If the avenge distance between the sun and earth is 1.5 \times 10^{11} m, find the avenge solar energy flux and the earth (solar constant) given the power radiated by the sun = 3.8 \times 10^{26} watt.

State and prove Poynting's theorem. Discuss the physical significance of each term in resulting equation.

Obtain expressions for electrostatic scalar potential magnetostatic vector potential and electromagnetic potential. How are the first two related to the third? Explain the idea of retarded potential.

Using Laplace's equation obtain an expression for the potential between two coaxial cylinders.

Show that it is possible to arrive at Stefan-Boltzmann law with the aid of Carnot's cycle using black body radiation as the working substance.

Calculate \omega_0 \Delta \omega and quality factor Q for LCR parallel resonant circuit given the values C = 0.4 \muF, L = 4 mH and R = 1 K\Omega.

A harmonic e.m.f. is applied to a parallel resonant circuit containing resistance R, inductance L and capacitance C. Derive expressions for resonance, angular frequency \omega_0 and the band width \Delta \omega.

Show that energy stored in a capacitor is \frac{1}{2} \frac{q^2}{C} while the energy stored in the inductor is \frac{1}{2} L i^2, where the symbols have their usual meaning.

A particle of mass 5g lies in a potential field given by U = (40x^2 + 80)\text{ erg/g}. Determine the frequency and time period of oscillations.

Define mach number A plane files horizontally at an altitude of 2 km at twice the speed of the sound in air. At what distance from the plane will an observer on the ground first heat it coming?

Distinguish between phase velocity and group velocity. Calling group velocity C and phade velocity C in a medium of refractive index n, establish the relation C_g = C \left(1 + \frac{\lambda}{n} \frac{dn}{d\lambda}\right) where \lambda refers to the wavelength of the related light in vacuum

Show that the interference fringes in uncoated thin films are distinct when seen in reflection, but very indistinct in transmission.

The light (\lambda = 6000\text{\AA}) from a laser of sectional diameter 1.0 cm and power 0.02 watt is loosed by a lens of focal length 10 cm. Determine the area at the image and intensity in it in watt/cm^2.

Briefly discuss the feasibility of a laser, emitting monochromatic Fermions, such as electrons.

Calculate the tension required to generate stationary waves with 4 loops in a string of length 1.0\text{ meter}, and mass 0.30\text{ g.} fixed to a tuning fork vibrating with frequency 200\text{ Hz}.

Describe how fresnel has accounted for the rotation of the plane of polarisation of light. Explain the action of a half-shade device.

Discuss the theory of diffraction grating and find conditions for the absent spectra. Distinguish between resolving power and dispersive power of a grating.

State Fourier's theorem. Discuss the conditions which a complex periodic curve must satisfy if it is to be analysed by this theorem. Show how the diffraction of waves at a single slit is related with a Fourier transform.

Write a short note on Holography.

Explain what you mean by processional torque. Deduce an expression for the time period of processional motion of gyroscope in terms of relevant quantities.