Explain how Michelson interferometer is used to determine the wavelength of light.
See Answer →i) Show that the radius of a dark Newton's ring is directly proportional to the square root of the radius of curvature of the lens used.
ii) Newton's rings are formed in reflected light of wavelength 5890×10-8 cm with a liquid between the plane and curved surfaces. The diameter of the fifth ring is 0.3 cm and the radius of curvature of the curved surface is 100 cm. Calculate the refractive index of the liquid, when the ring is bright.
See Answer →Using Heisenberg's Uncertainty Principle explain whether a particle trapped inside a one dimensional box of finite length can be at rest.
See Answer →Calculate the de Broglie wavelength of a 87Rb atom that has been laser cooled to 200 µK. (Assume that the kinetic energy is 3/2kBT).
See Answer →Determine the wavelengths of the photons scattered at (i) 60° and (ii) 90° when X- rays of wavelength 4.5 pm are scattered from a target.
See Answer →A star emits light with wavelength 420 nm. An observer on earth measures the wavelength of the light received from the star to be 600 nm. Calculate the speed with which the star is moving.
See Answer →What is a biprism? The inclined faces of a glass biprism (µ = 1.5) make an angle of 1º with its base. The biprism is illuminated by sodium lamp (λ. = 589 nm) and the eye piece is at a distance of 1 m from the slit. A convex lens inserted between the biprism and the eye piece gives clear images of coherent sources in the focal plane of the eye piece. If the images are 0.4 cm apart in one case and 0.16 cm apart in the second case, calculate the width of interference fringes observed on the screen.
See Answer →A particle of rest mass 2.0 kg has an initial speed of 2x108ms-1. A constant relativistic force of magnitude 1.5x106 N is exerted on the particle in the same direction as the initial relativistic momentum for 1000 s. Calculate the magnitudes of the initial and final relativistic linear momentum and its final speed.
See Answer →A particle is travelling through the Earth's atmosphere at a speed of 0.6c. To an Earth-bound observer, the distance it travels is 4.0 km. How far does the particle travel in its own frame of reference?
See Answer →A spacecraft A has a speed 0.80c with respect to the Earth. If the speed of another spacecraft B with respect to spacecraft A is 0.50c, what is the speed of B with respect to the Earth
See Answer →Show that superposition of two linearly polarised light waves having different amplitudes and a finite phase difference can be used to produce elliptically plane polarised waves. Also show that the linear polarisation and circular polarisation are special cases of elliptical polarisation.
See Answer →A stretched string of mass 20 g vibrates with a frequency of 30 Hz in its fundamental mode and the supports are 40 cm apart. The amplitude of vibrations at the antinode is 4 cm. Calculate the velocity of propagation of the wave on the string.
See Answer →A sinusoidal wave is described by
y (x, t) = 3.0 sin (3.52t - 2.01x) cm
where x is the position along the wave propagation. Determine the amplitude, wave number, wavelength, frequency and velocity of the wave.
See Answer →Using Maxwell’s equations in free space, derive the wave equation for the electric and magnetic field vectors. (5+5) c) The expression of the electric field associated with an electromagnetic wave in vacuum is given by
sin(2π x 108 t+kz)
Determine the wave number, frequency, the direction of propagation and the magnitude and direction of the magnetic field associated with the wave.
See Answer →A current is flowing in an infinitely long straight wire. Using Biot-Savart law, show that the resultant magnetic field at a point along a line perpendicular to the wire is inversely proportional to the distance of the point from the wire.
See Answer →Obtain an expression of Fermi-Dirac distribution function. Plot Fermi function versus energy at different temperatures.
See Answer →Define thermodynamic probability of a macrostate. Establish the Boltzmann relation between entropy and thermodynamic probability.
S = kB lnW.
See Answer →A horizontal, straight wire carrying 12.0 A current from west to east is in the earth’s magnetic field B. At this place, B is parallel to the surface of the earth, points to the north and its magnitude is 0.04 mT. Determine the magnetic force on 1 m length of the wire. If mass of this length of wire is 50 g, calculate the value of current in the wire so that its weight is balanced by the magnetic force.
See Answer →5.4x10 21 electrons are confined in a box of volume 1cm3 . Calculate their Fermi wavelength and Fermi energy.
See Answer →Consider a classical ideal gas consisting of N particles. The energy of a particle is given by
=cp where c is a constant and p is the magnitude of the momentum. Calculate (i) the partition function of the system, (ii) internal energy, and (iii) CV .