# Applied Physics 2005

Useful physical constants

Mass of electron = mo – 9-0 x 10-31 kg

Speed of light, C, = 3.0 x 108m/sec.

Plank’s constant, h, = 6.62 x 10?34 J. sec.

Q1 (a)State the fundamental postulates of the special theory of. relativity, and deduce the Lorentz transformation equation of space and time.

(b) Derive the formula for the variation of mass with velocity according to special theory of relativity.

(c) An electron is moving with speed 0.99C. What is its total energy ? Find the ratio of Newtonian kinetic energy to the relativistic kinetic.energy .

Q2 (a) What are the cardinal points of a coaxial lens system? State their properties and show their position in a diagram.

(b) What are the different methods for the production of ultrasonic waves ? Describe one of them in details. How will you determine the wavelength of these waves ?

(c) The volume of a room is 1200 m3. The wall area of the room is 220 m3, the floor area is 120 m3 and the ceiling area is 120 m2. The average sound absorption coefficient

(i)  for walls is 0.03,

(ii)  for the ceiling is 0.80 and

(iii)  for the floor is 0.06.

Calculate the average sound absorption and the reverberation time

Q3 (a) Give the theory of Fresnel’s Baptism to determine the wavelength of monochromatic light source

(b) Discuss the Fraunhofer diffraction at a single slit . Derive the necessary conditions for minima and maxima produced.

(C) A plane transmission grating has 16,000 lines to an inch over length of 5 inches. Find in the wavelength region of 6000 A. in the second order

(d)The resolving power of the grating and (5) the smaliesl wavelength difference that can be resolved .

Q4 (a) (i) What is meant by a digital circuit ? How does it differ from an analog circuit ?

(ii) Describe commutative , associative and distributive laws of Boolean Algebra .

(b) Define NAND and NOR gates and give their truth tables . Using NAND gates only obtain the following logic     operations

(i) AND

(ii) OR

(iii) NOT

(c)  State and Prove De Morgan’s theorem using truth table for two variables.

Q5 (a) Explain Compton effect and derive expression for Compton shift

(b)  Explain Bethe’s law . Compare it with Snell’s law in optics

(c) (i) If the uncertainty in position of electron is 4×10?10m, calculate the uncertainty in its momentum.

(ii) Calculate the longest wavelength that can be analyzed by a rock salt crystal of spacing.= 2.82

A in the first order .

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