1. a) The mathematical expression for one dimensional wave travelling along the positive x-direction is given as
y(x,t) = 0.02 sin (42 x -1886t)m
where x is in meters and t is in seconds. Determine the direction of propagation of the wave and calculate its amplitude, wavelength, frequency and velocity.
b) Determine the frequencies of the fundamental mode and the next two harmonics that can be set up on a sitar string of length 1.0 m. Take the speed of waves of the string to be 2.8 x103ms-1.
c) The electric field vectors of two light waves propagating along the positive z-direction are given as
2. a) Derive an expression for the displacement of the nth bright fringe in Young’s double-slit experiment when a thin transparent plate of refractive index
and thickness t is introduced in the path of one of the constituent interfering beams of light. Will there be any change in the fringe-width after the introduction of the plate?
b) i) Distinguish between fringes of equal inclination and fringes of equal thickness.
ii) Newton’s rings are formed in reflected light of wavelength 5890 x10-8cm 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.
c) Explain how Michelson interferometer is used to determine the refractive index of a thin plate.
3. a) What is a zone plate? How does a positive zone plate differ from a negative zone plate? Show that each Fresnel zone has nearly the same area.
b) In the Fraunhofer diffraction pattern due to a single slit, the intensity of the central spot is maximum. Explain on the basis of geometrical considerations.
c) The Fraunhofer diffraction pattern due to a single slit of width 0.4 cm is obtained with the help of a lens of focal length 30 cm. If the wavelength of light used is 5890 Å, calculate the distance of the first dark fringe and the consecutive bright fringe from the axis.
d) The radius of the fifth zone of a zone plate is 2 mm. Considering the zone plate as a converging lens, calculate its focal length for light of wavelength 4800 Å.
4. a) What do you understand by spatial and temporal coherence?
b) Explain the meaning of coherence length.
c) What is the difference between spontaneous emission of radiation and stimulated emission of radiation?
d) How is holography different from ordinary photography?
e) What are the advantages of using optical fibre as communication medium?
5. a) In a laser, the lasing levels are the first excited state and the ground state of the active medium. If the energy of the first excited state is 1.5eV, calculate the frequency of the laser light.
b) The refractive index of the core and cladding materials of an optical fibre is 1.46 and 1.38, respectively. Calculate the critical angle, numerical aperture and acceptance angle at the air-fibre interface.