PYQ Bank

Show that the interference fringes obtained in Young's two slit experiment are hyperbolic in shape. Under what conditions these are expected to appear straight?

Write the equation of motion for an oscillator driven by a simple harmonically varying force. Obtain the condition for maximum energy transfer to the oscillator.

The potential energy for the interaction between two gas molecules can be represented by the function. \phi(r) = -\phi_0 \left[ 2 \left(\frac{r_0}{r}\right)^6 - \left(\frac{r_0}{r}\right)^{12} \right] Where \phi_0 and r_0 are constant. Prove that for small oscillations the frequency is given by \omega = \left( \frac{144 \phi_0}{m r_0^2} \right)^{1/2} Where m is mass of each molecule.

The angular separation between two distant stars is 1 arc-second. If the effective wavelength of light is 5500 \text{\AA}; what should be the diameter of the objective of a telescope so that the stars are just resolved?

A fine slit is illuminate by monochromatic light of wave-length 6000 \text{\AA}. A thin wire is placed parallel to the slit and the diffraction pattern is observed on a screen at a distance of 1 m from the wire. In the shadow of the wire equidistant fringes of thickness 1.5 mm are observed. How do you explain this observation ? Calculate he diameter of the wire also.

Write a short note on Holography.

What is meant by temporal and spatial coherence ? Show that the coherence length L = \lambda Q, where \lambda is the mean wavelength and Q represents the purity of a spectral line.

What is a quarter wave plate? Explain its use in the production and detection of circularly polarized light. For calcite for \lambda = 5472 \text{\AA}, \mu_O = 1.658 and \mu_E = 1.486. If the minimum thickness of a plate that can be cut from calcite is 30 \mu\text{ m}, what should be the minimum thickness for preparing a quarter wave plate?

Obtain an expression for the ratio of the probabilities of stimulated and spontaneous emissions. What do you infer from this relation? How is population inversion interpreted thermodynamically?

Describe the working principle of a three level solid state laser giving the transitions involved in the laser action.

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.

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.

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)

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}.

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?

Write a short note on Fourier transformation.

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.