear Fission, The Energy Release in Fission, Mass and Energy distribution of fission products, Neutron emission in fission, Energetics of Spontaneous fission, Bohr Wheeler theory and Quantum effects, Neutron induced fission, Fission cross-section and threshold, Nuclear Fission as a source of Energy, The Nuclear Chain Reactio...

  UNIT–I Failures of the classical mechanics, black body radiation and spectral distribution of energy, Planck’s quantum hypothesis and average energy of Plank oscillator, Plank’s radiation law and discussion to obtain Wein’s, Rayleigh-Jeans and Stefan-Boltzmann laws using it, photoelectric effect, Compton effect, Wave-particle duality, De Broglie relation, Davison Germer experiment, group and phase velocities, Wave function, boundary and continuity conditions of wave function, physical significance of wave function and its interpretation. UNIT–II Uncertainity principle (i) Position & momentum (ii) Energy & Time (iii) Angular displacement and Angular momentum. its application such as (i) Non existence of electron in nucleus, (ii) Ground state energy of H–atom, (iii) Ground state energy of harmonic oscillator. Fundamental postulates of quantum mechanics, Eigenfunction and eigen values, Degenracy. Orthogonality of eigenfunction, Commutation relations, Ehrenfest's theorem and ...

  Unit-I Circuit Analysis, Network-some important definitions, loop and nodal equation, Kirchhofs Laws, driving point and transfer impedances, four terminal network parameters, Open circuit, short circuit and hybrid network theorems, Superposition, Thevenin, Norton, Reciprocity, Compensation and maximum power transfer. Unit-II Semiconductors, Intrinsic and extrinsic semiconductors, charge densities in N and P materials, conduction by drift and diffusion of charge, Formation of PN junction, PN diode equation, capacitance effect of diode. Rectification and power Supply, Half-wave and full wave rectifiers, calculation of Ripple factor, efficiency and regulation, bridge rectifier, Filters: shunt capacitor, L and p filters, Voltage regulation and voltage stabilization, Zener diode, Voltage multiplier circuits. Unit-III Transistor and Transistor Amplifiers, Notations and volt ampere relations for bipolar junction transistor, CB, CE, CC configurations, characteristic curves and their equi...

  Unit-I General Thermodynamical interactions, Dependence of the number of states of external parameters, General relations in equilibrium, equilibrium conditions, infinitesimal quasistatic process, Entropy of an ideal gas, Equilibrium of an isolated system, Equilibrium of a system in contact with reservoir (Gibb’s free energy), equilibrium between phases, Clausius-Clapeyron equation, Triple point,Vapour in equilibrium with liquid or solid, equilibrium conditions for a system of fixed volume in contact with heat reservoir (Helmholtz free energy), Equilibrium between phases and condition of chemical equilibrium and equilibrium condition for a system at constant pressure in contact with a heat reservoir (Enthalpy), Maxwell’s relations. Unit-II Thermal interactions of macroscopic Systems, system in contact with a heat reservoir, first law of thermodynamics and infinitesimal general interaction, Concept of temperature and quantitative idea of temperature scale (thermodynamical paramete...

  Unit-I Scalar and Vector Fields: Scalar and Vector Fields, Gradient of a scalar field, relation between conservative field and Potential, line, surface and volume integral of vector fields, concept of flux, Divergence and Curl of a vector field and their physical significance, Gauss’ divergence and Stokes curl theorem with proof, Del and Laplacian operator in Cartesian, Cylindrical and Spherical coordinates. Unit II Electrostatic: Electric potential and field due to arbitrary charge distribution, Multipole Expansion, potential and field due to dipole & its interaction with electric field, electrostatic energy of a uniformly charged sphere, classical radius of an electron. Atomic and molecular dipoles, induced dipole and polarizability, dielectrics and their electrical polarization, susceptibility and displacement vector, Capacity of a capacitor with partially and completely filled dielectrics, Gauss’ law in integral and differential form, Lorentz local field and Clausius-Moss...

Galilean Transformation Galilean Transformation: The relation of one Inertial Frame to another Inertial Frame If the position of a point relative to one inertial frame is given, the equation for finding the position of the same point as is determined in another inertial frame is called the Galilean transformation. The transformation equations of physical quantities from one inertial frame to another inertial frame are called the equations of the Galilean transformation. (a) Transformation of position When both inertial frames \( S \) and \( S' \) are mutually accelerated: Let the position vector of a point \( P \) are \( \vec{r} \) and \( \vec{r'} \) in inertial frame \( S \) and \( S' \) respectively. If \( S' \) is moving with constant velocity V Then in \( \Delta OO'P\) \( \vec{r}' = \vec{r} - \vec{V}t \) (1) where \( \vec{r} = xi+yj+zk\)    and    \( \vec{r'} = x'i+y'j+z'k\). in components,     \( ...

Newton's Laws of Motion Newton's Laws of Motion Newton's laws of motion are three fundamental laws given by Sir Isaac Newton . They describe the relationship between the motion of an object and the forces acting on it. 1. Newton's First Law — Law of Inertia An object remains at rest or continues to move with uniform velocity in a straight line unless acted upon by an external unbalanced force. F net = 0   ⇒   v = constant Example When a moving bus suddenly stops, passengers tend to move forward due to inertia. Types of Inertia Inertia of rest Inertia of motion Inertia of direction 2. Newton's Second Law — Law of Acceleration ...

Frame of Reference A frame of reference is a coordinate system (origin + three mutually perpendicular axes) together with a clock used to specify the position and time of events. 1. Inertial Frames Definition An inertial frame is a frame in which a free particle (net external force = 0) moves with constant velocity (Newton’s first law holds). Equivalently, it is a frame that is either at rest or moving with uniform velocity relative to a fixed star (or any other inertial frame). Properties Newton’s laws of motion are valid in their standard form: \(\mathbf{F} = m\mathbf{a}\) Acceleration of a free particle is zero. If \(S\) is inertial and \(S'\) moves with constant velocity relative to \(S\), then \(S'\) is also inertial. All inertial frames are equivalent for the formulation of the laws of classical mechanics (Galilean principle of relativity). Examples A frame fixed to the distant stars (approximately). A laboratory fram...

  Unit-I    1.1 Physical Laws and  1.2 Frames of Reference:  Inertial &  non-inertial frames,  1.3 Galilean transformations and  1.4 Invariance of physical laws,  1.5  Fictitious force ,  1.6 Uniformly rotating frames 1.7 Transformation of displacement, velocity and acceleration,  1.8 Coriolis force,  motion relative to earth, effect of rotation of earth on ‘g’,  Focault’s pendulum and its time period.  Unit-II    Conservation Laws and Dynamics of Particles:  Concept of centre of mass,  Centre of mass of a system of particles,  Equation of motion,  Conservation of linear momentum,  Relationship between (Lab and center of Mass frames in 1-D and 2-D reference)  Elastic and inelastic collision,  Motion of a system with varying mass,  Motion in a central force field,  Conservation of angular momentum,  Trajectory of a particle under gravitational force,...

Fresnel Diffraction Definition Fresnel diffraction is the diffraction of light in which the source and screen are at finite distances from the diffracting obstacle or aperture. Theory Fresnel diffraction is based on the Huygens–Fresnel principle . According to this principle, every point on a wavefront acts as a source of secondary wavelets. These wavelets spread into the region behind the obstacle or aperture and interfere with one another. In Fresnel diffraction, the incident wavefront is generally spherical or cylindrical . Therefore, the curvature of the wavefront cannot be neglected. Fresnel Half-Period Zones The wavefront is divided into a number of zones called Fresnel half-period zones . The path difference between waves reaching the observation point from two consecutive zones is: Δ = λ/2 Therefore, the waves from successive zones reach the observation point with a phase difference of...

  Diffraction of Light Diffraction is the phenomenon of the bending and spreading of light waves around the edges of an obstacle or through a narrow aperture when the size of the obstacle or aperture is comparable to the wavelength of light. It is a clear demonstration of the wave nature of light and occurs due to the superposition and interference of secondary wavelets . Types of Diffraction Diffraction is mainly of two types: 1. Fresnel Diffraction In Fresnel diffraction, the source and the screen are at finite distances from the diffracting obstacle or aperture. The incident wavefront is generally spherical or cylindrical . Examples: Diffraction by a straight edge Diffraction by a narrow slit Diffraction by a circular aperture 2. Fraunhofer Diffraction In Fraunhofer diffraction, the source and the screen are effectively at infinite distances from the diffracting aperture or obstacle. In practice, lenses are used to produce parallel incident and diffracted wavef...

Fizeau’s Fringes Fizeau’s fringes are fringes of equal thickness produced by the interference of light reflected from the two surfaces of a thin wedge-shaped film . They are generally straight, parallel, and equally spaced . They are localized near the film. The thickness of the film varies from point to point. The optical path difference depends on the thickness of the film . For a film of refractive index μ , thickness t , and refracted angle r : Δ = 2μt cos r For a wedge-shaped air film at nearly normal incidence: Δ = 2t The condition for dark fringes in reflected light is: 2t = mλ If the wedge angle is θ , then: t = xθ Therefore: 2xθ = mλ The fringe width is: β = λ / (2θ) Difference Between Haidinger’s and Fizeau’s Fringes Property Haid...

1. Determination of Wave Length of a Monochromatic Light Source In Newton’s experiment if we use a light source of unknown wave length (say sodium lamp) then we can determine the wavelength of light source by measuring the diameters of Newton’s ring. If D n is diameter of nth dark ring formed due to air film then D n 2 = 4nλR Where n is any integer number. Similarly if D n+p is the diameter of ( n+p ) th ring D n+p 2 = 4(n + p)λR Using this equation, we can write D n+p 2 − D n 2 = 4(n + p)λR − 4nλR = 4pλR or λ = D n+p 2 − D n 2 ⁄ 4pR      ...... (5.20) Where p is any integer number and R is radius of curvature of plano-convex lens. 2. Determination of Refractive Index of a Liquid by Newton’s Rings Experiment In Newton’s rings experiment the diameter of n th dark ring...

Newton's rings in a special case of wedge shaped film in which an air film is formed between a glass plate and a convex surface of lens. The thickness of air film is zero at the center and increases gradually towards the outside. When a plano-convex lens of large focal length is placed on a plane glass plate, a thin air film is formed between the lower surface of plano-convex lens and upper surface of glass plate. When a monochromatic light falls on this film the light reflected from upper and lower surfaces of air film, and after interference of these rays, we get an inner dark spot surrounded by alternate bright and dark rings called Newton's rings. These rings are first observed by Newton and hence called Newton's rings. Experimental Arrangement for Reflected Light The experimental arrangement for Newton's rings experiment. A beam of monochromatic source S is made parallel by using a convex lens L. The parallel ...

The two surfaces of the thin film are slightly inclined to each other at an angle \( \theta \). Therefore, the thickness of the film gradually increases from one end to the other. The ray \(SA\) is the incident ray falling on the upper surface of the thin film at \(A\). At \(A\), the incident light is partially reflected and partially transmitted. A part of the incident light is reflected directly from the upper surface at \(A\) and travels along \(AR_1\). This is the first reflected ray. The remaining part of the incident ray enters the thin film at \(A\). It travels inside the film and reaches the lower surface at \(B\). At \(B\), a part of the light is reflected back towards the upper surface. It reaches the upper surface at \(C\) and emerges along \(CR_2\)...

Haidinger's Fringes Haidinger's fringes are a system of concentric circular interference fringes produced by the interference of two beams whose path difference depends on their angle of inclination . They are also known as fringes of equal inclination . Formation in a Michelson Interferometer In a Michelson interferometer, let \(d\) be the separation between the two reflecting surfaces and let a ray make an angle \(\theta\) with the normal. The optical path difference between the two interfering beams is: \[ \Delta = 2d\cos\theta \] Condition for Bright Fringes For constructive interference, the condition for bright fringes is: \[ 2d\cos\theta = n\lambda \] where: \(d\) = separation between th...

Determination of Refractive Index or Thickness A thin transparent film of thickness \(t\) and refractive index \(\mu\) is placed normally to the light ray between the mirror \(M_2\) and the beam splitter plate. Due to the insertion of the film, the optical path of the light ray increases by \[ 2(\mu - 1)t \] Consequently, the white fringe is displaced from its original position. The displacement of mirror \(M_1\) is adjusted with the help of a micrometer screw until the cross-wire of the telescope again coincides with the white fringe. Let the displacement of mirror \(M_1\) be \(x\). The optical path difference produced due to the insertion of the thin film becomes equal to the optical path difference produced by the displacement of mirror \(M_1\). Since ...