END TERM EXAMINATION
B.TECH. FIRST SEMESTER
Time: 3 hours Maximum Marks:75
☞Note: Attempt any five questions including Q.No.1 which is compulsory. Select one question from each unit. Draw neat scientific diagrams wherever necessary. Work in SI units. Assume date wherever necessary.
Question 1: Attempt any nine of the following:
(a) Two coherent sources whose intensity ratio is 4:1 produce interference fringes, find the ratio of maximum intensity in the interference pattern.
(b) A slit is located ‘at infinity’ in front of lens of focal length I m and is illuminated normally with light of wavelength 600 nm. The first minima on either side of the central maximum of the diffraction pattern observed in the focal plane of the lens are separated by 6 nm. What is the width of the slit?
(c) The axes of a polarizer and analyzer are oriented at 30° to each other.
(i) If un-polarizer light of intensity I0 is incident on them, what is the intensity of the transmitted light.
(ii) Polarized light of intensity I0is incident on this polarizer-analyzer system. If the amplitude of the light makes an angle of 30° with the axis of the polarizer, what is the intensity of the transmitted light?
(d) What is the role of the core in an optical fibre.
(e) A source is emitting 100 W of green light at a wavelength of 500 nm. How many photons per second are emerging from the source.
(f) A loudspeaker cannot be used for the production of ultrasonic waves. Justify.
(g) A 1 kg object is lifted from the floor to a table 30 cm above the floor. By how much did the mass of the object increase because of its increased potential energy?
(h) Explain the principle of the Magnetic Resonance Imaging technique.
(i) Derive the definition of Curie as a unit of activity. Assume that the half-life of radium is 1620 years having an atomic weight of 226 kg/k mol.
(j) Find the frequency of rotation of a proton in a cyclotron whose magnetic fields is I T. Assume that the mass of the proton is 1.67 × 10-27 kg.
(a) Explain the terms temporal and spatial coherence in the context of the interference phenomenon. Explain why interference due to division of amplitude is observed in thin films.
(b) Illustrate with a neat scientific, well labelled diagram the formation of fringes due to a Fresnel’s Bi-prism.
(c) Illustrate with a neat scientific, well labelled diagram the necessity of an extended source to observe fringes in a thin film.
(d) Derive the relation for path difference and subsequently the width of a single band for a wedge shaped film.
(e) An interference pattern is first obtained using a bi-prism set-up. When a thin sheet of glass (μ=1.5) μm thickness is introduced in the path of one of the interfering rays, the central fringe is shifted to a position normally occupied by the fifth fringe. Calculate the wavelength of light used.
(a) Distinguish between Fraunhoffer and Fresnel diffraction.
(b) Derive the intensity pattern for a Fraunhofer’s diffraction due to a single slit using the analytical method.
(c) Show that the intensity pattern due to N slits is the product of two terms the diffraction pattern due to a single slit and the interference pattern due to N slits.
(d) Transparency and opacity ratio in a grating having 5000 lines in one cm, is 1:2 which orders of the maxima will be missing in the diffraction grating?
(a) Explain the superposition of polarized light. Hence, differentiate between plane polarized, circularly polarized and elliptically polarize lights.
(b) Differentiate between uni-axial and bi-axial crystals.
(c) Illustrate with a series of neat scientific, well labelled diagrams the formation of a Nicol prism from a double refracting crystal.
(d) A plane polarized light is incident on a quarts plate is cut parallel to the axis. Calculate the least thickness of the plate for which the o-end e-ray recombine to form a plane polarized light.
Assume that μe =1.5533;
μ0= 1.5442 and
(a) Illustrate with a schematic scientific diagram, the dependence of refractive index on the radial distance for a graded index optical fibre.
(b) Define and explain numerical aperture for an optical fibre..
(c) Show that the fraction of atoms in the excited state is much smaller than that in the ground state at a temperature of 3000 k and an energy gap of 2eV.
(d) State the characteristics of the spontaneous stimulated emission using the concept of Einstein’s A and B coefficient. Further derive that the probability of radiation-induced transitions per unit time equals the probability of stimulated emissions per unit time.
(a) At what speed will an object of length 100 cm be measured as 50 cm an observer at rest.
(b) The total energy of the particle is exactly twice its rest energy. Calculate the velocity of the particle.
(c) Explain the Michelson-Morely experiment stating clearly its aim and results derived therein. How did the results of the experiments lead to the special theory of relativity?
(d) Explain the concept of time dilation citingan experimental evidence.
(a) An ultrasonic interferometer-based is used to measure the velocity of ultrasonic waves in sea water. The distance between two consecutive anti-nodes is found to be 0.4 mm. calculate the velocity of waves in sea water. Frequency of the waves generated by the crystal is 1.5 MHz.
(b) Enumerate the different methods for the production of ultrasonic waves and describe ine of them in detail. How will you determine the wavelength of these waves?
(c) We want to generate an ultrasonic wave of frequency ‘f’ by both the popular methods i.e. magneto-striction and piezo-electric methods. What should be the length of the nickel rod for the magneto-striction method and the thickness of the quarts crystal for the piezoelectric method. Assume
the Young’s modulus of nickel=2.14×1011N/m2;
Density of nickel=8908kg/m3;
Young modulus for quartz=7.9×1010 N/m2;
Density of quartz= 2650 kg/m3.
(a) A cyclotron is used to accelerate protons having a mass half that of the deuterons.
(i) If the magnetic field has an intensity of 2.0 T, what is the change in the frequency of the oscillating electric field.
(ii) What is the maximum energy acquired by the protons if the potential applied across the does of the cyclotron are 25kV?
(b) Explain how the credibility of the laws of conservation of energy and momentum led to the concept of endoergic and exoergic nuclear reactions.
(c) The binding energy per nucleon for 238U is about 7.5 MeV, whereas it is about 8.5 meV for nuclei of half that mass. If a 238U nucleus were split into two equal size nuclei, about how much energy would be released in the process?
(d) If the magnetic field is directed upwards and the particles are moving counterclockwise in a cyclotron, what is the charge on the particles?
(a) The half-life of 60Co is nearly 5.25 years. Find the duration it will take for the activity of the sample to decrease to (i) (1/2) of its original value, (ii) (1/4) of its original value.
(b) The temperature at the core of the sun is 2×107 K. The hydrogen atoms present, in the presence of protons, converts into deuterium atoms, which further converts into helium atoms. Write the Stellar-thermo nuclear reactions. Further using the concept of energy-mass equivalence, calculate the energy released in this process in watt-hours.
(c) Enunciate the phenomenon of nuclear fission and fusion giving at least two equations each as an example.