## Engineering Physics - Dec 2015

### First Year Engg (Semester 1)

TOTAL MARKS:

TOTAL TIME: HOURS

### Solve any one question from Q1 and Q2

**1 (a)** Prove that in Newton's rings by reflected light the diameter of dark ring is proportional to square root of a natural number.(6 marks)
**1 (b)** Explain any two factors affecting the acoustics of a hall and remedies on that.(3 marks)
**1 (c)** The classroom has dimension, 20×15×5 m^{3}. The reverberation time is 3.5 sec. Calculate the total absorption of its surface and the average absorption.(3 marks)
**2 (a)** Explain piezoelectric effect. Explain how piezoelectric oscillator is used to produce ultrasonic waves, with the help of a neat circuit diagram.(6 marks)
**2 (b)** The resultant amplitude of a wave when monochromatic light is diffracted from a single slit is $ E_\theta = E_m = \dfrac {\sin \alpha }{\alpha} $. Then derive the condition of minima.(3 marks)
**2 (c)** A soap film having refractive index 1.33, and thickness 5×10^{-5} cm is viewed at an angle of 35° to the normal. Find the wavelength of light in the visible spectrum which will be absent from the reflected light.(3 marks)

### Solve any one question from Q3 and Q4

**3 (a)** Explain construction and working of Ruby Laser with the help of energy level diagram.(6 marks)
**3 (b)** What is Fermi level? Explain Fermi-Dirac probability distribution function.(3 marks)
**3 (c)** Plane polarized light of wavelength 5×10^{-5} cm is incident on a piece of quarter cut parallel to the optic axis. Find the least thickness of quarter for which the O-ray and E-ray combine to from plane polarized light.

Given: μ_{0}=1.5442, μ_{e}=1.5633.(3 marks)
**4 (a)** Explain Hall Effect. Derive the equation of Hall voltage and Hall coefficient.(6 marks)
**4 (b)** State and prove Malus law.(3 marks)
**4 (c)** Calculate the number of acceptors to be added to a germanium sample to obtain the resistivity of 20 Ω cm.

Given: μ=1700cm^{2}/V.sec.(3 marks)

### Solve any one question from Q5 and Q6

**5 (a)** Deduce Schr�dinger's time independent wave equation.(6 marks)
**5 (b)** Define phase (wave) velocity. Show that the phase velocity of matter wave is greater than the velocity of light.(4 marks)
**5 (c)** Calculate the deBroglie wavelength of electron of energy 1 keV.(3 marks)
**6 (a)** State Heisenberg's uncertainty principle and prove it by thought experiment of electron diffraction at a single slit.(6 marks)
**6 (b)** What is wave function? Explain what is normalization of wave function.(4 marks)
**6 (c)** The lowest energy of an electron trapped in a rigid box is 4.19 eV. Find the width of the box in A.U.(3 marks)

### Explain:

**7 (a) (i)** Critical field.(3 marks)
**7 (a) (ii)** Meissner effect.(3 marks)
**7 (b)** Explain any two properties of nano-particles in brief.(4 marks)
**7 (c)** Explain the applications of nano-particles in electronic industry.(3 marks)
**8 (a)** Explain the synthesis of nano-particles by chemical method in colloidal form with diagram and example.(6 marks)
**8 (b)** Explain in brief the BCS theory of superconductivity.(4 marks)
**8 (c)** Give any six applications of superconductivity.(3 marks)