Explain the phenomenon of pulse dispersion in a step index optical fibre.
Explain the phenomenon of self focusing of laser beams.
How does Doppler effect of light of relativistic physics qualitatively differ from its non-relativistic analogue ? Calculate the Doppler shift in the frequency of a photon travelling along the y-axis. with respect to an observer moving along the x-axis with a constant speed v.
Obtain an expression for the intensity of light in the Fraunhofer diffraction pattern due to a circular aperture. What is Airy pattern ? Explain with a neat diagram.
Two transverse harmonic waves, each of amplitude 5mm, wavelength 1m and speed 3 m/s are travelling in opposite directions along a stretched string fixed at both ends. Obtain an expression for the standing wave Produced. Locate the position at the nodes and antinodes.
An ideal massless spring of force constant k has a mass m attached to one of its ends, the other and being fixed to a rigid support. The spring is horizontal floor, A resistive force -bv, proportional to the velocity v acts on the mass. Assuming the damping to be light, obtain the frequency of oscillation. When m = 0.1\text{ kg} and k = 10\text{ N/m}, it is found that the frequency of oscillation is \sqrt{1/2} times the frequency in the absence of damping. Calculate the value of the constant b.
Write the Lagrange's equation for a system of particles which is acted upon by Conservative forces. What is a cyclic coordinate ? Show that the generalized momentum conjugate to a cyclic coordinate is conserved.
Write the Euler's equations for the rotational motion of a rigid body with one point fixed, under the action of torque N. Apply these equations to discuss the rotational motion of a symmetrical top in the absence of any force other than the reaction at the fixed point.
An observer S_1 sees two bodies A and B having equal rest mass approach each other with equal but opposite velocities 4c/5. To a second observe S_2, the body A is at rest. What us the velocity of the body B as seen by observe S_2? What are the kinetic energies of the body B in the frames of S_1 and S_2?
A block of mass m, attached to an ideal massless spring of force constant k, is at rest on a smooth horizontal floor. A second block of mass 2 m, moving with an initial velocity strikes the free end of the spring. The collision is one dimensional and elastic. (i) Calculate the maximum compression of the spring. (ii) What are the velocities of the block long time after the collision?
(i) Discuss the variation of free carrier concentration with temperature for an intrinsic and extrinsic semiconductors. (ii) Explain the effect of negative and positive voltage feedback on an amplifier characteristics.
Write down the characteristics of an ideal operational amplifier. Explain the term virtual ground. Draw a circuit diagram showing virtual ground in an operational amplifier.
Explain Meissner effect and Josephson effect. Describe their applications in the field of superconductivity.
(i) Show that a negative logic OR gate is like a positive logic AND gate. (ii) Distinguish between Hadrons and Leptons.
What are the main applications of JFET? Discuss their advantages over bipolar transistors. Explain the working of n-channel JFET with the help of a schematic diagram.
Distinguish between particle and antiparticle. How antiparticles were discovered?
Mention the conservation laws for strong, electromagnetic, and weak interactions.
(i) What is the lowest non zero angular momentum for an elementary particle? Name at least three elementary particles having such an angular momentum. (ii) Write the spectral symbol of the term with S= 1/2, J = 5/2 and g = 6/7.
(i) Explain how neutrino was discovered from the [[UNCLEAR]]-decay of radioactive nuclei. (ii) Show that for a cubic lattice, the difference between the successive h, k, l planes is given by d_{h,k,l} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}
Explain shell model of the nucleus. Give evidence for nuclear shell structure. What are the limitations of the shell model?