Explain the general principle of laser action. What do you mean by population inversion ? Discuss the transitions involved in the ruby laser. A pulsed laser is rate at 10\text{mw}. It generates 3\text{ ns} wide pulses at frequency 500\text{ Hz}. Compute the instaneous power in the pulse.
Give an account of the origin of optical activity in eqartz crystal. A wafer of crystalline eqartz of thickness. 2.945 \times 10^{-5}\text{ m} is used to change a beam of linearly polarised light (\lambda = 589\text{ nm}) into circularly polarised light. Find the difference in refractive index for the two waves in the crystal, assuming this to be minimum thickness that will produce the effect.
Write a short note on Formation and reconstruction of hologram.
Define coherent length. A helium-neon laser emits radiation at wavelength \lambda = 632.8\text{ nm} with \Delta\lambda = 2\text{ pm}. Calculate the coherence wavelength.
An interference pattern is obtained by using two coherent sources of light, and the intensity variation is observed to be \pm 10\% of the average intensity. Determine the relative intensities of the interfering sources.
The refractive indices of material of wavelength 5090\text{ \AA}, 5340\text{ \AA} and 5890\text{ \AA} are equal to 1.64, 1.640 and 1.630 respectively. Estimate the phase group velocities of light near \lambda = 5340\text{ \AA}.
N coherent oscillation given by \zeta_K a \cos = (\omega t + K \phi) \quad K = 1, 2, 3, \ldots N are added, where a and \phi are independent of K. Deduce the expression for amplitude of the resultant oscillation.
Give a mathematical explanation for the production of beats. Calculate the velocity of sound in a gas in which two wave of length 60.0\text{ cm} and 60.6\text{ cm} produce 5 beats per sec.
A vibrating source is moving in a medium with speed V_s which is greater than the speed V of propagation of the wave in the medium. Apply Huygens principle to show that a conical wave front of half angle \sin^{-1}\left(\frac{V}{V_s}\right) is generated.
Write a short note on Rutherford Scattering.
Find the fractional decrease of kinetic energy of a particle of mass m_1 when a head-on elastic collision takes place with another particle of mass m_2 initially at rest. In this context show why hydrogen would be best to be used for slowing down neutrons. Actually \text{D}_2\text{O}, not \text{H}_2\text{O} is used why?
A rocket of mass 1000\text{ kg} is ready for a vertical take off. The exhaust velocity of its fuel is 4.5\text{ km/s}. Deduce (i) the minimum rate of fuel ejection so that the rocket weight be just balance, (ii) the velocity acquired in 8\text{ s} if the fuel ejection rate is 2.50\text{ kg/s}. (You may neglect the effect of changing mass of the rocket in the given conditions.)
Write a short note on Conchs forces.
A radioactive nucleus mass m_0\text{ amu} emits an alpha particle with kinetic energy E_a. If the disintegration occurs when the nucleus is free, deduce an expression for the energy evolved (E_t) during the disintegration.
Write a short note on Mass energy equivalence.
State Lorentz transformation equations. Show that for v/c \ll 1, the lorentz transformation equations reduce to Galilean transformation equations. Explain the physical significances of Larentz transformations.
Define Reynold's number, the cross sectional radius of a pipeline decreases following the relation. r = r_0 e^{-ax}, where a = 0.6\text{ m}^{-1}, x is the distance (in \text{m}) from the pipeline inlet. Calculate the ratio of Reynold's number for two cross sections separated by \Delta x = 3\text{m}.
A top is spinning with an angular velocity \omega about its axis which is initially vertical Find the condition of stability, if the axis be given a slight nutation.
Prove that the rate of angular momentum of a system about a fixed line is equal to the total torque of the external forces about that line
A satellite, revolving in a circular equatorial orbit at height 1.36 \times 10^4\text{ km} from earth's surface from west to east, appears over some spot at the equator every 6\text{ hrs}. Show that the data are consistent with known earth's radius 6.4 \times 10^3\text{ km} and g = 9.8\text{ ms}^{-2} at earth's surface.
