Obtain the intensity pattern due to Fraunhofer diffraction at two parallel slits. Each slit has a width ‘a’ and the separation between the slits is d. How many interference fringes will appear in the central diffraction maximum, it d = 4a?
In a biprism experiment the fringe-width with lightly of wavelength \lambda = 5900\text{ \AA} is 0.43\text{ mm}. On introducing a mica sheet in the path of one of the interfering rays the central fringe shifts by 1.89\text{ mm}. If refractive index of mica is 1.59, calculate the thickness of the sheet.
Write a short note on Fourier transformation.
Show that for forced oscillations amplitude resonance and energy resonance do not occur at the same frequency.
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.
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}.
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
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.
Write a short note on Holography.
Briefly discuss the feasibility of a laser, emitting monochromatic Fermions, such as electrons.
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.
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?
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.
Show that the interference fringes in uncoated thin films are distinct when seen in reflection, but very indistinct in transmission.
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}.
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.
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.
