Show that if an ideal gas is compressed isothermally its compressibility is \frac{1}{p}, whereas if it is compressed adiabatically its compressibility is \frac{1}{\gamma p} where \gamma = C_p / C_v.
ifos-2012-subject-04-001
What are bosons ? Based on Bose-Einstein statistics, derive the expression for Bose-Einstein condensation.
ifos-2012-subject-04-006
Explain the thermodynamic behaviour of an ideal Fermi gas. What are fermions ?
ifos-2012-subject-04-005
Explain the physical significance of the Poynting vector \bar{S}. What is represented by the closed integral \oint \bar{S} \cdot d\bar{a} for a closed surface of area \bar{a} ?
ifos-2012-subject-03-007
If considered a blackbody as a radiation-filled cavity at a uniform temperature T, demonstrate with an appropriate figure the electromagnetic wave patterns inside the cavity of length L for wavelengths \lambda = L, \frac{3}{2} L and 2L.
ifos-2012-subject-03-009
Show that the complex propagation constant k of an electromagnetic wave propagating in an isotropic dielectric medium with conductivity \sigma can be given by k = k_r + i k_i with k_r \approx \frac{2\pi}{\lambda_o} n \left[ 1 + \frac{1}{8} \left( \frac{\sigma}{\omega \varepsilon} \right)^2 \right] and k_i \approx \frac{2\pi}{\lambda_o} n \left[ \frac{1}{2} \left( \frac{\sigma}{\omega \varepsilon} \right) \right] where n = \sqrt{\varepsilon / \varepsilon_o} and \lambda_o = \omega / 2\pi c; \varepsilon and c being the permittivity of the dielectric and velocity of light in free space, respectively.
ifos-2012-subject-03-006
For the above system, show that the energy per unit cavity volume in the frequency range of \nu and \nu + d\nu can be given by u(\nu)d\nu = \frac{8\pi\nu^2 k_B T}{c^3} d\nu where k_B is the Boltzmann's constant. Discuss the limitations of this formula and how did Planck put forward the correct analysis.
ifos-2012-subject-03-005
Find out the number of photons in a cavity of volume 1\cdot 00\text{ cm}^3 under thermal equilibrium at temperature T = 1000\ {}^\circ\text{K}. Assume that \int_0^\infty \frac{x^2 dx}{e^x - 1} = 2\cdot 405.
ifos-2012-subject-03-001
How do you justify the statement : "A current carrying conductor, although has no net charge experiences a force when placed in a magnetic field."
ifos-2012-subject-03-004
A long straight solenoid has 100 turns in the secondary and 3000 turns per centimeter in the primary. The area of cross-section of the solenoid is 3 square centimeters. Calculate the mutual inductance.
ifos-2012-subject-03-003
Explain the term 'mutual inductance' between two coils carrying current. Describe a method of determining mutual inductance between two coils of wire with relevant theory.
ifos-2012-subject-03-002
The dielectric constant of a medium is 3. The Electric field in the dielectric is 10^6\text{ Vm}^{-1}. What are the electric displacement and polarization ?
ifos-2012-subject-03-008
Explain the Fraunhofer diffraction at a single slit and obtain the condition for minima. Derive the expression for resolving power of a grating.
ifos-2012-subject-02-005
What are Einstein's A and B coefficients ? Establish a relation between them.
ifos-2012-subject-02-008
An optical waveguide has core and cladding of refractive indices 1\cdot 46 and 1\cdot 45 respectively. (i) Calculate the maximum number of modes with wavelength \lambda = 900\text{ nm} that can travel if it is a planar waveguide of core thickness 10\ \mu\text{m}. (ii) What is the number of modes if it is a cylindrical fiber of diameter 10\ \mu\text{m} ?
ifos-2012-subject-02-007
A step-index silica fiber consists of core of refractive index 1\cdot 450 and diameter 90\ \mu\text{m}. If the numerical aperture of the fiber is 0\cdot 16, calculate : (i) the acceptance angle of the fiber, (ii) refractive index of the cladding, and (iii) if the fiber is immersed in water of refractive index 1\cdot 33, how does the acceptance angle change ?
ifos-2012-subject-02-006
Two lenses of focal lengths 8\text{ cm} and 4\text{ cm} are placed at a certain distance apart. Calculate the distance between the lenses if they form an achromatic combination.
ifos-2012-subject-02-004
A body describing simple harmonic motion (SHM) has a maximum acceleration of 8\ \pi\text{m/sec}^2 and a maximum speed of 1\cdot 6\text{ m/sec}. Find the time period (T) and the amplitude (A) of SHM.
ifos-2012-subject-02-003
When two tuning forks were sounded together, 24 beats were produced in 6\text{ seconds}. After loading one tuning fork with wax, they produced 30 beats in 6\text{ seconds}. If the unloaded fork frequency is 512, what is the frequency of the other ?
ifos-2012-subject-02-002
Explain mathematically the phenomenon of beats. How does it differ from that of interference ?
ifos-2012-subject-02-001