Give an account of the origin of optical activity in eqartz crystal. A wafer of crystalline eqartz of thickness. 2.945 \times 10^{-5}\text{ m} is used to change a beam of linearly polarised light (\lambda = 589\text{ nm}) into circularly polarised light. Find the difference in refractive index for the two waves in the crystal, assuming this to be minimum thickness that will produce the effect.
Write a short note on Formation and reconstruction of hologram.
Define coherent length. A helium-neon laser emits radiation at wavelength \lambda = 632.8\text{ nm} with \Delta\lambda = 2\text{ pm}. Calculate the coherence wavelength.
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.
An interference pattern is obtained by using two coherent sources of light, and the intensity variation is observed to be \pm 10\% of the average intensity. Determine the relative intensities of the interfering sources.
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.
State Rayleigh Criterison for limit of resolution. Show that \frac{I_{\text{middle}}}{I_{\text{max}}} = \frac{8}{\pi^2}
Show that the particle velocity in case of a plane progressive wave is given by \frac{\partial y}{\partial t} = -V \frac{\partial y}{\partial x} (where V is the wave velocity). Hence obtain the differential equation of wave motion.
A particle executing simple harmonic motion, has an acceleration (\pi^2/3)\text{ cm/sec}^2 when the displacement is 1\text{ cm}. Determine the period.
Give an outline of Fresnel's explanation of optical rotation. How does optical rotation due to a material vary with \lambda? For an optically active material the difference between the refractive indices for right-handed and left-handed vibrations (\mu_R - \mu_L) for \lambda = 4500\text{ \AA} is 12 \times 10^{-5}. Estimate the optical rotation caused by 1\text{mm} thick plate in light of 1 = 4500\text{ \AA}. [Assume (m_R - m_L) as independent of \mu.]
A ruby laser produces a beam of light of wavelength 0.3\text{ \AA} with a circular cross-section 1\text{ cm} in diameter. Calculate the diameter of this beam at a distance of 1000\text{ kilometers}.
A diffraction grating with 3 \times 10^4 lines is used in the second order in the range of wavelength 6000\text{\AA}. Find the smallest \Delta\lambda it can resolve.
Distinguish between Fresnel and Fraunhofer classes of diffraction of light. Discuss the theory of a plane grating and hence find an expression for the angular dispersion of a plane grating.
Give a mathematical analysis of forced vibration and hence explain the phenomenon of amplitude resonance.
Explain the laws of refraction of light on the basis of Huygens principle.
A particle of mass 10 g lies in a potential given by V(x) = 32 x^2 + 0.2 where x is in metres and V(x) in joules. Write down the equation of motion and solve it. What is the frequency of oscillation?
The phase velocity of surface waves of wavelength \lambda is v_p = \left( \frac{2 \pi T}{\lambda \rho} + \frac{g \lambda^{1/2}}{2 \pi} \right) where T is the surface tension and \rho the density of the liquid and g is acceleration due to gravity. Find the group velocity and express it in terms of the phase velocity. For which wavelength is the phase velocity a minimum ?
Write a note on He-Ne laser.
Deduce the possible thickness of a quarter wave plate of quartz which is to be used for sodium light of wavelength 5890 Å, (\mu_o = 1.558, \mu_e = 1.486.)
Define geometrical resolving power of an optical instrument. Derive the expression for the resolving power of a microscope and comment on the relation between resolving power and magnifying power, if any exists.
