BE Computer Engineering (Pokhara University) Applied Physics (PU, PHY 110) Question Paper 2078

(a) Set up the differential equation of a damped harmonic oscillator and obtain its solution for the under-damped case. Hence define the logarithmic decrement and the quality factor (Q-factor) of the oscillator. (8)

(b) A body of mass 0.2 kg is attached to a spring of force constant 80 N/m and oscillates in a medium that exerts a damping force proportional to velocity with damping constant b = 4 kg/s. Calculate (i) the angular frequency of the damped oscillation and (ii) the time in which the amplitude falls to 1/e of its initial value. (6)

(a) Explain the formation of Newton's rings by reflected light. Derive expressions for the diameters of the bright and dark rings and show that the diameter of the dark rings is proportional to the square root of the natural numbers. (9)

(b) In a Newton's rings experiment the diameter of the 10th dark ring changes from 1.40 cm to 1.27 cm when a liquid is introduced between the lens and the glass plate. Calculate the refractive index of the liquid. (5)

(a) State Maxwell's equations in differential form for a non-conducting, charge-free medium and explain the physical significance of each equation, including the concept of displacement current. (8)

(b) Starting from Maxwell's equations, derive the wave equation for the electric field in free space and obtain an expression for the velocity of electromagnetic waves in vacuum. Show that this velocity equals the speed of light. (6)

(a) Derive the time-independent Schrödinger wave equation for a particle of mass m moving in one dimension. (6)

(b) Apply it to a particle confined in a one-dimensional infinite potential well of width L. Obtain the normalized wave functions and the expression for the allowed energy levels, and sketch the wave functions and probability densities for the first three states. (8)

(a) Distinguish between Fresnel and Fraunhofer classes of diffraction. (3)

(b) A plane transmission grating has 5000 lines per cm. Find the angle of diffraction for the second-order principal maximum when light of wavelength 5890 Å is incident normally on the grating. (4)

(a) State and explain Brewster's law. Show that when light is incident at the polarizing angle, the reflected and refracted rays are mutually perpendicular. (4)

(b) Calculate the polarizing angle for light passing from air into glass of refractive index 1.54. (3)

Explain the terms spontaneous emission, stimulated emission and population inversion. With the help of a suitable energy-level diagram, describe the principle of operation of a He-Ne laser.

(a) Define acceptance angle and numerical aperture of an optical fibre and derive an expression relating the numerical aperture to the refractive indices of the core and cladding. (4)

(b) An optical fibre has a core of refractive index 1.50 and a cladding of refractive index 1.47. Calculate its numerical aperture and acceptance angle. (3)

(a) Explain the Hall effect and derive an expression for the Hall coefficient. State two applications of the Hall effect. (4)

(b) The Hall coefficient of a specimen of doped silicon is found to be 3.66 × 10⁻⁴ m³/C. Determine the type and concentration of the charge carriers. (3)

(a) Distinguish between polar and non-polar dielectrics. Explain the different types of polarization that can occur in a dielectric material. (4)

(b) State the Clausius-Mossotti relation and explain the physical quantities involved in it. (3)

(a) Distinguish between diamagnetic, paramagnetic and ferromagnetic materials with one example of each. (3)

(b) Draw and explain the B-H hysteresis loop of a ferromagnetic material. Indicate retentivity and coercivity on the loop and state the significance of the area enclosed by the loop. (4)

(a) State Heisenberg's uncertainty principle and use it to explain why an electron cannot exist inside the nucleus. (4)

(b) Calculate the de Broglie wavelength of an electron that has been accelerated through a potential difference of 100 V. (3)