Section A
Q1.
(a)
A bead slides on a wire in the shape of a cycloid described by the equations
x = a ( heta - sin heta)
y = a (1 + cos heta)
with 0 le heta le 2pi.
Find the Lagrangian and equation of motion.
(b) Show that the relativistic invariance laws of conservation of momentum lead to the concepts of variation of mass with velocity and mass energy equivalence.
(c) A parallel beam of light of wavelength 5890 Å is incident at an angle of 30^{circ} on a plane transmission grating with 15000 lines/inch. Find the highest order of spectrum that can be observed.
(d) Discuss absorption loss in an optical fibre comparing and contrasting the intrinsic and extrinsic absorption mechanisms.
(e) Although the principle of operation of a basic LASER is based upon two energy levels, why does one need a 3-level or a 4-level scheme to achieve satisfactory lasing ? Explain your answer with special reference to a Ruby-laser.