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Physics 7. [4] - II Ex/PH/T/2A/T/66/2012 B ACHELOR OF ENGINEERING EXAMINATION, 2012 a) Light of wavelength 5893 Å is reflected at nearly normal incidence from a soap film of refractive index 1.42. What is ( 1st Year, 2nd Semester ) the least thickness of the film that will appear as black? P HYSICS - II A Deduce the necessary expression used in the calculation. 3+7 Time : Three hours Answer any five questions. b) Derive an expression for the intensity at a point in the Fraunhofer type of diffraction produced by a single slit illuminated by monochromatic light. 8. Full Marks : 100 1. a) i) 10 State and prove Gauss’s law in electrostatics. 6 ii) Use Gauss’s law to calculate the electrostatic field due a) Distinguish between polarised and unpolarised light. Explain to a uniform spherical charge distribution of radius R at the terms (i) plane of polarization and (ii) plane of vibration. an internal point distant r from the centre of the charge distribution. b) Explain Brewster’s law. Show, by Brewster’s law, that light incident on a transparent substance at polarising angle gives b) i) reflected and refracted rays at right angles to each other. What is meant by an electric dipole? Calculate the electrostatic potential at a point Q (r, θ) r due to an electric dipole of moment p . [(r, θ) is c) Calculate the minimum number of lines in a grating which will just resolve the lines of wavelengths 5890 Å and 5896 Å in the second order. 4 measured w.r.t the centre of the dipole]. 8+7+5 5 ii) Obtain expressions for the radial and transverse components of the electric field intensity at Q (r, θ) . 5 2. i) State biot-Savarti law. 2 ii) Using Biot-Savarti law find the magnetic field at an axial point at a distance ‘x’ from the centre of a circular coil of radius R carrying current ‘i’. 7 iii) Use the above expression to calculate the field at a point on the axis of a solenoid. 8 [ Turn over A [2] [3] iv) Discuss the case when the solenoid is long. What is the field 3. i) at one end of the solenoid? 3 Give a quantitative statement of Faraday’s law. 2 iv) Deduce Bragg’s law of X-ray diffraction. Can visible light be Bragg-diffracted from a crystalline material? 5. with the necessary underlying theory. 3 of 40 volts. Ignoring relativistic corrections obtain the 5 de Broglie wavelength of the electron. iv) Deduce an expression for the growth of current in a circuit 4 b) X-rays with λ = 1·0Å are scattered from a carbon block. with resistance and inductance. What is meant by “time constant”? 8 ii) An electron is accelerated through a potential difference iii) Find out the equivalent inductance of two inductors when connected in series. Which experiment conclusively proved the wave like nature of electrons? Give an account of the experiment ii) Define coefficient of self and mutual inductance. What are their units in SI system? a) i) 5 The scattered radiation is viewed at 90o to the incident beam. 6 (i) What is the Compton shift ∆λ? (ii) What kinetic energy is v) A 2V battery of negligible internal resistance is applied to a imparted to the recoil electron? 8 coil of inductance 1 henry and of resistance 1 ohm. Calculate the time required by the current to attain a value half of that in the steady state. 4. i) 4 State the postulates which led to Bohr’s theory of line spectra. 2 6. a) What is meant by interference of light? What are the conditions for sustained interference of light? 2+3 b) Derive an expression for the intensity at a point in the region of interference due to superposition of two sinusoidal waves with nearly equal amplitudes. Show graphically the intensity ii) Derive an expression for energy of radiation when an electron jumps from one orbit to another in a hydrogen like atom. 5 iii) Explain the origin of continuous and characteristic X-ray spectra. What is meant by Kα line? Hence show that the interference pattern does not violet the law of conservation of energy. 6+4 c) If the amplitudes of two coherent light waves are in the ratio 1:4, calculate the ratio of maximum and minimum intensity An X-ray tube is operated at 50 kV. Calculate the minimum wavelength produced in X-ray spectra. variation with phase difference between the two waves. in the interference pattern. 5 5+3 [ Turn over