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.

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.

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?

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

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.

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.

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.

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 10^{8 _t+kz)}

Determine the wave number, frequency, the direction of propagation and the magnitude and direction of the magnetic field associated with the wave.

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.

Obtain an expression of Fermi-Dirac distribution function. Plot Fermi function versus energy at different temperatures.

Define thermodynamic probability of a macrostate. Establish the Boltzmann relation between entropy and thermodynamic probability.

S = k_B lnW.

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.

5.4x10 ²¹ electrons are confined in a box of volume 1cm³ . Calculate their Fermi wavelength and Fermi energy.

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) C_V .

The energy of a capacitor is 4.0 _uJ after it has been charged by a 1.5 V battery. Calculate its energy when it is charged by a 6.0 V battery.

Derive Planck’s law of radiation and hence obtain Rayleigh-Jeans law and Wien’s law.

When two phases of a substance coexist in equilibrium at constant temperature and pressure, their specific Gibb’s free energies are equal. Using this fact, obtain Clausius-Clapeyron equation. 

Explain the phenomenon of polarisation of a dielectric. Show that, when a dielectric material is filled between the plates of a capacitor, the value of capacitance increases by factor of K, the dielectric constant of the material.

Define thermodynamic potentials. Derive Maxwell’s relations from thermodynamic potentials. 

Two particles carrying 4C and - 2C charges are placed on a 1 m long straight wire. Determine the point on the line joining these particles where the electric potential is zero with reference to the positively charged particle.