Discuss the working principle of He-Ne laser indicating the transitions involved in the process. Determine the power output of a laser in which a 3.0\text{ J} pulse is delivered in 1.0\text{ ns}.

A left circularly polarized beam of light (\lambda = 6000\text{ \AA}) is incident on a quartz crystal (Optic axis parallel to the surface). Find the state of polarisation of the emergent beam. (Thickness of quartz crystal = 2.3 \times 10^{-5}\text{ m}, \mu_e = 1.5538, \mu_o = 1.5444)

A body of mass m supported by a spiral spring causes an extension of d is the spring. The body is set in vertical oscillations of small amplitude. Find an expression for the periodic time of the oscillations.

Show that for forced oscillations amplitude resonance and energy resonance do not occur at the same frequency.

Write a short note on Fourier transformation.

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.

Write a short note on Holography.

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?

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.

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.

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

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

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.

Write a short note on Formation and reconstruction of hologram.

What is Fraunhofer diffraction? Under what conditions may it be observed ? Find an expression for the intensity distribution in double slit Fraunhofer diffraction, taking the result for diffraction at a single slit as given.

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.

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.