IGNOU BPHCT-137 - Wave and Optics

PART A 1. a) Obtain an expression for energy transported by a progressive wave on a taut string. Also show that the power transported by the wave is proportional to the wave velocity. b) The fundamental frequency of a string instrument is 580 Hz. (i) Calculate the frequency of the first and third harmonics generated on it. (ii) If the tension in the string is doubled, calculate the new fundamental frequency. c) Show that when two in-phase linearly polarised light waves are superposed, the resultant wave has fixed orientation as well as amplitude. Depict the orientation of electric field vector of the resultant wave in the reference plane. 2. a) Explain how Michelson interferometer can be used to determine the wavelength of light? b) In a Young’s double slit experiment, a monochromatic light of wavelength 600nm is used. The slits are 0.2mm apart. An interference pattern is observed on a screen 0.6 m away. Calculate the distance between the central maxima and the third minima on the screen. c) A Michelson interferometer is illuminated with monochromatic light. When one of the mirrors is moved 2.5 x 10–5m, 100 fringes cross the field of view. Determine the wavelength of the incident light. d) Obtain an expression of the displacement of the nth bright fringe in double slit experiment when a thin transparent plate of thickness t and refractive index μ is introduced in the path of one of the two interfering waves. How the fringe-width is affected with the introduction of the plate? e) Interference fringes are formed by reflection from a thin air wedge by using sodium light of wavelength of 5893 Å When viewed perpendicularly, 12 fringes are observed in a distance of 1cm. Calculate the angle of wedge. PART B 3. a) In the experimental set up to observe diffraction pattern of a straight edge, the distance of the edge from the source is 30 cm and the distance of the screen from the edge is 40 cm. The wavelength of the light used is 480 x 10–5 cm. Calculate the position of the first and third minima from the edge of the geometrical shadow. b) Obtain an expression for intensity distribution in a single slit diffraction pattern. c) A plane light wave of wavelength 580 nm falls on a long narrow slit of width 0.5 mm. (i) Calculate the angles of diffraction for the first two minima. (ii) How are these angles influenced if the width of slit is changed to 0.2 mm? (iii) If a convex lens of focal length 0.15 m is now placed after the slit, calculate the separation between the second minima on either side of the central maximum. 4. a) Explain the three light-matter interactions with the help of atomic level diagrams. Write the corresponding Einstein’s equations. b) Explain the role of resonant cavity in determining the coherence and monochromaticity of a laser light. c) Describe the types of optical fibres. How can the pulse dispersion in the optical fibre be reduces? d) A laser cavity of 25 cm length sustains the radiation of 6300 Å. Calculate the number of modes and mode separation. If the spread in wavelength is 0.02 Å, calculate the coherence length and coherence time. e) The refractive indices of core (n1) and cladding (n2) materials of two optical fibres A and B are as follows: (n1)A = 1.46 and (n2)A = 1.38 and (n1)B = 1.52 and (n2)B = 1.41 Which of the two fibres will have higher gathering capacity?

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. PART B 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.