What do you understand by a perfect black body? Can it be realised in practice ? Show that the ratio of the emissive power to the absorptive power for all bodies at a given temperature is equal to the emissive power of a perfectly black body.
A network PQRS is connected as shown in the figure below. Apply Kirchhoff's law and show that the current flowing through the 20\ \Omega resistor PR is 0.029 A.
Two microscope slides of length 10 cm each form a wedge. At one end they are in contact and at the other end they are separated by a thin wire of diameter d (see the diagram below). Interference fringes are obtained when illuminated vertically by a monochromatic light of \lambda = 500\text{ nanometers}. The fringe spacing is found to be 1.25 cm. Estimate the diameter of the wire.
Differentiates between Rayleigh and Raman scatterings. Why is Raman scattering considered to be a breakthrough in molecular spectroscopy ? What are the advantages of using laser light in Raman spectroscopy ?
Water vapor shows Infrared absorption bands at 1595\text{ cm}^{-1}, 3652\text{ cm}^{-1} and at 3756\text{ cm}^{-1}. If the Raman spectrum is observed with the Argon Ion Laser 514.5\text{ nm}, at what wavelengths would you expect to find the Raman Stokes lines ?
A quartz quarter wave plate is to be used with the sodium light (\lambda = 5896\text{ \AA}). What should be its thickness ?
A narrow slit illuminated by monochromatic light of \lambda = 6400\text{ \AA} is placed at a distance of 3 metres from a straight edge. If the distance between the straight edge and the screen is 6 metres, calculate the distance between the first and the fourth dark bands.
A thin converging lens and a thin diverging lens are placed coaxially at a distance of 5 cm. If the focal length of each lens is 10 cm, find for the combination (i) the focal length, (ii) the power, (iii) the positions of the principal points.
Show that the ratio of the focal lengths of the two lenses in an achromatic doublet is given by \frac{f_1}{f_2} = - \frac{w_1}{w_2} where w_1 and w_2 are the dispersive powers of the lenses of focal lengths f_1 and f_2 respectively.
A siren of frequency 900 Hz is going towards a wall away from an observer at a speed 10 m/sec. Determine : (i) Frequency of sound directly heard from the siren. (ii) Frequency of sound reflected from the wall. (iii) Number of beats per second heard by the observer. (Velocity of sound = 330 m/sec)
Write down the equation of motion for a damped harmonic oscillator assuming the damping force proportional to the velocity of the particle. Obtain the general solution for its displacement as a function of time. Discuss the cases of 'overdamping', 'under-damping' and 'critical damping'.
For a freely falling body from the height h' on the surface of the earth in the northern hemisphere with a latitude \theta, show that the deviation of the body towards east at the final stage is given by \frac{1}{3} \omega \cos \theta \left(\frac{8h^3}{g}\right)^{1/2}, where \omega is the angular velocity of the earth and 'g' is the acceleration due to gravity.
If a single stage rocket is fired vertically from rest at the earth's surface burns its fuel in a time of 30 sec and their relative velocity = 3 km sec{}^{-1}, what must be the mass ratio m_0/m for a final velocity v of 8 km sec{}^{-1} ?
A particle moves in space with the Lagrangian L = \frac{1}{2} m (\dot{x}^2 + \dot{y}^2 + \dot{z}^2) - V + A \dot{x} + B \dot{y} + C \dot{z} where A, B, C are given functions of x, y, z. Find the corresponding Hamiltonian in terms of coordinates and momenta.
A meson of rest mass \pi comes to rest and disintegrates to a muon of rest mass \mu and a neutrino of zero rest mass. Show that the kinetic energy of motion of the muon is T = \frac{(\pi - \mu)^2 c^2}{2 \pi}
Write down the expression for the relativistic mass of a particle moving with a velocity v in terms of its rest mass. Establish from the above expression Einstein's mass-energy relation E = mc^2.
What do you mean by the moments and products of inertia ? Show that the angular momentum vector is related to the angular velocity components by linear transformation relations.
Explain the operation of the following circuit is a gate. Draw the truth table and find the operation carried out by this gate neglecting the source impedance.
junction saturation voltages and diode voltages in forward direction. Find the minimum value of h_{fe}.
Derive the various current components in a p-n-p transistor when it is actively biased. Using Ebers-Moll model, show that for the common-emitter configuration I_C = -\alpha I_E - I_{CO} \left(E^{V_C/V_T} - 1\right) where the symbols have the usual meaning.
Calculate the gain of the following amplifier circuit :
Given that g_m = 10\text{ mV/A}, r_d = 1\ \Omega and Z_L = 10\text{ k}\Omega.
