Osm Physics by Ashish

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: Let the position vector of a point \( P \) be in inertial frame \( S \) be \( \vec{r} \). Then \( \vec{r}' = \vec{r} - \vec{v}t \)     (or)     \( x' = x - vt,\quad y' = y,\quad z' = z \) (17) where \( x,\; y,\; z \) are the coordinates of the point \( P \) and \( x',\; y',\; z' \) are the coordinates of the same point in frame \( S' \). Physical Laws and Frames of Reference     15 (b) When both inertial frames \( ...

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 invariance of physical laws,  Fictitious force,  Uniformly rotating frames 1.4 Transformation of displacement, velocity and acceleration,  1.5 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,  Kepler’s laws,...

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...