A wave is represented by \Psi_1 = 10 \cos(5x - 25t). Find wavelength \lambda, velocity v, frequency f and the direction of propagation. If it interferes with another was given by \psi_2 = 20 \cos(5x + 25t + \pi/3), find the amplitude and the phase of the resultant wave. (All dimensions are in SI system).
How do you know that the light is a transverse wave? What is a quarter wave plate? How is it constructed?
Discuss the Fresnel diffraction pattern formed by a straight edge using the Cornu's spiral.
Derive the expression for resolving power of a diffraction grating with N lines. Calculate the minimum number of lines in the diffraction grating if it has to resolve the yellow lines of sodium (589.0\text{ nm} and 589.6\text{ nm}) in the first order.
In an experiment using a Michelson interferometer, explain with the help of suitable ray diagrams.
(i) Why do we need extended source of light,
(ii) Why do we get circular fringes, and
(iii) Shifting of fringes inwards or outwards as we shift the movable mirror.
Using the rocket equation and its integral find the final velocity of a single stage rocket. Given that
(i) the velocity of the escaping gas is 2500\text{ m/s},
(ii) the rate of loss of mass is. (where m_0) is the initial mass and 0.27 m_0 is the final mass).
An observer A sees two events at the same space point (\Delta x = \Delta y = \Delta z = 0) and separated in time by \Delta t = 10^{-6}\text{ s}. Another observer B sees them to be separated by \Delta t' = 3 \times 10^{-6}\text{ s}. What is the separation in space of the two events as observed by B? What is the speed of B relative to A?
Two spaceships are moving at a velocity of 0.9\text{ c} relative to the Earth in opposite directions. What is the speed of one spaceship relative to the other? (c = \text{velocity of light})
Derive the relationship between the impact parameter and the scattering angle for the scattering of an particle of charge +2e by a nucleus of charge +Ze. Calculate the impact parameter for an angle of deflection of 30^\circ if the kinetic energy of the alpha particle is 6 \times 10^{-13}\text{ J}.
Using the Lagrangian for the system of a planet and the Sun obtain the equation of motion. Use them to get the equations for the orbit.
(i) FETs have unique properties which make BJTs not suitable for some important applications. What are these most important FET applications? (ii) Briefly describe FETs as variable resistors.
(i) Obtain reciprocal lattice to normal BCC lattice. (ii) Describe Josephson junction and the effect. How is it exploited in the formation of a SQUID? Write down the applications of a SQUID. (iii) Distinguish between intrinsic and extrinsic semiconductors. Explain the concept of hole.
Explain a solar cell employing its characteristics on output quantity Venus quantities like load current, radiance and temperature.
(i) Give a qualitative account of BCS theory of superconductivity. (ii) Obtain an expression for conductivity of an intrinsic semiconductor. How does it vary with temperature? (iii) The resistivity of an intrinsic semiconductor is 4.5\text{ ohm-m} at 20^\circ\text{C} and 2.0\text{ ohm-m} at 32^\circ\text{C}. Calculate the energy band gap.
(i) What are sequential switching circuits (ii) Describe a simple sequential circuit. (iii) Describe a clocked RS Flip-Flop, (iv) Briefly describe ROMs.
Combinational switching circuit can perform an addition of the numbers held in two registers. (i) Write down the math table for the addition of two bits. (ii) Write down a Boolean expression for the necessary circuit functions. (iii) Arrive at the Exclusive-OR function. (iv) Draw the logic diagram for the circuit which performs the addition.
Describe briefly the various cycles for energy production in stars, relating them to the life history of a star. "Fusion reactors operate in the core of stars but have not become a reality on earth as yet." Comment on the statement.
Discuss briefly the concepts of fission barrier, excitation energy and activation energy on the basis of liquid drop model. Why {}^{235}_{92}\text{U} is fissionable by thermal neutrons while {}^{238}_{92}\text{U} is not ?
Use conservation laws to find the nature of residual nucleus when 50.0\text{ MeV} proton beam strikes the beryllium ({}^{9}_{4}\text{Be}) target nucleus producing a beam of neutrons.
A nuclear reactor operates at a power level of 10^8\text{ W}. What will be the flux of neutrons required to maintain this power level ? Given that a free neutron has an average lifetime of 10^{-3}\text{ second} before its capture in a uranium nucleus and energy released per fission is 200\text{ MeV}.
