PHE-09 Solved Assignment 2019 | Optics (English Medium)

Description

Note: Attempt all questions. Symbols have their usual meanings. The marks for each question are indicated against it. Your answers to descriptive questions should be in your own words.

1. Answer any four parts:
   a) The electrical breakdown in air occurs at electric field strength of 3.5MV m^-1. Calculate the corresponding intensity of a plane wave
   b) Highlight the advantages offered by Fresnel bi-prism arrangement for observing interference patterns.
   c) Compare the Fraunhofer diffraction patterns of single slit and double slits.
   d) Discuss temporal and spatial coherences.
   e) Explain light transmission through optical fibres.
2. a) Obtain expressions for reflection and transmission amplitude coefficients when electric vector associated with a plane monochromatic e. m. wave is in the plane of incidence.
   b) Show that plane polarised light and circularly polarised light are special cases of elliptically polarised light.
3. a) A double slit interference pattern is produced by a parallel beam of light passing through two slits of unequal widths 20 λ and 40 λ, respectively, where λ is the wavelength of the light used. The distance between the centres of the slits is 1,000 λ. If the fringes are observed on a screen far off from the slits (D >> 1,000 λ), calculate the separation of two adjacent maxima.
   b) A plano-convex lens of radius 1.0 m is placed on an optically flat glass plate and is illuminated by an extended monochromatic source. Assume that the point of contact is perfect. The diameters of the 15th and 5th dark rings in the reflected light are 5.90×10^-3 m and 3.36×10^-3 m. Next, the space between the lens and the glass plate is filled with a liquid. The diameter of the 5th ring changes to 3.0×10^-3 m. Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the wavelength of light is 589 nm .
4. a) A plane wave of wavelength 600 nm falls on a long narrow slit of width 0.6 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 0.2 m is now placed after the slit, calculate the separation between the second minima on either side of the central maximum.
   b) For the arrangement described in 4(a) above, repeat the calculations for the first two maxima on either side of the central maximum.
   c) Use Fresnel construction to discuss diffraction pattern produced by a circular opaque disc.
5. a) An atomic system, consisting of two energy levels with population of higher energy level less than that of the lower level, is in thermal equilibrium. Show that the absorption of radiation dominates stimulated emission if radiation of appropriate frequency is introduced into the system. Comment on the consequences of this fact for laser action.
   b) Two energy levels of an atomic system are separated by energy corresponding to frequency .H100.314z× Assume that all atoms are in one or the other of these two energy levels. Compute the fraction of atoms in the upper energy level at temperature 400 K. Take k_B = 1.38 x 10^-23 JK^-1 and h = 6.6 x 10^-34 Js.
   c) The refractive indices of the core and cladding materials of an optical fibre are 1.53 and 1.34 respectively. Calculate the numerical aperture and light gathering capacity of the fibre.

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